diff --git a/8-correlation/main.ipynb b/8-correlation/main.ipynb new file mode 100644 index 0000000..c4b4e34 --- /dev/null +++ b/8-correlation/main.ipynb @@ -0,0 +1,399 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 17, + "id": "01ea2da4", + "metadata": {}, + "outputs": [], + "source": [ + "# data for the OLS\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "theta0 = 2.6486\n", + "theta1 = 4.98\n", + "m = 500\n", + "disp = 1\n", + "x = np.linspace(0,5,m)\n", + "y = theta0+theta1*x+disp*np.random.randn(m)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "0f0c131a", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(x,y, '.k')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "c21073a6", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "np.float64(0.990800615658485)" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "xMean = x.mean()\n", + "yMean = y.mean()\n", + "\n", + "Sxx = np.sum((x - xMean)**2)\n", + "Syy = np.sum((y - yMean)**2)\n", + "Sxy = np.sum((x - xMean) * (y - yMean))\n", + "\n", + "r = Sxy / np.sqrt(Sxx * Syy)\n", + "r" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "aff5adac", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([-0.95082413, -0.64573564, 0.87130595, -0.53988214, -0.56134601,\n", + " 0.718763 , -1.57062343, 0.39547852, 0.28642336, 0.67589762,\n", + " -0.05256052, 0.52740588, -0.2622087 , 0.95248882, 0.77106812,\n", + " 1.04923914, -0.56930707, 0.0336549 , -1.23845916, 1.34279223,\n", + " -1.28317243, 0.23367606, 1.5810006 , -1.28925369, -0.91503262,\n", + " -0.47238037, -0.51189083, 0.22029059, 0.1362538 , 0.10890607,\n", + " 1.45135919, 1.07239237, -0.9002686 , 1.64189709, -0.28342477,\n", + " -1.09095379, -0.95598686, -0.40362419, -1.11918067, 0.20567161,\n", + " -0.87438623, -1.84805568, -0.00444769, -0.11272938, 0.50923524,\n", + " -0.89881567, 1.16206936, -1.9768896 , -0.05677879, 0.38329957,\n", + " 0.0615791 , 0.8993067 , -0.24370477, 1.25224753, 0.60692638,\n", + " 0.95457789, 0.98691527, -0.1311992 , 2.58603558, 1.0730014 ,\n", + " 0.17406217, -1.29052871, 0.20098696, 0.45699896, -0.52684263,\n", + " 0.10757726, -1.89143251, -0.49583779, -1.25280976, -0.59317229,\n", + " -1.81655035, -0.07774643, 0.15291058, -0.75178735, 0.62247512,\n", + " -0.32728714, -1.19090979, -0.43800424, -0.16657564, -0.06809202,\n", + " -1.10897576, 0.96155511, -1.27332763, -1.69728706, 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0.88953047, -0.76267675, -0.74691851, -0.88915534,\n", + " 1.40348052, -0.32213203, 0.85653684, 0.54061916, -0.06615145,\n", + " -0.06541276, -0.1874332 , 1.64653204, 0.27782626, -1.56029627,\n", + " 1.65082298, 0.67656205, -1.58084623, -0.43152429, 1.2077006 ,\n", + " -0.01064432, 0.39992249, 0.7204933 , -0.97893129, 0.3783936 ,\n", + " 1.42397314, 2.2570722 , 0.73192937, -0.6796615 , 0.79733617,\n", + " -1.22591839, -0.3439277 , 0.04718119, 1.01248675, -0.25599286,\n", + " -0.78884594, 0.40217221, 0.54593394, 0.77981857, 1.6034912 ,\n", + " -0.58348904, 0.23082941, -0.84446779, 0.0897946 , 0.32875383,\n", + " 0.5969846 , 0.2950068 , -1.85252387, 0.20742835, -1.99840818,\n", + " 1.13742464, 0.32724843, 0.80450174, 0.25135255, 0.6623171 ,\n", + " -0.92213262, -0.07474869, -1.32358274, -1.36633224, -0.17526807,\n", + " -1.49026666, -0.04415546, 0.51904066, -0.10048653, 0.10796533])" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "t1 = Sxy / Sxx\n", + "t0 = yMean - t1 * xMean\n", + "\n", + "yHat = t0 + t1 * x\n", + "residuals = y - yHat\n", + "residuals" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "1bbd0418", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "np.float64(0.9816858599892329)" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "R2 = r**2\n", + "R2" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "97695f62", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Correlation r: 0.990800615658485\n", + "Intercept t0: 2.715728336655882\n", + "Slope t1: 4.987467248897177\n", + "R2: 0.9816858599892329\n" + ] + } + ], + "source": [ + "print(\"Correlation r:\", r)\n", + "print(\"Intercept t0:\", t0)\n", + "print(\"Slope t1:\", t1)\n", + "print(\"R2:\", R2)" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "id": "765bfa69", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.scatter(x, y, color='black', alpha=0.3)\n", + "plt.plot(x, yHat, ':r')\n", + "plt.xlabel(\"x\")\n", + "plt.ylabel(\"y\")\n", + "plt.title(\"Simple Linear Regression\")\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "id": "5411bc06", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.scatter(x, residuals, color=\"red\", alpha=0.3)\n", + "plt.axhline(0, color='black')\n", + "plt.xlabel(\"x\")\n", + "plt.ylabel(\"Residuals\")\n", + "plt.title(\"Residual Plot\")\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "e8e3850a", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Correlation r: 0.999445617564577\n", + "Intercept b0: 0.15000000000000036\n", + "Slope b1: 1.9833333333333332\n", + "R²: 0.9988915424690386\n" + ] + }, + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "x = np.array([1, 2, 3, 4, 5, 6, 7, 8], dtype=float)\n", + "y = np.array([2.2, 4.1, 5.9, 8.3, 10.1, 12.0, 13.8, 16.2], dtype=float)\n", + "\n", + "x_mean = x.mean()\n", + "y_mean = y.mean()\n", + "\n", + "Sxx = np.sum((x - x_mean)**2)\n", + "Syy = np.sum((y - y_mean)**2)\n", + "Sxy = np.sum((x - x_mean) * (y - y_mean))\n", + "\n", + "r = Sxy / np.sqrt(Sxx * Syy)\n", + "\n", + "b1 = Sxy / Sxx\n", + "b0 = y_mean - b1 * x_mean\n", + "\n", + "y_hat = b0 + b1 * x\n", + "residuals = y - y_hat\n", + "\n", + "R2 = r**2\n", + "\n", + "print(\"Correlation r:\", r)\n", + "print(\"Intercept b0:\", b0)\n", + "print(\"Slope b1:\", b1)\n", + "print(\"R²:\", R2)\n", + "\n", + "plt.scatter(x, y)\n", + "plt.plot(x, y_hat)\n", + "plt.xlabel(\"x\")\n", + "plt.ylabel(\"y\")\n", + "plt.title(\"Simple Linear Regression\")\n", + "plt.show()\n", + "\n", + "plt.scatter(x, residuals)\n", + "plt.axhline(0)\n", + "plt.xlabel(\"x\")\n", + "plt.ylabel(\"Residuals\")\n", + "plt.title(\"Residual Plot\")\n", + "plt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".venv (3.14.3)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.14.3" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/9-confident-hypothesis/main.ipynb b/9-confident-hypothesis/main.ipynb new file mode 100644 index 0000000..54fb3b8 --- /dev/null +++ b/9-confident-hypothesis/main.ipynb @@ -0,0 +1,218 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "5b299da0", + "metadata": {}, + "source": [ + "Lab Example 1 — Sampling variability and CLT\n", + "\n", + "Objective: show that individual measurements vary, but sample means are more stable.\n", + "\n", + "Students should:\n", + "\n", + "1. Generate a non-normal population.\n", + "2. Take many random samples.\n", + "3. Compute the mean of each sample.\n", + "4. Plot the distribution of the sample means." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "07e7f5cc", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "np.random.seed(10)\n", + "\n", + "population = np.random.exponential(scale=2.0, size=100000)\n", + "\n", + "sample_size = 30\n", + "n_samples = 1000\n", + "\n", + "sample_means = []\n", + "\n", + "for i in range(n_samples):\n", + " sample = np.random.choice(population, size=sample_size, replace=True)\n", + " sample_means.append(sample.mean())\n", + "\n", + "plt.hist(population, bins=40)\n", + "plt.title(\"Original population\")\n", + "plt.xlabel(\"Value\")\n", + "plt.ylabel(\"Frequency\")\n", + "plt.show()\n", + "\n", + "plt.hist(sample_means, bins=40)\n", + "plt.title(\"Distribution of sample means\")\n", + "plt.xlabel(\"Sample mean\")\n", + "plt.ylabel(\"Frequency\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "8e78d8f7", + "metadata": {}, + "source": [ + "Even when the original data are not normally distributed, the distribution of sample means tends to become approximately normal when the sample size increases." + ] + }, + { + "cell_type": "markdown", + "id": "411bd317", + "metadata": {}, + "source": [ + "# Lab Example 2 — Confidence interval for a mean\n", + "\n", + "Objective: estimate a parameter with uncertainty.\n", + "\n", + "Use the repeated measurement example:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "615beff5", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean: 9.999333333333333\n", + "Standard deviation: 0.04832430129073875\n", + "95% confidence interval: 9.972572227269502 10.026094439397163\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "from scipy import stats\n", + "\n", + "measurements = np.array([9.91, 10.03, 9.98, 10.05, 10.01, 9.96, 10.08, 9.94,\n", + " 10.02, 9.99, 10.04, 9.97, 10.06, 9.95, 10.00])\n", + "\n", + "n = len(measurements)\n", + "xbar = measurements.mean()\n", + "s = measurements.std(ddof=1)\n", + "\n", + "confidence = 0.95\n", + "alpha = 1 - confidence\n", + "\n", + "t_critical = stats.t.ppf(1 - alpha/2, df=n-1)\n", + "margin_error = t_critical * s / np.sqrt(n)\n", + "\n", + "ci_lower = xbar - margin_error\n", + "ci_upper = xbar + margin_error\n", + "\n", + "print(\"Mean:\", xbar)\n", + "print(\"Standard deviation:\", s)\n", + "print(\"95% confidence interval:\", ci_lower, ci_upper)" + ] + }, + { + "cell_type": "markdown", + "id": "75ec3573", + "metadata": {}, + "source": [ + "Interpretation:\n", + "\n", + "We do not report only the mean. We report the mean with an interval that reflects uncertainty.\n", + "\n", + "Suggested question:\n", + "\n", + "Does the confidence interval include 10\\,\\Omega?" + ] + }, + { + "cell_type": "markdown", + "id": "e2024490", + "metadata": {}, + "source": [ + "# Lab Example 3 — Hypothesis test for a nominal value\n", + "\n", + "Objective: test whether the measured component is statistically consistent with a reference value.\n", + "\n", + "For the resistor example:\n", + "\n", + "H_0: \\mu = 10\n", + "\n", + "H_a: \\mu \\neq 10\n", + "\n", + "Python:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "2fee9dc6", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "t statistic: -0.05343044448672866\n", + "p-value: 0.9581438956150026\n" + ] + } + ], + "source": [ + "from scipy import stats\n", + "\n", + "mu0 = 10.0\n", + "\n", + "t_statistic, p_value = stats.ttest_1samp(measurements, popmean=mu0)\n", + "\n", + "print(\"t statistic:\", t_statistic)\n", + "print(\"p-value:\", p_value)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".venv (3.14.3)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.14.3" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/session-5-error/main-live.ipynb b/session-5-error/main-live.ipynb new file mode 100644 index 0000000..cf9f12e --- /dev/null +++ b/session-5-error/main-live.ipynb @@ -0,0 +1,251 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "2411ab62", + "metadata": {}, + "source": [ + "# Part A - Repeated measurements\n", + "- a representative value, using the samples mean \n", + "- the measurements variability, using the sample standard deviation" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "79441225", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([4.98, 5.01, 5. , 5.03, 4.99, 5.02, 4.97, 5.01])" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import numpy as np \n", + "import pandas as pd\n", + "import matplotlib.pyplot as plt\n", + "\n", + "vSamples = np.array([4.98, 5.01, 5.00, 5.03, 4.99, 5.02, 4.97, 5.01])\n", + "vSamples" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "f4fb3a51", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean voltage is = 5.0013 V\n", + "Sample standard deviation is = 0.0203 V\n" + ] + } + ], + "source": [ + "vMean = vSamples.mean() # np.mean(vSample)\n", + "vSTD = vSamples.std(ddof=1) #sample standar deviation\n", + "\n", + "print(f\"Mean voltage is = {vMean:.4f} V\")\n", + "print(f\"Sample standard deviation is = {vSTD:.4f} V\")" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "26b4bdf2", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(8,4))\n", + "plt.plot(vSamples, 'ok', label=\"Samples\")\n", + "plt.axhline(vMean, linestyle=\"--\", linewidth=2, label=f\"Mean = {vMean:.4f}\")\n", + "plt.xlabel(\"Measurements\")\n", + "plt.ylabel(\"Voltage [V]\")\n", + "plt.ylim([4.9,5.1])\n", + "plt.grid(alpha=0.3)\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "8893bdc0", + "metadata": {}, + "source": [ + "1. What is the estimated voltage?\n", + "2. What does the sample standard deviation tell us?\n", + "3. Are the measurements relatively precise or widely scattered?" + ] + }, + { + "cell_type": "markdown", + "id": "3482af0e", + "metadata": {}, + "source": [ + "# Part B - Propagation of uncertainty of one variable\n", + "Example area of a cricle" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "2c2306b1", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Radius: r = 10.0000 +/- 0.2000 mm\n", + "Area: A = 314.1593 +/- 12.5664 mm^2\n" + ] + } + ], + "source": [ + "r = 10.0\n", + "sigmar = 0.2\n", + "Area = np.pi*r**2\n", + "sigmaA = sigmar*(2*np.pi*r)\n", + "\n", + "print(f\"Radius: r = {r:.4f} +/- {sigmar:.4f} mm\")\n", + "print(f\"Area: A = {Area:.4f} +/- {sigmaA:.4f} mm^2\")" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "id": "1c60ddad", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "sigmarValues = np.linspace(0.01, 0.5, 10)\n", + "sigmaAValues = (np.pi*2*r)*sigmarValues\n", + "\n", + "plt.figure(figsize=(6,4))\n", + "plt.plot(sigmarValues, sigmaAValues, 'ok')\n", + "plt.title(\"Propagation of uncertainty\")\n", + "plt.xlabel(\"Uncertainty in radius [mm]\")\n", + "plt.ylabel(\"Uncertainty in area [mm^2]\")\n", + "plt.grid(alpha=0.3)\n", + "plt.savefig(\"uncertainty.png\", dpi=300, bbox_inches=\"tight\")\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "56766593", + "metadata": {}, + "source": [ + "# Part c - Propagation of uncertainty for several variables\n", + "Example: Resistance from voltage and current.\n", + "- $V=12.0 \\pm 0.2$\n", + "- $I=2.0 \\pm 0.05$" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "id": "a6583ccf", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Resistance: R = 6.0000 +/- 0.1803 ohms\n" + ] + } + ], + "source": [ + "V = 12.0\n", + "sigmaV = 0.2\n", + "I = 2.0 \n", + "sigmaI = 0.05\n", + "\n", + "R = V/I\n", + "sigmaR = np.sqrt((sigmaV/I)**2 + (sigmaI*V/I**2)**2)\n", + "print(f\"Resistance: R = {R:.4f} +/- {sigmaR:.4f} ohms\")" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "id": "d57fa95d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Contribution from voltage uncertainty: 30.7692%\n", + "Contribution from current uncertainty: 69.2308%\n" + ] + } + ], + "source": [ + "termV = (sigmaV / I)**2\n", + "termI = ((V * sigmaI) / (I**2))**2\n", + "total = termV + termI\n", + "\n", + "percent_V = 100 * termV / total\n", + "percent_I = 100 * termI / total\n", + "\n", + "print(f\"Contribution from voltage uncertainty: {percent_V:.4f}%\")\n", + "print(f\"Contribution from current uncertainty: {percent_I:.4f}%\")" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".venv (3.14.3)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.14.3" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/session-5-error/uncertainty.png b/session-5-error/uncertainty.png new file mode 100644 index 0000000..9445183 Binary files /dev/null and b/session-5-error/uncertainty.png differ diff --git a/session-6-distributions/main-session.ipynb b/session-6-distributions/main-session.ipynb new file mode 100644 index 0000000..dd97d53 --- /dev/null +++ b/session-6-distributions/main-session.ipynb @@ -0,0 +1,665 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "5d24fc75", + "metadata": {}, + "outputs": [], + "source": [ + "# General used libriries\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy.stats import binom, poisson, norm, expon " + ] + }, + { + "cell_type": "markdown", + "id": "5f8545a0", + "metadata": {}, + "source": [ + "# Bernoulli distribution" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "38c1af9c", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "P(X=1) = 0.7\n", + "P(X=0) = 0.30000000000000004\n", + "Mean = 0.7\n", + "Variance = 0.21000000000000002\n" + ] + } + ], + "source": [ + "# Bernoulli distribution:\n", + "p = 0.7\n", + "print(\"P(X=1) = \", p)\n", + "print(\"P(X=0) = \", 1-p)\n", + "print(\"Mean = \", p)\n", + "print(\"Variance = \", p*(1-p))" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "2ab9219a", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "First 20 observations:\n", + "[1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 0 0 1 1 1]\n", + "Sample mean: 0.675\n", + "Sample variance: 0.21959459459459454\n" + ] + } + ], + "source": [ + "# Bernoulli observations \n", + "# repeating a success|failures experiment many times\n", + "p = 0.7\n", + "n = 1000 #samples\n", + "np.random.seed(33)\n", + "berData = np.random.binomial(1, p, size=n)\n", + "print(\"First 20 observations:\")\n", + "print(berData[:20])\n", + "\n", + "print(\"Sample mean: \", berData.mean())\n", + "print(\"Sample variance: \", berData.var(ddof=1))" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "e2ae2434", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "values, counts = np.unique(berData, return_counts=True)\n", + "plt.bar(values, counts/n, width=0.4, color=\"grey\")\n", + "plt.xticks([0, 1])\n", + "plt.xlabel(\"Outcomes\")\n", + "plt.ylabel(\"Relative frequency\")\n", + "plt.title(\"Simulated Bernoulli Distribution\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "98f319fd", + "metadata": {}, + "source": [ + "# Binomial distribution\n", + "The binomial distribution counts the number of successes in $n$ independent Bernoulli trials." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "974eccf3", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "P(X=2) = 0.2711\n", + "Mean= 1.6\n", + "Variance= 1.4720000000000002\n" + ] + } + ], + "source": [ + "p = 0.08\n", + "n = 20\n", + "k = 2\n", + "\n", + "prob = binom.pmf(k, n, p)\n", + "print(f\"P(X=2) = {prob:.4f}\")\n", + "print(\"Mean= \", n*p)\n", + "print(\"Variance= \", n*p*(1-p))" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "87d14367", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x = np.arange(0, n+1)\n", + "pmf = binom.pmf(x, n, p)\n", + "plt.bar(x, pmf, color=\"grey\", width=0.6)\n", + "plt.xlabel(\"Number of succeses\")\n", + "plt.ylabel(\"Probability\")\n", + "plt.title(\"Binomial distribution: n=20, p=0.08\")\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "9c8de1d2", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Simulated mean: 1.6011\n", + "Theoretical mean: 1.6\n", + "--------------\n", + "Simulated var: 1.4717259625962598\n", + "Theoretical var: 1.4720000000000002\n" + ] + } + ], + "source": [ + "# Binomial simuation\n", + "n = 20 #sample\n", + "p = 0.08\n", + "nPop = 10_000\n", + "np.random.seed(33)\n", + "binomData = np.random.binomial(n,p,size=nPop)\n", + "\n", + "print(\"Simulated mean: \", binomData.mean())\n", + "print(\"Theoretical mean: \", n*p)\n", + "print(\"--------------\")\n", + "print(\"Simulated var: \", binomData.var(ddof=1))\n", + "print(\"Theoretical var: \", n*p*(1-p))" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "ec289f08", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.hist(binomData, bins=np.arange(-0.5,n+1.5,1), density=True, color=\"grey\")\n", + "plt.plot(x, pmf, 'ok')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "5ce9af51", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1.88693329e-01 3.28162312e-01 2.71090605e-01 1.41438577e-01\n", + " 5.22707783e-02 1.45449122e-02 3.16193744e-03 5.49902164e-04\n", + " 7.77035666e-05 9.00910917e-06 8.61740877e-07 6.81218085e-08\n", + " 4.44272664e-09 2.37737880e-10 1.03364296e-11 3.59527985e-13\n", + " 9.76978221e-15 1.99893242e-16 2.89700351e-18 2.65171946e-20\n", + " 1.15292150e-22]\n" + ] + }, + { + "data": { + "text/plain": [ + "0.32816231158747255" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "print(pmf)\n", + "20*0.08*(1-0.08)**(19)" + ] + }, + { + "cell_type": "markdown", + "id": "2612a6fd", + "metadata": {}, + "source": [ + "# Poisson distribution\n", + "- $P(X=k) = e^{-\\lambda} \\lambda^k/k!$\n", + "- $E[X] = \\lambda$\n", + "- $Var(X) = \\lambda$" + ] + }, + { + "cell_type": "markdown", + "id": "e94cffe1", + "metadata": {}, + "source": [ + "Example: Let $X$ be the number of flaws per metre per cable, with average rate $\\lambda=3$." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "c629df8b", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "P(X=0) = 0.049787068367863944\n", + "P(X=2) = 0.22404180765538775\n", + "Mean = 3\n", + "Var = 3\n" + ] + } + ], + "source": [ + "lam = 3\n", + "print(\"P(X=0) = \", poisson.pmf(0, lam))\n", + "print(\"P(X=2) = \", poisson.pmf(2, lam))\n", + "print(\"Mean = \", lam)\n", + "print(\"Var = \", lam)" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "e8882be4", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x = np.arange(0, 15)\n", + "pmfPoisson = poisson.pmf(x, lam)\n", + "\n", + "plt.bar(x, pmfPoisson, width=0.7)\n", + "plt.xlabel(\"Count\")\n", + "plt.ylabel(\"Probability\")\n", + "plt.title(r\"Poisson distribution: $\\lambda=3$\")\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "id": "dd34877c", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Simulated mean: 2.9953\n", + "Theoretical mean: 3\n", + "Simulated Var: 2.9753754475447542\n", + "Theoretical Var: 3\n" + ] + } + ], + "source": [ + "# Poisson distribution\n", + "lam = 3\n", + "samples = 10_000\n", + "poiData = np.random.poisson(lam, size=samples)\n", + "\n", + "print(\"Simulated mean: \", poiData.mean())\n", + "print(\"Theoretical mean: \", lam)\n", + "\n", + "print(\"Simulated Var: \", poiData.var(ddof=1))\n", + "print(\"Theoretical Var: \", lam)" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "id": "abcf172f", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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OkiVLOv773/86Dhw44Ndu8PreekvrdZw8edL8P7jllltMeSIjIx1169Z1vPnmm2ZoAPf9+vTp4yhWrJj5/1O2bFnz3nt3X0/rs+JNhwbQ/WbMmOHzaway6CnwLVQCACD0aI2n9kLUQSMzMk8f7I0cIABApqVjOWnzp/YwI/hBRpADBADIdLRnpObGaW6RJoLr2E5ARhAAAQAyHe35pV3fNelZ5xzTpG8gI8gBAgAAtkMOEAAAsB0CIAAAYDvkAKVBh5LXWbh1cDNmFAYAIHPQkX10ihUdOT+t+RvdEQClQYMf7xmpAQBA5qDT4ujI6JdDAJQG5+R8egJ16HwAABD6kpKSTAWG+yS76SEASoOz2UuDHwIgAAAyF1/SV0iCBgAAtkMABAAAbIcACAAA2A4BEAAAsB0CIAAAYDsEQAAAwHYIgAAAgO0QAAEAANshAAIAALZDAAQAAGyHAAgAANgOARAAALAdAiAAAGA7BEAAAMB2CIAAAIDtZA12AYBAiY5bEJSTu2dks6A8LwDAd9QAAQAA2yEAAgAAtkMABAAAbIccIISm5GSR5ctFDhwQKVpUpEEDkfDwgD9tWEqy1EzYLIVOHZPE3AVkdVQFSQkL/PMCAK4vAiCEnrlzRWJjRRIS/l0XFSUyfrxIq1YBe9qY7T/LkCXTpNjJI651+/NEytDGT8uicnUD9rwAgOuPJjCEXvDTpo1n8KP27bu0XrcHKPiZMu81KeIW/Chd1vW6HQBgHQRACK1mL635cThSb3Ou69370n5+bvbSmh9z33vbP391u+4HALAGAiCEDs358a758Q6C4uMv7edHmvOjzV7p/WfQ9bpd9wMAWAMBEEKHJjz7cz8facKzP/cDAIQ+AiCEDu3t5c/9fKS9vfy5HwAg9BEAIXRoV3ft7ZUlS9rbdX2JEpf28yPt6q69vVLS2a7rdbvuBwCwBgIghA4d50e7uivvIMi5PG6c38cD0nF+tKu7ue+97Z+/up3xgADAOgiAEFp0nJ85c0SKF/dcrzVDuj5A4wDpOD/dWg6Sg3kiPdbrsq5nHCAAsJYsDkdafY7tLSkpSfLlyycnTpyQvHnzBrs4tpyVPVgjMvvjeZkNHgBC//rNSNAISRp0rCxZ2TbPCwC4vmgCAwAAtkMABAAAbIcACAAA2A4BEAAAsB0CIAAAYDsEQAAAwHYIgAAAgO0QAAEAANshAAIAALZDAAQAAGyHAAgAANgOARAAALAdAiAAAGA7BEAAAMB2CIAAAIDtEAABAADbIQACAAC2QwAEAABshwAIAADYDgEQAACwHQIgAABgOwRAAADAdgiAAACA7RAAAQAA2yEAAgAAtkMABAAAbCckAqDJkydLdHS05MiRQ2rVqiWrV69Od9933nlHGjRoIAUKFDC3Jk2apNrf4XDI4MGDpWjRopIzZ06zz44dO67DKwEAAJlB0AOg2bNnS9++fWXIkCGybt06qVKlisTExEhiYmKa+y9btkzat28vS5culRUrVkiJEiWkadOmsm/fPtc+o0aNkgkTJsjUqVNl1apVkitXLnPMs2fPXsdXBgAAQlUWh1aXBJHW+NSoUUMmTZpkllNSUkxQ06tXL4mLi7vi45OTk01NkD6+Y8eOpvanWLFi0q9fP+nfv7/Z58SJE1K4cGF5//33pV27dlc8ZlJSkuTLl888Lm/evH54lfYWHbdA7GTPyGbBLgIA2FJSBq7fQa0BOn/+vKxdu9Y0UbkKFBZmlrV2xxdnzpyRCxcuSMGCBc3y7t275eDBgx7H1JOhgVZ6xzx37pw5ae43AABgXUENgI4cOWJqcLR2xp0uaxDji+eff97U+DgDHufjMnLMESNGmCDJedMaKAAAYF1BzwG6FiNHjpRZs2bJ559/bhKor9bAgQNNdZnzFh8f79dyAgCA0JI1mE8eGRkp4eHhcujQIY/1ulykSJHLPvbNN980AdC3334rlStXdq13Pk6Pob3A3I9ZtWrVNI8VERFhbgAAwB6CWgOUPXt2qVatmixZssS1TpOgdblOnTrpPk57eb3yyiuycOFCqV69use20qVLmyDI/Zia06O9wS53TAAAYB9BrQFS2gW+U6dOJpCpWbOmjBs3Tk6fPi1dunQx27VnV/HixU2ejnr99dfNGD8zZswwYwc583py585tblmyZJHevXvL8OHDpWzZsiYgeumll0yeUMuWLYP6WgEAQGgIegDUtm1bOXz4sAlqNJjRZiqt2XEmMe/du9f0DHOaMmWK6T3Wpk0bj+PoOEIvv/yyuf/cc8+ZIOrpp5+W48ePS/369c0xryVPCAAAWEfQxwEKRYwD5F+MAwQAuB4yzThAAAAAwUAABAAAbIcACAAA2A4BEAAAsB0CIAAAYDsEQAAAwHYIgAAAgO0QAAEAANshAAIAALZDAAQAAGyHAAgAANgOARAAALAdAiAAAGA7BEAAAMB2CIAAAIDtEAABAADbIQACAAC2QwAEAABshwAIAADYDgEQAACwHQIgAABgOwRAAADAdgiAAACA7RAAAQAA2yEAAgAAtkMABAAAbIcACAAA2A4BEAAAsB0CIAAAYDsEQAAAwHYIgAAAgO1kOABaunRpYEoCAAAQqgHQvffeKzfffLMMHz5c4uPjA1MqAACAUAqA9u3bJz179pQ5c+ZImTJlJCYmRj755BM5f/58YEoIAAAQ7AAoMjJS+vTpI+vXr5dVq1bJrbfeKt27d5dixYrJs88+Kxs2bPB3GQEAAEInCfrOO++UgQMHmhqhU6dOyXvvvSfVqlWTBg0ayObNm/1XSgAAgGAHQBcuXDBNYPfff7+UKlVKFi1aJJMmTZJDhw7Jzp07zbqHH37Yn+UEAADwm6wZfUCvXr1k5syZ4nA45PHHH5dRo0ZJxYoVXdtz5colb775pmkSA+Cj5GSR5ctFDhwQKVpUpEEDkfBwTh8AhEoAtGXLFpk4caK0atVKIiIi0s0Tors84KO5c0ViY0USEv5dFxUlMn68SKtWnEYACIUmsCFDhpjmLe/g5+LFi/LDDz+Y+1mzZpVGjRr5r5SAlYOfNm08gx+1b9+l9bodABD8AOjuu++Wo0ePplp/4sQJsw1ABpq9tObH4Ui9zbmud+9L+wEAghsAae5PlixZUq3/66+/TP4PAB9pzo93zY/nfzYRHWxU9wMABCcHSHN+lAY/nTt39mgCS05Olo0bN0rdunX9WzrAyjTh2Z/7AQD8HwDly5fPVQOUJ08eyZkzp2tb9uzZpXbt2tK1a1ffnxmwO+3t5c/9AAD+D4CmT59u/kZHR0v//v1p7gKulXZ1195emvCcVh6QNjXrdt0PABD8XmDk+gB+oOP8aFd35Z1X51weN47xgAAgWDVAOuXFkiVLpECBAnLHHXekmQTttG7dOn+WD7A2za2bMyftcYA0+GEcIAAIXgDUokULV9Jzy5YtA1MSwCKi4xZk8BEREtZ+stRM2CyFTh2TxNwFZHVUBUlZHS6y2vdj7RnZLMNlBQC7yuLQrGZ4SEpKMknfOrZR3rx5OTvXPSDA1SAAAmB3SRm4fl/TbPAAAACWbQLT3J/L5f24S2uUaAAAgEwXAI3TZEwAAAA7BUCdOnUKfEkAAABCKQDSpCJnMpHevxyShgEAgGVygA4cOCCFChWS/Pnzp5kP5JwkVecFAwAAyPQB0HfffScFCxY095cuXRroMgEAAAQ/AGrUqFGa9wEAACw9Gaq7Y8eOybvvvitbt241y7fffrt06dLFVUsEAAAQyjI8EOIPP/xgZoSfMGGCCYT0pvdLly5ttgEAAFiuBqhHjx7Stm1bmTJlioTrbNYiJvG5e/fuZttvv/0WiHICAAAErwZo586d0q9fP1fwo/R+3759zTYAAADLBUB33nmnK/fHna6rUqWKv8oFAAAQ3CawjRs3uu4/++yzEhsba2p7ateubdatXLlSJk+eLCNHjgxcSQEAAPwki0NHMLyCsLAwM8jhlXa1ykCIOtp1vnz55MSJE4xs7QfRcQv8cRhcwZ6RzThHAGwtKQPXb59qgHbv3u2vsgEAAGSOHKBSpUr5fMsobTrTbvU5cuSQWrVqyerVq9Pdd/PmzdK6dWuzv9Y2pTVL/csvv2y2ud/Kly+f4XLhH1qjt2yZyMyZl/5aoIYPAICrGghRbdmyRfbu3Svnz5/3WN+8eXOfjzF79mzTe2zq1Kkm+NGAJiYmRrZv327mHfN25swZKVOmjDz88MPSp0+fdI9boUIF+fbbb13LWbNe9cu0t7lzRWJjRRIS/l0XFSUyfrxIq1bBLBkAANckw5HBrl275KGHHjLj/bjnBTknSM1IDtCYMWOka9euZhRppYHQggUL5L333pO4uLhU+9eoUcPcVFrbXS8qa1YpUqRIRl+a5WUkFydm+88yZd5rqaoJUzQYat1aurUcJIvK1Q1AKQEACMFu8NoDTEd9TkxMlBtuuME0S+kI0NWrV5dl2kTiI605Wrt2rTRp0uTfwoSFmeUVK1bItdixY4cUK1bM1BZ16NDB1FRdzrlz50zilPvNzsJSkmXIkmmX7ntv++evbtf9AACwRQCkwcmwYcMkMjLSBCx6q1+/vowYMcJ0kffVkSNHTG1R4cKFPdbr8sGDB+VqaVPa+++/LwsXLjSjVWsCd4MGDeTkyZPpPkbLrlnjzluJEiXEzmombJZiJ4+k++HQ9bpd9wMAwBYBkAYtefLkMfc1CNq/f7+5rwnQmrsTbPfdd5/JEapcubLJJ/rqq6/k+PHj8sknn6T7mIEDB5ouc85bfHy82FmhU8f8uh8AAJk+B6hixYqyYcMG0wymtS2jRo2S7Nmzy7Rp00yTk680eNIpNA4dOuSxXpf9mb+TP39+ufXWWy87TUdERIS54ZLE3AX8uh8AAJm+BujFF1+UlJQUc1+bwpxNTFrTorPC+0qDpmrVqsmSJUtc6/S4ulynTh3xl1OnTskff/whRYsW9dsxrW51VAXZnydSLr3Lqel63a77AQBgixogbVZyuuWWW2Tbtm1y9OhRKVCggKsnmK+0C3ynTp1MAnXNmjVNN/jTp0+7eoV17NhRihcvbnJ0nInT2v3eeX/fvn2yfv16yZ07tymL6t+/vzz44IOmSU6b54YMGWJqmtq3b5/Rl2pbKWHhMrTx06YXWIp3L7B//up23Q8AgMzomgbIcebKXG3ScNu2beXw4cMyePBgk/hctWpVk7zsTIzW3luaZO2kAc0dd9zhWn7zzTfNrVGjRq4eaAkJCSbY+euvv+Smm24yCdo6V5neh++0i7t2ddfeXprw7HQwT6QJfugCDwCw/Fxg7i5evChDhw41zV3avKS0BqZXr16mtiVbtmyS2Vl1LrCrmZNLu7prby9NeNacH232ouYnNDEXGAC7S/L3XGDuNNCZO3euSX525upo13idgkJrXbTrOaxDg52VJSsHuxgAAPhVhgOgGTNmyKxZs0x3cyftcq7NYNr0RAAEAAAs1wtMu4vrZKTetFu89uwCAACwXADUs2dPeeWVV8z0EU56/9VXXzXbAAAALNEE1spr5m+daT0qKkqqVKlilnVgRO2W3rhx48CUEgAA4HoHQJpR7a5169Yey3afOwsAAFgwAJo+fXrgSwIAABDqAyHqAIbOyU/LlSvHQIMAAMC6SdA6VcUTTzxh5tZq2LChuRUrVkyefPJJOXPmTGBKCQAAEMwASOfv+v777+XLL7+U48ePm9sXX3xh1vXr18+fZQMAAAiNJrDPPvtM5syZI3fddZdr3f333y85c+aURx55hIEQAQCA9WqAtJnLOVmpu0KFCtEEBgAArBkA6fxfOunp2bNnXev+/vtvM0Gqc24wAAAASzWBjRs3Tu69995UAyHmyJFDFi1aFIgyAgAABDcAqlSpkuzYsUM+/vhj2bZtm1mnk6B26NDB5AEBAABYKgC6cOGClC9fXubPny9du3YNXKkAAABCJQcoW7ZsHrk/AAAAtkiC7tGjh7z++uty8eLFwJQIAAAg1HKAfvnlF1myZIl88803Jh8oV65cHtvnzp3rz/IBAAAEPwDKnz9/qtngAQAALB0AMTM8AACwTQ5QSkqKyf2pV6+e1KhRQ+Li4swAiAAAAJYNgF599VUZNGiQ5M6dW4oXLy7jx483CdEAAACWDYA+/PBDeeutt8xoz/PmzTOzwetgiFozBAAAYMkAaO/evWbWd6cmTZpIlixZZP/+/YEqGwAAQHADIB33R+f78h4YUUeHBgAAsGQvMIfDIZ07d5aIiAjXOh0V+plnnvEYC4hxgAAAgGUCoI4dO5omL3ePPfZYIMoEAAAQGgHQ+++/H9iSAAAAhFoOUMmSJaVnz56yePFi5gEDAAD2CIA++ugjk//TvXt3iYyMlLZt25pu8MePHw9sCQEAAIIVADVq1EhGjx4tO3bskJ9++kmqVq0qEydOlCJFisg999wj48aNk127dvm7fAAAAMELgNxVqFBBBg4cKCtXrpQ9e/ZI+/btzQzxFStWNLcFCxb4v6QAAADBmgzVm9YAde3a1dxOnz4t33zzjWTPnt0/pQMAAAiFACgpKemy2xs3buzaL2/evFdfMgAAgFAJgPLnz59qPKD0JCcnX02ZAAAAQisAmj59usTFxZlRoevUqWPWrVixQj744AMZMWKEREdHB6KcAAAAwQuAdFb4MWPGmMRnp+bNm0ulSpVk2rRpsmzZMv+VDgAAIBR6gWltT/Xq1VOt13WrV6/2V7kAAABCJwAqUaKEvPPOO6nW/9///Z/ZBgAAYLkmsLFjx0rr1q3l66+/llq1apl1WvOjAyR+9tlngSgjAABAcGuA7r//fvn999/lwQcflKNHj5qb3td1ug0AAMCSAyFqU9drr73m/9IAAACE6lQYy5cvl8cee0zq1q0r+/btc02W+uOPP/q7fAAAAMEPgDTPJyYmRnLmzCnr1q2Tc+fOmfUnTpygVggAAFgzABo+fLhMnTrV9ATLli2ba329evVMQAQAAGC5AGj79u3SsGHDVOvz5csnx48f91e5AAAAQicA0tnfd+7cmWq95v+UKVPGX+UCAAAInQCoa9euEhsbK6tWrTKTou7fv18+/vhj6d+/v3Tr1i0wpQQAAAhmN3idCDUlJUUaN24sZ86cMc1hERERJgDq1auXP8sGAAAQ/AAoOTlZfvrpJ+nRo4cMGDDANIWdOnVKbr/9dsmdO3dgSggAABDMACg8PFyaNm0qW7dulfz585vABwAAwPI5QBUrVpRdu3YFpjQAAAChOg6Q5vvMnz9fDhw4IElJSR43AAAAyyVBOyc8bd68uekF5uRwOMyy5gkBAABYKgBaunRpYEoCAAAQagFQx44dZfLkydKoUSOzvGHDBpME7T4dBgAAgKVygHSww7///tu13KBBA4mPjw9UuQAAAIIfAGmOz+WWAQAALNsLDAAAwFZJ0Fu2bJGDBw+6aoC2bdtmRoJ2V7lyZf+WEAAAIJgBkM7/5d709cADD5i/2v2dbvAAAMByAdDu3bsDWxIAAIBQC4BKlSoV2JIAAACE6kCIACxER25fvlzkwAGRokV1fAud9TjYpQKAgCMAAuxq7lyR2FiRhIR/10VFiYwfL9KqVTBLBgDWD4B0dOk33njD9C6rUqWKTJw4UWrWrJnmvps3b5bBgwfL2rVr5c8//5SxY8dK7969r+mYgFVExy3wed+Y7T/LlHmvpRoLI0WDodatpVvLQbKoXF2fjrVnZLMMlxUAbD0O0OzZs6Vv374yZMgQWbdunQlWYmJiJDExMc39z5w5I2XKlJGRI0dKkSJF/HJMwG7CUpJlyJJpl+57b/vnr27X/QDAqq4qALp48aJ8++238vbbb8vJkyfNuv3796caE+hKxowZI127dpUuXbqYecWmTp0qN9xwg7z33ntp7l+jRg1Ts9OuXTuJiIjwyzEBu6mZsFmKnTyS7n9+Xa/bdT8AsKoMB0Da9FSpUiVp0aKF9OjRQw4fPmzWv/7669K/f3+fj3P+/HnTlNWkSZN/CxMWZpZXrFiR0WJd0zHPnTsnSUlJHjfAqgqdOubX/QDAFgFQbGysVK9eXY4dOyY5c+Z0rX/ooYdkyZIlPh/nyJEjkpycLIULF/ZYr8vO0aYz6mqPOWLECMmXL5/rVqJEiat6fiAzSMxdwK/7AYAtAqDly5fLiy++KNmzZ/dYHx0dLfv27ZPMaODAgXLixAnXjVnuYWWroyrI/jyRkpLOdl2v23U/ALCqDAdAKSkpppbFW0JCguTJk8fn40RGRkp4eLgcOnTIY70up5fgHKhjaj5R3rx5PW6AVaWEhcvQxk9fuu+97Z+/ul33AwCrynAA1LRpUxk3bpxrWecB0+Rn7XV1//33+3wcrUGqVq2aR7OZBle6XKdOnYwWK2DHBKxIu7hrV/eDeSI91utyRrrAA4BtxgEaPXq06VauPazOnj0rjz76qOzYscPUvsycOTNDx9Lu6p06dTI5RTpOjwZWp0+fNj24VMeOHaV48eImR8eZ5Kwz0jvva5Pb+vXrJXfu3HLLLbf4dEwAl2iQs7hsLdPbSxOeNedHm72o+QFgBxkOgKKiomTDhg0ya9Ys2bhxo6n9efLJJ6VDhw4eSdG+aNu2relFpoMbapJy1apVZeHCha4k5r1795peXE7a1f6OO+5wLb/55pvm1qhRI1m2bJlPxwTwLw12VpaszCkBYDtZHA6HIyMP0FqfHDlyiJVpN3jtDaYJ0VbKB8rISMGArxgJGkBmvH5nOAeoUKFCpolp8eLFJr8GAAAgs8lwAPTBBx+YKSl0IETNz9G5uNasWROY0gEAAIRCAKQDHn766aema/lrr71mkpJr164tt956qwwbNiwQZQQAAAiNyVB1zB/tWfXNN9+YZOhcuXLJ0KFD/Vs6AACAUAqANBn6k08+kZYtW8qdd94pR48elQEDBvi3dAAAAKHQDX7RokUyY8YMmTdvnmTNmlXatGljaoEaNmwYiPIBAAAEPwDSHKAHHnhAPvzwQzPyc7Zs2fxfKgAAgFAKgDT5OSNzfgEAAGTKAEgHFnIOKKTjJupyeqw0cCAAALBxAFSgQAE5cOCAGQQxf/78ZgJUbxoY6fq0ZooHAADIdAHQd999JwULFjT3ly5dGugyAQAABD8A0slGnUqXLi0lSpRIVQukNUDx8fH+LyEAAECwxwHSAEhnW/em4wDpNgAAAMsFQM5cH2+nTp2y/CzxAADAGnzuBt+3b1/zV4Ofl156SW644QbXNk18XrVqlVStWjUwpQQAAAhGAPTrr7+6aoB+++03yZ49u2ub3q9SpYr079/fn2UDAAAIbgDk7P2lE6COHz+e8X4AAIB9RoKePn16YEoCAAAQqgGQWrNmjZkJfu/evXL+/HmPbXPnzvVX2QAAAEKjF9isWbOkbt26snXrVvn888/lwoULsnnzZjNYYr58+QJTSgAAgGAGQK+99pqMHTtWvvzyS5P8rPlA27Ztk0ceeURKlizpz7IBAACERgD0xx9/SLNmzcx9DYBOnz5tusb36dNHpk2bFogyAgAABDcA0olRT548ae4XL15cNm3aZO4fP35czpw549/SAQAAhEISdMOGDWXx4sVSqVIlefjhhyU2Ntbk/+i6xo0bB6KMAAAAwQ2AJk2aJGfPnjX3X3jhBcmWLZv8/PPP0rp1a3nxxRf9WzoAAIBQCIAKFizouh8WFiZxcXH+LhMAAEDwA6CkpCSfD5g3b95rKQ8AAEBoBED58+dPcwb4tGaJ14lRAQAAMn0A5JwHDAAAwDYBUKNGjQJfEgAAgFAdB0gtX75cHnvsMTMlxr59+8y6jz76SH788Ud/lw8AACD4AdBnn30mMTExkjNnTlm3bp2cO3fOrD9x4oSZJgMAAMByAdDw4cNl6tSp8s4775gxgJzq1atnAiIAAADLBUDbt283o0F705ngdToMAAAAywVARYoUkZ07d6Zar/k/ZcqU8Ve5AAAAQicA6tq1q5n/a9WqVWbcn/3798vHH38s/fv3l27dugWmlAAAAMGcCkOnvkhJSTETn+rs79ocFhERYQKgXr16+bNsAAAAoREAaa2PToI6YMAA0xR26tQpuf322yV37tzy999/m95hAAAAlhsHSGXPnt0EPjVr1jS9wcaMGSOlS5f2b+kAAACCGQDpeD8DBw6U6tWrmwEQ582bZ9ZPnz7dBD5jx46VPn36BKKMAAAAwWkCGzx4sLz99tvSpEkT+fnnn+Xhhx+WLl26yMqVK03tjy6Hh4f7t3QAAADBDIA+/fRT+fDDD6V58+ayadMmqVy5sly8eFE2bNhwxZniAQAAMmUTWEJCglSrVs3cr1ixoun5pU1eBD8AAMCyAVBycrJJfHbKmjWr6fkFAABg2SYwh8MhnTt3NjU/6uzZs/LMM89Irly5PPabO3eu/0sJAAAQjACoU6dOHsuPPfaYP8sBAAAQegGQdncHAACw9UCIAAAAmRUBEAAAsB0CIAAAYDsEQAAAwHYIgAAAgO0QAAEAANshAAIAALZDAAQAAGyHAAgAANgOARAAALAdAiAAAGA7BEAAAMB2CIAAAIDtEAABAADbIQACAAC2QwAEAABshwAIAADYTtZgFwCADSUniyxfLnLggEjRoiINGoiEhwe7VABsJCRqgCZPnizR0dGSI0cOqVWrlqxevfqy+3/66adSvnx5s3+lSpXkq6++8tjeuXNnyZIli8ft3nvvlUx/wVi2TGTmzEt/dRnIjObOFYmOFrn7bpFHH730V5d1PQDYJQCaPXu29O3bV4YMGSLr1q2TKlWqSExMjCQmJqa5/88//yzt27eXJ598Un799Vdp2bKluW3atMljPw14Dhw44LrN1MAhs+KCAavQz3KbNiIJCZ7r9+27tJ4gCMB1ksXhcDgkiLTGp0aNGjJp0iSznJKSIiVKlJBevXpJXFxcqv3btm0rp0+flvnz57vW1a5dW6pWrSpTp0511QAdP35c5s2bd1VlSkpKknz58smJEyckb968EhIXDO+3KUuWS3/nzBFp1cqnQ0XHLQhAAWF3e0Y2821HrbXUmh7v4Mf9Mx0VJbJ7N81hAAJ+/Q5qDdD58+dl7dq10qRJk38LFBZmllesWJHmY3S9+/5Ka4y891+2bJkUKlRIypUrJ926dZO//vor3XKcO3fOnDT3W0jQC0ZsbOrgRznX9e5NcxgyB835SS/4cX6m4+Mv7QcAARbUAOjIkSOSnJwshQsX9livywcPHkzzMbr+Svtr89eHH34oS5Yskddff12+//57ue+++8xzpWXEiBEmYnTetAYqJHDBgJVowrM/9wOAa2DJXmDt2rVz3dck6cqVK8vNN99saoUaN26cav+BAweaPCQnrQEKiSCICwasRHt7+XM/AMisAVBkZKSEh4fLoUOHPNbrcpEiRdJ8jK7PyP6qTJky5rl27tyZZgAUERFhbiGHCwYyAV9zy8JSkuXHPJFS5OSRNKueU7SGN0+k1P8qSVIWLvBf7hEAhFoAlD17dqlWrZppqtKeXM4kaF3u2bNnmo+pU6eO2d5bc1/+sXjxYrM+PQkJCSYHqGiI/LIM1gUDCKaUsHAZ2vhpmTLvNfPZdf9M67LS7bofAFi+G7w2Pb3zzjvywQcfyNatW03Csvby6tKli9nesWNH00TlFBsbKwsXLpTRo0fLtm3b5OWXX5Y1a9a4AqZTp07JgAEDZOXKlbJnzx4TLLVo0UJuueUWkyydGS8Y5r73tn/+csFAZrKoXF3p1nKQCdzd6bKu1+0AYIscIO3WfvjwYRk8eLBJZNbu7BrgOBOd9+7da3qGOdWtW1dmzJghL774ogwaNEjKli1rurtXrFjRbNcmtY0bN5qASrvCFytWTJo2bSqvvPJKaDZz+XjBGLJkmhQ7ecTjgqHBDxcMZDb6mV1ctpbUTNgshU4dk8TcBWR1VAVqfgDYaxygUBTocYCuZjwebQ7jggH8ixwgANdy/Q56DRB8bw5bWbIypwsAACvkAAEAAFxvBEAAAMB2CIAAAIDtEAABAADbIQACAAC2QwAEAABshwAIAADYDgEQAACwHQIgAABgOwRAAADAdgiAAACA7RAAAQAA2yEAAgAAtkMABAAAbIcACAAA2A4BEAAAsB0CIAAAYDsEQAAAwHYIgAAAgO0QAAEAANshAAIAALZDAAQAAGyHAAgAANgOARAAALAdAiAAAGA7BEAAAMB2CIAAAIDtEAABAADbIQACAAC2QwAEAABshwAIAADYTtZgFwAArpvkZJHly0UOHBApWlSkQQOR8HDeAMCGCIAA2MPcuSKxsSIJCf+ui4oSGT9epFWrYJYMQBDQBAbAHsFPmzaewY/at+/Set0OwFYIgABYv9lLa34cjtTbnOt69760HwDbIAACYG2a8+Nd8+MdBMXHX9oPgG0QAAGwNk149ud+ACyBJGgAmVJ03AKf9qu9d4/M8mG/dl/ukZUbrnzMPSOb+fS8AEIbNUAALG11VAXZnydSUtLZrut1u+4HwD4IgABYWkpYuAxt/PSl+97b/vmr23U/APZBAATA8haVqyvdWg6Sg3kiPdbrsq7X7QDshRwgALagQc7isrWkZsJmKXTqmCTmLmCavaj5AeyJAAiAbWiws7Jk5WAXA0AIoAkMAADYDgEQAACwHQIgAABgOwRAAADAdgiAAACA7RAAAQAA2yEAAgAAtkMABAAAbIeBEAEg0JKTRZYvFzlwQKRoUZEGDUTCmXsMCCYCIAAIpLlzRWJjRRIS/l0XFSUyfrxIq1aceyBIaAIDgEAGP23aeAY/at++S+t1O4CgIAACgEA1e2nNj8OReptzXe/el/YDcN3RBAYAGRAdt8Cn/Wrv3SizvGt+vIOg+Hhp9/gonyZo3TOyWUaKCeAKqAECgAAodOqYX/cD4F8EQAAQAIm5C/h1PwD+RQAEAAGwOqqC7M8TKSnpbNf1ul33A3D9EQABQACkhIXL0MZPX7rvve2fv7pd9wNw/REAAUCALCpXV7q1HCQH80R6rNdlXa/bA0p7mC1bJjJz5qW/9DgDXOgFBgABpEHO4rK1pGbCZpPwrDk/2uwV8JofBmAELosACAACTIMdX7q6+30ARu8xiJwDMM6ZE9hRqJn6A5kATWAAYCXBHoBRg6/oaJG77xZ59NFLf3X5eox6TZMfMlsANHnyZImOjpYcOXJIrVq1ZPXq1Zfd/9NPP5Xy5cub/StVqiRfffWVx3aHwyGDBw+WokWLSs6cOaVJkyayY8eOAL8KAAgBOumqDwMwmv2sNPWHHQMvuz2v1QKg2bNnS9++fWXIkCGybt06qVKlisTExEhiYmKa+//888/Svn17efLJJ+XXX3+Vli1bmtumTZtc+4waNUomTJggU6dOlVWrVkmuXLnMMc+ePXsdXxkABIHOOO/P/TJDzZMdAy+7PW8AZHFodUkQaY1PjRo1ZNKkSWY5JSVFSpQoIb169ZK4uLhU+7dt21ZOnz4t8+fPd62rXbu2VK1a1QQ8+nKKFSsm/fr1k/79+5vtJ06ckMKFC8v7778v7dq1u2KZkpKSJF++fOZxefPmlWANpQ8AGWWm4Jg56Ir7tWv/mn+n4NCaAL0YXsnSpSJ33SV+owGVXoDTq/XKkkUkKkpk926R8PDrk2ulz6kClWtlt+fNgIxcv4OaBH3+/HlZu3atDBw40LUuLCzMNFmtWLEizcfoeq0xcqe1O/PmzTP3d+/eLQcPHjTHcNKToYGWPtaXAAgAMvsAjEVOHkmzij/ln274vg7A6OsPtuZbvpcJPuz37Jiv5H8LT/sv8MpIk5+/A6/L1XhpUKA1Xi1a+DfwstvzBlBQA6AjR45IcnKyqZ1xp8vbtm1L8zEa3KS1v653bneuS28fb+fOnTM3J40cnZFkIKScOxOQ4wKABjgvNOwkYxeMNicjLI0BGHX7xQv/fuf5w76InJLk436+fAf6/P37xx++73fnnVfcreKQRT4drkbCJpnuQ+DVpd0w+SWq4hWPt2lojH8DvoULRRo08O2Yofy8GeT83PjSuEU3eBEZMWKEDB06NNXJ0aY4AMhs3v/nlq5/giN/itcWEl92nDPMp+PlGyf+9dRTl252eb0PPODnA4b483o5efKkaf0J2QAoMjJSwsPD5dChQx7rdblIkSJpPkbXX25/519dp73A3PfRPKG0aBOce7Oa5iEdPXpUbrzxRsnibNsMARrZalAWHx8fkNykUMPrtTbeX2vj/bW2pBC9HmnNjwY/mgt8JUENgLJnzy7VqlWTJUuWmJ5czuBDl3v27JnmY+rUqWO299a2xn8sXrzYrFelS5c2QZDu4wx49I3S3mDdunVL85gRERHm5i5//vwSqvTDFkofuEDj9Vob76+18f5aW94QvB5dqeYnZJrAtOalU6dOUr16dalZs6aMGzfO9PLq0qWL2d6xY0cpXry4aaZSsbGx0qhRIxk9erQ0a9ZMZs2aJWvWrJFp06aZ7Vpjo8HR8OHDpWzZsiYgeumll0w06AyyAACAvQU9ANJu7YcPHzYDF2qSstbaLFy40JXEvHfvXtMzzKlu3boyY8YMefHFF2XQoEEmyNEeYBUr/ptk9txzz5kg6umnn5bjx49L/fr1zTF14EQAAICgB0BKm7vSa/JapmNLeHn44YfNLT1aCzRs2DBzsxJtptMBI72b66yK12ttvL/WxvtrbREWuB4FfSBEAAAA202FAQAAcL0RAAEAANshAAIAALZDAAQAAGyHACiTmDx5skRHR5uu/Dqx6+rVq8WKdLynGjVqSJ48eaRQoUJm7Kbt27eLXYwcOdI1lpWV7du3Tx577DEz2nrOnDmlUqVKZjwvK9L5DnUsMh2TTF/rzTffLK+88opPcxVlBj/88IM8+OCDZqw1/ew6J6Z20tepw5zoyPz6+nWi6h07dogVX++FCxfk+eefN5/nXLlymX10LLv9+/eLVd9fd88884zZR8fzywwIgDKB2bNnmwEjtcvhunXrpEqVKhITEyOJiYliNd9//7306NFDVq5caUb41i+Upk2bmnGdrO6XX36Rt99+WypXrixWduzYMalXr55ky5ZNvv76a9myZYsZ2LRAgQJiRa+//rpMmTJFJk2aJFu3bjXLo0aNkokTJ4oV6P9N/U7SH2lp0dc6YcIEmTp1qhmRXwMD/f46e/asWO31njlzxnxHa8Crf+fOnWt+wDVv3lys+v46ff755+Z725cpKEKGdoNHaKtZs6ajR48eruXk5GRHsWLFHCNGjHBYXWJiov5Mdnz//fcOKzt58qSjbNmyjsWLFzsaNWrkiI2NdVjV888/76hfv77DLpo1a+Z44oknPNa1atXK0aFDB4fV6P/Vzz//3LWckpLiKFKkiOONN95wrTt+/LgjIiLCMXPmTIfVXm9aVq9ebfb7888/HVZ9vQkJCY7ixYs7Nm3a5ChVqpRj7NixjsyAGqAQd/78eVm7dq2pNnbSkbF1ecWKFWJ1J06cMH8LFiwoVqa1Xjq1i/v7bFX/+9//zNQ3OpipNnPecccd8s4774hV6ej1Ojfh77//bpY3bNggP/74o9x3331idbt37zYj/Lt/rnWeJm3Gt8P3l/M7TJuFQnl+yWuh83c+/vjjMmDAAKlQoYJkJiExEjTSd+TIEZND4JwaxEmXt23bZulTp/+xNBdGm0vcpzqxGp3PTqvLtQnMDnbt2mWahLRZV6ez0df97LPPmsmRdV5Aq4mLizMTMpcvX17Cw8PN/+dXX31VOnToIFanwY9K6/vLuc3KtJlPc4Lat28fchOG+os26WbNmtX8H85sCIAQ0rUimzZtMr+WrSo+Pt5M8Kv5TnaZq04DW60Beu2118yy1gDp+6w5IlYMgD755BP5+OOPzRyG+gt5/fr1JrDXXAkrvl5covmLjzzyiEkC14DfitauXSvjx483P+C0liuzoQksxEVGRppfjYcOHfJYr8tFihQRq9K54ebPny9Lly6VqKgosSr9AtFk9jvvvNP8itKbJoJr0qje19oCq9HeQLfffrvHuttuu81MfGxF2jSgtUDt2rUzvYO0uaBPnz6mx6PVOb+j7Pb95Qx+/vzzT/Pjxqq1P8uXLzffXyVLlnR9f+lr7tevn+m1HOoIgEKcNgtUq1bN5BC4/4LW5Tp16ojV6K8lDX60R8F3331nug5bWePGjeW3334ztQLOm9aOaPOI3tfg12q0SdN7aAPNjylVqpRYkfYM0rw9d/q+6v9jq9P/vxrouH9/aXOg9gaz4veXe/CjXf2//fZbM9SDVT3++OOyceNGj+8vrdnUoH/RokUS6mgCywQ0V0KryvXCWLNmTTPGgnZN7NKli1ix2UubCr744gszFpAzT0ATJ3UMEavR1+id36TdhPVL06p5T1r7oYnB2gSmFwod02ratGnmZkU6horm/OivZG0C+/XXX2XMmDHyxBNPiBWcOnVKdu7c6ZH4rBdC7bigr1mb+4YPHy5ly5Y1AZF2EdeLpI7xZbXXq7Wbbdq0MU1CWoOtNbjO7zDdrj9orfb+3ugV4OnwFhr0litXTkJesLuhwTcTJ050lCxZ0pE9e3bTLX7lypWWPHX6kUzrNn36dIddWL0bvPryyy8dFStWNN2hy5cv75g2bZrDqpKSksz7qf9/c+TI4ShTpozjhRdecJw7d85hBUuXLk3z/2ynTp1cXeFfeuklR+HChc373bhxY8f27dsdVny9u3fvTvc7TB9nxffXW2bqBp9F/wl2EAYAAHA9kQMEAABshwAIAADYDgEQAACwHQIgAABgOwRAAADAdgiAAACA7RAAAQAA2yEAAgAAtkMABCCk6VQCvXr1kjJlykhERISUKFHCTC/hPr/U9aCzXc+bN++6PieAwGEuMAAha8+ePWby1Pz588sbb7xhZlPXySZ1okWdN27btm3BLiKATIoaIAAhq3v37qbmRSdMbd26tdx6661mQlGdIHjlypVmn71790qLFi0kd+7ckjdvXjPB6qFDh1zH6Ny5c6qJN3WCzrvuusu1rPefffZZee6558wkjzqZ48svv+zaHh0dbf4+9NBDpjzO5Q0bNsjdd99tJrXV565WrZqsWbMm4OcFwLUjAAIQko4ePSoLFy40NT25cuVKtV1rhVJSUkzwo/t+//33snjxYtm1a5e0bds2w8/3wQcfmOdZtWqVjBo1SoYNG2aOp3755Rfzd/r06XLgwAHXcocOHSQqKsosr127VuLi4sxs2ABCH01gAELSzp07RedqLl++fLr7aB7Qb7/9Jrt37za5QerDDz80tUQalNSoUcPn56tcubIMGTLE3C9btqxMmjTJHP8///mP3HTTTa6gS2uHnLT2acCAAa4y6uMAZA7UAAEISRr8XMnWrVtN4OMMftTtt99uAhXdlhEaALkrWrSoJCYmXvYx2hT31FNPSZMmTWTkyJHyxx9/ZOg5AQQPARCAkKS1KZpvc62JzmFhYamCKU2k9ubddKXPrU1sl6N5Qps3b5ZmzZrJd999Z4Kvzz///JrKC+D6IAACEJI0GTkmJkYmT54sp0+fTrX9+PHjctttt0l8fLy5OW3ZssVs02BEafOV5u24W79+fYbLowFScnJyqvWamN2nTx/55ptvpFWrViZPCEDoIwACELI0+NGgo2bNmvLZZ5/Jjh07TNPWhAkTpE6dOqbpSbvGazLyunXrTG+xjh07SqNGjaR69ermGPfcc4/pmaW5Qfp4zfPZtGlThsuiPb80J0jHJTp27Jj8/fff0rNnT1m2bJn8+eef8tNPP5m8Iw3KAIQ+AiAAIUsHP9TARrua9+vXTypWrGiSkjUQmTJlimmm+uKLL6RAgQLSsGFDExDpY2bPnu06htYivfTSS6aLuyZFnzx50gRJGTV69GjTK0zzje644w4JDw+Xv/76yxxLa4G0+/19990nQ4cO9fNZABAIWRy+ZBoCAABYCDVAAADAdgiAAACA7RAAAQAA2yEAAgAAtkMABAAAbIcACAAA2A4BEAAAsB0CIAAAYDsEQAAAwHYIgAAAgO0QAAEAANshAAIAALbz/wGxIqvxfKYxZwAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.hist(poiData, bins=np.arange(-0.5, 15.5,1), density=True)\n", + "plt.plot(x, poisson.pmf(x, lam),'or')\n", + "plt.xlabel(\"Counts\")\n", + "plt.ylabel(\"Relative Freq/Probability\")\n", + "plt.title(\"Poisson: Simulated vs Theory\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "cb795b6e", + "metadata": {}, + "source": [ + "# Normal distribution\n", + "If $X\\sim N(\\mu, \\sigma^2)$, then:\n", + "- $\\mu$ is the mean,\n", + "- $\\sigma$ is the standard deviation" + ] + }, + { + "cell_type": "markdown", + "id": "0416787f", + "metadata": {}, + "source": [ + "Example: Suppose a sensor output is a normally distributed with mean 50 and standard deviation 4. We compute the probability that the output is less than 58. " + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "id": "ea59f656", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "np.float64(0.9772498680518208)" + ] + }, + "execution_count": 45, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "mu = 50 \n", + "sigma = 4\n", + "proba = norm.cdf(58, loc=mu, scale=sigma)\n", + "proba" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "id": "763cf868", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x = np.linspace(mu - 4*sigma, mu + 4*sigma, 400)\n", + "pdf = norm.pdf(x, loc=mu, scale=sigma)\n", + "\n", + "plt.figure(figsize=(8,4))\n", + "plt.plot(x, pdf)\n", + "plt.axvline(58, linestyle='--')\n", + "plt.xlabel(\"x\")\n", + "plt.ylabel(\"Density\")\n", + "plt.title(\"Normal Distribution\")\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "id": "90c5658f", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Simulated mean: 50.004935022325526\n", + "Theoretical mean: 50\n", + "Simulated std: 3.9780626491745017\n", + "Theoretical std: 4\n" + ] + } + ], + "source": [ + "mu = 50\n", + "sigma = 4 \n", + "samples = 10_000\n", + "\n", + "normData = np.random.normal(loc=mu, scale=sigma, size=samples)\n", + "print(\"Simulated mean: \", normData.mean())\n", + "print(\"Theoretical mean: \", mu)\n", + "print(\"Simulated std: \", normData.std(ddof=1))\n", + "print(\"Theoretical std: \", sigma)" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "id": "0b94b1c6", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.hist(normData, bins=50, density=True)\n", + "plt.plot(x, pdf, 'or')\n", + "plt.xlabel(\"Value\")\n", + "plt.ylabel(\"Density\")\n", + "plt.title(\"Normal: Simulation vs Theory\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "995adcee", + "metadata": {}, + "source": [ + "# Central Limit Theorem\n", + "The central limit theorem (CLT) states that the sampling distribution of the sample mean becomes approximately normal as the sample size increases." + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "id": "b22b9a32", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "population = np.random.exponential(scale=2, size=100_000)\n", + "plt.hist(population, bins=50, density=True)\n", + "plt.xlabel(\"Value\")\n", + "plt.ylabel(\"Density\")\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e1d70f56", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 62, + "id": "39dad6b6", + "metadata": {}, + "outputs": [], + "source": [ + "def SampleMeans(population, sampleSize, nRep=5_000):\n", + " means = []\n", + " for _ in range(nRep):\n", + " sample = np.random.choice(population, size=sampleSize, replace=True)\n", + " means.append(sample.mean())\n", + " pass\n", + " return np.array(means)" + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "id": "2e324399", + "metadata": {}, + "outputs": [], + "source": [ + "mean5 = SampleMeans(population, 5)\n", + "mean30 = SampleMeans(population, 30)\n", + "mean100 = SampleMeans(population, 100)" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "id": "e96babca", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.hist(mean5, bins=40, density=True, color=\"orange\", alpha=0.3)\n", + "plt.hist(mean30, bins=40, density=True, color=\"green\", alpha=0.3)\n", + "plt.hist(mean100, bins=40, density=True, color=\"blue\", alpha=0.3)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 72, + "id": "5a18e86e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Population mean: 1.9932073011758906\n", + "Population var: 4.025192782387372\n", + "Mean of 5 samples: 1.9998045611349438\n", + "Var of 5 samples: 0.7837744844351563\n", + "Mean of 30 samples: 1.992377755782367\n", + "Var of 5 samples: 0.13206867208626297\n", + "Mean of 100 samples: 1.994853961830046\n" + ] + } + ], + "source": [ + "# Numerical Check\n", + "print(\"Population mean: \", population.mean())\n", + "print(\"Population var: \", population.var())\n", + "\n", + "print(\"Mean of 5 samples: \", mean5.mean())\n", + "print(\"Var of 5 samples: \", mean5.var(ddof=1))\n", + "print(\"Mean of 30 samples: \", mean30.mean())\n", + "print(\"Var of 5 samples: \", mean30.var(ddof=1))\n", + "print(\"Mean of 100 samples: \", mean100.mean())" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".venv (3.14.3)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.14.3" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/session-6-distributions/main.ipynb b/session-6-distributions/main.ipynb index 1890439..1502ca4 100644 --- a/session-6-distributions/main.ipynb +++ b/session-6-distributions/main.ipynb @@ -20,7 +20,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 2, "id": "62fc7999", "metadata": {}, "outputs": [], @@ -34,7 +34,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 3, "id": "52e8c8bb", "metadata": {}, "outputs": [ @@ -61,7 +61,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 4, "id": "e8285330", "metadata": {}, "outputs": [ @@ -70,9 +70,9 @@ "output_type": "stream", "text": [ "First 20 observations:\n", - "[1 1 0 0 0 1 1 0 1 1 1 0 0 1 0 0 1 1 0 1]\n", - "Sample mean: 0.693\n", - "Sample variance: 0.21296396396396394\n" + "[1 0 0 1 1 1 1 0 1 0 1 0 0 1 1 1 1 1 1 1]\n", + "Sample mean: 0.712\n", + "Sample variance: 0.20526126126126118\n" ] } ], @@ -98,13 +98,13 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 5, "id": "02a6d407", "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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", 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" ] @@ -146,7 +146,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 6, "id": "51dd4e92", "metadata": {}, "outputs": [ @@ -174,7 +174,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 7, "id": "41a6efb0", "metadata": {}, "outputs": [ @@ -213,7 +213,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 8, "id": "741ee2d7", "metadata": {}, "outputs": [ @@ -221,9 +221,9 @@ "name": "stdout", "output_type": "stream", "text": [ - "Simulated mean: 1.5811\n", + "Simulated mean: 1.5818\n", "Theoretical mean: 1.6\n", - "Simulated variance: 1.4365664466446644\n", + "Simulated variance: 1.4380525652565255\n", "Theoretical variance: 1.4720000000000002\n" ] } @@ -244,13 +244,13 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 9, "id": "bc6f1103", "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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", 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" ] @@ -290,7 +290,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 10, "id": "d6d2a5f6", "metadata": {}, "outputs": [ @@ -316,7 +316,7 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 11, "id": "262e9381", "metadata": {}, "outputs": [ @@ -353,7 +353,7 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 12, "id": "f241431b", "metadata": {}, "outputs": [ @@ -361,9 +361,9 @@ "name": "stdout", "output_type": "stream", "text": [ - "Simulated mean: 2.9968\n", + "Simulated mean: 3.0051\n", "Theoretical mean: 3\n", - "Simulated variance: 2.9834881088108816\n", + "Simulated variance: 3.0315771477147715\n", "Theoretical variance: 3\n" ] } @@ -383,13 +383,13 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 13, "id": "2f9e2a0c", "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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", 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" ] @@ -428,7 +428,7 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 14, "id": "c73731b8", "metadata": {}, "outputs": [ @@ -454,7 +454,7 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 15, "id": "e28013a8", "metadata": {}, "outputs": [ @@ -492,7 +492,7 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 16, "id": "9617ab65", "metadata": {}, "outputs": [ @@ -500,9 +500,9 @@ "name": "stdout", "output_type": "stream", "text": [ - "Simulated mean: 49.950383162899335\n", + "Simulated mean: 50.002185302479354\n", "Theoretical mean: 50\n", - "Simulated std: 4.0548202451563125\n", + "Simulated std: 3.9891411700286694\n", "Theoretical std: 4\n" ] } @@ -523,13 +523,13 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 17, "id": "f3182d6f", "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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", 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" ] @@ -567,7 +567,7 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 18, "id": "8917aabe", "metadata": {}, "outputs": [ @@ -589,7 +589,7 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 19, "id": "37a5afbd", "metadata": {}, "outputs": [ @@ -632,13 +632,13 @@ }, { "cell_type": "code", - "execution_count": 29, + "execution_count": 26, "id": "cd561dd9", "metadata": {}, "outputs": [ { "data": { - "image/png": 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", + "image/png": 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LJ06c6Fv28ssvO5deeqkZUaYXfW76HtX3pT8dx6a3veaaawKW33nnnWa57u9gnnvuOSczM9Nsb+vWrZ3evXubMV864s2l47+mTZvme89eccUVztatW82+qj6aa/78+U6LFi0Cni+A2sXpf+oTegGgobRqpcP99UxMWhVu7PRAJK1yb9261etNiWr68bxWU7WSGW2nNvaS/r+i76Gf//znXm8KYAV6ZgGElPYXVqdtBzptwP/gGeCBBx4wY7W0tQL/pX2/Gu61NQJA/dAzCyCkdESSHryi0wb0qHLtC9SL9id26tSJvY2A0VjuLFb8l/Yqa8AHUH+EWQAhpQdkrV692nyErL+U9SQIOoz+4YcfZk8DAEKOnlkAAABYi55ZAAAAWIswCwAAAGvFXM+snhlGTzOpg7NDNcAdAAAAoaOTYw8fPmxO9KLTcOoSc2FWgyxHVAMAAES/0tJSOeecc+pcJ+bCrFZk3Z2jpzwEAABAdCkvLzfFRze31SXmwqzbWqBBljALAAAQverTEsoBYAAAALAWYRYAAADWIswCAADAWoRZAAAAWIswCwAAAGsRZgEAAGAtwiwAAACsRZgFAACAtQizAAAAsBZhFgAAANYizAIAAMBa8V5vQCxIn7Qi6PKS/GER3xYAAIDGhMosAAAArEWYBQAAgLUIswAAALAWYRYAAADWIswCAADAWoRZAAAAWIswCwAAAGsRZgEAAGAtwiwAAACsRZgFAACAtQizAAAAsBZhFgAAANYizAIAAMBahFkAAABYizALAAAAaxFmAQAAYC3CLAAAAKxFmAUAAIC1CLMAAACwFmEWAAAA1iLMAgAAwFqEWQAAAFiLMAsAAABrEWYBAABgLcIsAAAArEWYBQAAgLUIswAAALAWYRYAAADWIswCAADAWvFeb0AsS5+0IujykvxhEd8WAAAAG1GZBQAAgLUIswAAALAWYRYAAADWIswCAADAWoRZAAAAWIswCwAAAGsRZgEAAGAtwiwAAACsRZgFAACAtQizAAAAsBZhFgAAANaKijA7b948SU9Pl8TERBkwYIBs2LChXrd76aWXJC4uTnJycsK+jQAAAIg+nofZZcuWyYQJEyQvL0+Ki4slIyNDsrOzpaysrM7blZSUyMSJE+Wyyy6L2LYCAAAgungeZp9++mm56667ZOzYsXLeeefJs88+Ky1atJAFCxbUepvKykq59dZbZdq0adK1a9eIbi8AAACih6dhtqKiQjZt2iRDhgz5/w1q0sRcLyoqqvV2jz32mLRv317uuOOOkz7G8ePHpby8POACAACAxsHTMLt//35TZU1JSQlYrtf37NkT9DZvvvmmvPDCC/L888/X6zFmzJghbdq08V06deoUkm0HAACA9zxvMzgVhw8flttuu80E2eTk5HrdZvLkyXLo0CHfpbS0NOzbCQAAgMiIFw9pIG3atKns3bs3YLleT01NrbH+jh07zIFf119/vW9ZVVWV+RofHy/btm2Tbt26BdymefPm5gIAAIDGx9PKbEJCgmRmZkphYWFAONXrAwcOrLF+z5495f3335fNmzf7LjfccIMMHjzY/JsWAgAAgNjiaWVW6Viu3Nxc6devn2RlZUlBQYEcPXrUTDdQo0ePlrS0NNP7qnNoe/XqFXD7tm3bmq/VlwMAAKDx8zzMjhw5Uvbt2ydTp041B3317dtXVq5c6TsobOfOnWbCAQAAAFBdnOM4jsQQHc2lUw30YLCkpKSIPGb6pBWntH5J/rCwbQsAAEBjymuUPAEAAGAtz9sMUL9KLtVaAACAmqjMAgAAwFqEWQAAAFiLMAsAAABrEWYBAABgLcIsAAAArEWYBQAAgLUIswAAALAWYRYAAADWIswCAADAWoRZAAAAWIswCwAAAGsRZgEAAGAtwiwAAACsRZgFAACAtQizAAAAsBZhFgAAANYizAIAAMBahFkAAABYizALAAAAaxFmAQAAYC3CLAAAAKxFmAUAAIC1CLMAAACwFmEWAAAA1iLMAgAAwFqEWQAAAFiLMAsAAABrEWYBAABgrXivNwD1kz5pRdDlJfnD2IUAACBmUZkFAACAtQizAAAAsBZhFgAAANYizAIAAMBahFkAAABYizALAAAAaxFmAQAAYC3CLAAAAKxFmAUAAIC1CLMAAACwFmEWAAAA1iLMAgAAwFqEWQAAAFiLMAsAAABrEWYBAABgLcIsAAAArEWYBQAAgLUIswAAALAWYRYAAADWIswCAADAWlERZufNmyfp6emSmJgoAwYMkA0bNtS67iuvvCL9+vWTtm3bSsuWLaVv377ym9/8RmJV+qQVQS8AAACxwPMwu2zZMpkwYYLk5eVJcXGxZGRkSHZ2tpSVlQVdv127dvLwww9LUVGRbNmyRcaOHWsuq1ativi2AwAAwFtxjuM4Xm6AVmL79+8vc+fONderqqqkU6dOMn78eJk0aVK97uPCCy+UYcOGyfTp00+6bnl5ubRp00YOHTokSUlJEgleVEpL8odF/DEBAABC4VTymqeV2YqKCtm0aZMMGTLk/zeoSRNzXSuvJ6M5vLCwULZt2yaXX3550HWOHz9udoj/BQAAAI2Dp2F2//79UllZKSkpKQHL9fqePXtqvZ2m9FatWklCQoKpyM6ZM0e+/e1vB113xowZJtm7F636AgAAoHHwvGe2IVq3bi2bN2+Wd955Rx5//HHTc7t27dqg606ePNmEX/dSWloa8e0FAABAeMSLh5KTk6Vp06ayd+/egOV6PTU1tdbbaStC9+7dzb91msEHH3xgKrBXXHFFjXWbN29uLgAAAGh8PK3MaptAZmam6Xt16QFgen3gwIH1vh+9jfbGAgAAILZ4WplV2iKQm5trZsdmZWVJQUGBHD161IzbUqNHj5a0tDRTeVX6Vdft1q2bCbB/+tOfzJzZ+fPne/xMAAAAEHNhduTIkbJv3z6ZOnWqOehL2wZWrlzpOyhs586dpq3ApUH3nnvukc8//1zOOOMM6dmzp/z2t7819wMAAIDY4vmc2UhjziwAAEB0s2bOLAAAAHA6CLMAAACIrTD7ySefhH5LAAAAgEiEWZ3xOnjwYHPg1ddff92QuwAAAAC8CbPFxcXSp08fM1ZLT25w9913y4YNG05/awAAAIBwh1kdn/XMM8/Irl27ZMGCBbJ792659NJLpVevXvL000+bUVsAAABAVB8AFh8fLzfddJMsX75cZs6cKdu3b5eJEydKp06dzMkONOQCAAAAURlmN27caE5g0KFDB1OR1SC7Y8cOWb16tanaDh8+PHRbCgAAAITiDGAaXBcuXCjbtm2Ta6+9VhYvXmy+umfqOvfcc2XRokWSnp7ekLsHAAAAwhdm58+fL7fffruMGTPGVGWDad++vbzwwgsNuXsAAAAgfGFW2wg6d+7sq8S69My4paWl5nsJCQmSm5vbkLsHAAAAwhdmu3XrZg7u0uqrvwMHDpgWg8rKyobcLUIofdKKGstK8oexjwEAQKPSoAPAtAIbzJEjRyQxMfF0twkAAAAIfWVWT5Kg4uLiZOrUqdKiRQvf97Qa+49//MPMoAUAAACiLsy+++67vsrs+++/b/piXfrvjIwMM54LAAAAiLowu2bNGvN17Nix5gxgSUlJ4douAAAAIDwHgOmMWQAAAMCaMKunrdUTIWg1Vv9dl1deeSUU2wYAAACEJsy2adPGHPjl/hsAAACwJsz6txbQZgAAAABr58x+9dVXcuzYMd/1zz77TAoKCuQvf/lLKLcNAAAACH2YHT58uCxevNj8++DBg5KVlSWzZ882y+fPn9+QuwQAAAAiM82guLhYfv7zn5t///73v5fU1FQzg/bll182J1MYN25cQ+4WHpziVnGaWwAAEFOVWW0xaN26tfm3thbodIMmTZrIRRddZFoOAAAAgKgNs927d5fXXntNSktLZdWqVTJ06FCzvKysjBMpAAAAILrDrLYS6Glr09PTZcCAATJw4EBflfaCCy4I9TYCAAAAoeuZvfnmm+XSSy+V3bt3S0ZGhm/5VVddJTfeeGND7hIAAACITJhVetCXXvzpVAMAAAAgqsPs0aNHJT8/XwoLC02fbFVVVcD3P/nkk1BtHwAAABDaMHvnnXfKunXr5LbbbpMOHTr4TnMLAAAARH2Y/fOf/ywrVqyQSy65JPRbBAAAAIRzmsGZZ54p7dq1a8hNAQAAAG/D7PTp0814Lj15AgAAAGBVm8Hs2bNlx44dkpKSYmbNNmvWrMbpbgEAAICoDLM5OTmh3xIAAAAgEmE2Ly+vITcDAAAAvO+ZVQcPHpRf//rXMnnyZDlw4ICvveCLL74I5fYBAAAAoa3MbtmyRYYMGSJt2rSRkpISueuuu8x0g1deeUV27twpixcvbsjdAgAAAOGvzE6YMEHGjBkjH3/8sSQmJvqWX3vttbJ+/fqG3CUAAAAQmcrsO++8I7/61a9qLE9LS5M9e/Y05C7hofRJK4IuL8kfFvFtAQAACHtltnnz5lJeXl5j+UcffSRnn312Q+4SAAAAiEyYveGGG+Sxxx6TEydOmOtxcXGmV/bBBx+UESNGNOQuAQAAgMiEWT1pwpEjR0wV9quvvpJBgwZJ9+7dpXXr1vL444835C4BAACAyPTM6hSD1atXy9///nd57733TLC98MILzYQDAAAAIGrDbFVVlSxatMiM4dKxXNpicO6550pqaqo4jmOuAwAAAFHXZqBhVftl77zzTnNyhN69e8v5558vn332mRnVdeONN4ZvSwEAAIDTqcxqRVbnyBYWFsrgwYMDvve3v/1NcnJyzAkTRo8efSp3CwAAAIS/Mrt06VJ56KGHagRZdeWVV8qkSZPkxRdfbNiWAAAAAOEMs3oa26uvvrrW719zzTXmgDAAAAAg6sLsgQMHJCUlpdbv6/e+/PLLUGwXAAAAENowW1lZKfHxtbfZNm3aVP7zn/+cyl0CAAAAkTkATKcZ6NQCPZ1tMMePH2/QRsybN09mzZole/bskYyMDJkzZ45kZWUFXff55583B5lt3brVXM/MzJQnnnii1vUBAADQeJ1SZTY3N1fat29vTpoQ7KLfO9VJBsuWLZMJEyZIXl6eFBcXmzCbnZ0tZWVlQddfu3atjBo1StasWSNFRUXSqVMnGTp0qBkVBgAAgNgS52i51UMDBgyQ/v37y9y5c30nZdCAOn78eDMdoT6tD2eeeaa5fX2CdHl5uQnehw4dkqSkJImE9EkrxEYl+cO83gQAABCDyk8hrzXodLahUlFRIZs2bZLJkyf7ljVp0sScFlerrvVx7NgxOXHihLRr167W1gf/9gfdOWh4CCfgAgAAa9sMQm3//v2mslp9QoJe1/7Z+njwwQelY8eOJgAHM2PGjIBWCK36AgAAoHHwNMyervz8fHnppZfk1VdflcTExKDraNVXS9TupbS0NOLbCQAAgPDwtM0gOTnZjPPau3dvwHK9npqaWudtn3rqKRNm//rXv0qfPn1qXU8nL9Q2fQEAAAB287Qym5CQYEZrFRYW+pbpAWB6feDAgbXe7sknn5Tp06fLypUrpV+/fhHaWgAAAEQbTyuzSsdy6cgvDaU6K7agoECOHj0qY8eONd/XCQVpaWmm91XNnDlTpk6dKkuWLJH09HRfb22rVq3MBQAAALHD8zA7cuRI2bdvnwmoGkz79u1rKq7uQWE7d+40Ew5c8+fPN1MQbr755oD70Tm1jz76aMS3HwAAADE8ZzbSmDN7ehjNBQAAoimvWT3NAAAAALGNMAsAAABrEWYBAABgLcIsAAAArEWYBQAAgLUIswAAALAWYRYAAADWIswCAADAWp6fAQx2SZ+0IuhyTqYAAAC8QGUWAAAA1iLMAgAAwFqEWQAAAFiLMAsAAABrEWYBAABgLcIsAAAArEWYBQAAgLUIswAAALAWJ01A2E6mwIkUAABAuFGZBQAAgLUIswAAALAWYRYAAADWIswCAADAWoRZAAAAWIswCwAAAGsRZgEAAGAtwiwAAACsxUkTENETKShOpgAAAEKFyiwAAACsRZgFAACAtQizAAAAsBZhFgAAANYizAIAAMBahFkAAABYizALAAAAaxFmAQAAYC3CLAAAAKxFmAUAAIC1OJ0tIo7T3AIAgFChMgsAAABrEWYBAABgLcIsAAAArEWYBQAAgLUIswAAALAWYRYAAADWIswCAADAWsyZRVTPny3JH+bJtgAAADtQmQUAAIC1CLMAAACwFmEWAAAA1iLMAgAAwFqEWQAAAFjL8zA7b948SU9Pl8TERBkwYIBs2LCh1nX/+c9/yogRI8z6cXFxUlBQENFtBQAAQHTxNMwuW7ZMJkyYIHl5eVJcXCwZGRmSnZ0tZWVlQdc/duyYdO3aVfLz8yU1NTXi2wsAAIDoEuc4juPVg2sltn///jJ37lxzvaqqSjp16iTjx4+XSZMm1Xlbrc7ef//95nIqysvLpU2bNnLo0CFJSkoSr+an4vQwfxYAgMbrVPKaZ5XZiooK2bRpkwwZMuT/N6ZJE3O9qKgoZI9z/Phxs0P8LwAAAGgcPAuz+/fvl8rKSklJSQlYrtf37NkTsseZMWOGSfbuRSu/AAAAaBw8PwAs3CZPnmxK1O6ltLTU600CAABAiMSLR5KTk6Vp06ayd+/egOV6PZQHdzVv3txcAAAA0Ph4FmYTEhIkMzNTCgsLJScnx3cAmF7/0Y9+5NVmwRK1HVTHgWEAAMQWz8Ks0rFcubm50q9fP8nKyjJzY48ePSpjx4413x89erSkpaWZvlf3oLF//etfvn9/8cUXsnnzZmnVqpV0797dy6cCAACAWAuzI0eOlH379snUqVPNQV99+/aVlStX+g4K27lzp5lw4Nq1a5dccMEFvutPPfWUuQwaNEjWrl3ryXMAAABAjM6Z9QJzZhs32gwAALCfFXNmAQAAgNNFmAUAAIC1CLMAAACwFmEWAAAA1vJ0mgEQifmzHBQGAEDjRWUWAAAA1iLMAgAAwFqEWQAAAFiLMAsAAABrEWYBAABgLaYZICYnHCimHAAAYD8qswAAALAWYRYAAADWIswCAADAWvTMImbRSwsAgP2ozAIAAMBahFkAAABYizALAAAAa9EzC9Sjl5aZtAAARCfCLFAPHCwGAEB0os0AAAAA1iLMAgAAwFqEWQAAAFiLMAsAAABrEWYBAABgLaYZAKeBMV4AAHiLyiwAAACsRZgFAACAtWgzAEKMEywAABA5VGYBAABgLSqzQIRQsQUAIPSozAIAAMBahFkAAABYizYDwGPMqgUAoOGozAIAAMBaVGaBKMTBYgAA1A9hFrAIIRcAgEC0GQAAAMBaVGaBRoCDyAAAsYrKLAAAAKxFZRaIMfTdAgAaE8IsEGOhFQCAxoQwC8Cg7xYAYCN6ZgEAAGAtKrMAakV/LQAg2lGZBQAAgLWozAII68FlJfnD2MMAgLChMgsAAABrUZkFEFZUcQEA4USYBRA1OOAMAHCqCLMAYuIEEPTuAkDjFBVhdt68eTJr1izZs2ePZGRkyJw5cyQrK6vW9ZcvXy5TpkyRkpIS6dGjh8ycOVOuvfbaiG4zALvQ7gAAjZPnYXbZsmUyYcIEefbZZ2XAgAFSUFAg2dnZsm3bNmnfvn2N9d966y0ZNWqUzJgxQ6677jpZsmSJ5OTkSHFxsfTq1cuT5wCgcQnnqYCpEANAaMU5juOIhzTA9u/fX+bOnWuuV1VVSadOnWT8+PEyadKkGuuPHDlSjh49Kq+//rpv2UUXXSR9+/Y1gfhkysvLpU2bNnLo0CFJSkoS238xAkBdCM8AbHQqec3TymxFRYVs2rRJJk+e7FvWpEkTGTJkiBQVFQW9jS7XSq4/reS+9tprQdc/fvy4ubh0p7g7KVKqjh+L2GMBgL/ODyxnhzTQ1mnZYdl3vfJWRfTxABu5Oa0+NVdPw+z+/fulsrJSUlJSApbr9Q8//DDobbSvNtj6ujwYbUeYNm1ajeVa/QUAoDZtChr34wE2OHz4sKnQRnXPbLhp1de/kqttDAcOHJCzzjpL4uLiIvKXhQbn0tLSiLU1IDrxXgDvBfAzAfx+qB+tyGqQ7dix40nX9TTMJicnS9OmTWXv3r0By/V6ampq0Nvo8lNZv3nz5ubir23bthJpGmQJs+C9AH4ugN8PICvUz8kqslFxOtuEhATJzMyUwsLCgMqpXh84cGDQ2+hy//XV6tWra10fAAAAjZfnbQbaApCbmyv9+vUzs2V1NJdOKxg7dqz5/ujRoyUtLc30vqr77rtPBg0aJLNnz5Zhw4bJSy+9JBs3bpTnnnvO42cCAACAmAuzOmpr3759MnXqVHMQl47YWrlype8gr507d5oJB66LL77YzJZ95JFH5KGHHjInTdBJBtE6Y1ZbHPLy8mq0OiD28F4A7wXwMwH8fmiEc2YBAACAhvK0ZxYAAAA4HYRZAAAAWIswCwAAAGsRZgEAAGAtwmyYzZs3T9LT0yUxMVEGDBggGzZsCPdDIso8+uij5mxz/peePXt6vVmIgPXr18v1119vzmCjr7tOXvGnx9/qJJcOHTrIGWecIUOGDJGPP/6Y1ybG3gdjxoyp8TPi6quv9mx7ER46YrR///7SunVrad++veTk5Mi2bdsC1vn666/l3nvvNWcpbdWqlYwYMaLGiaJQE2E2jJYtW2bm6OporuLiYsnIyJDs7GwpKysL58MiCp1//vmye/du3+XNN9/0epMQATozW/+/1z9qg3nyySflF7/4hTz77LPyj3/8Q1q2bGl+RugvNMTO+0BpePX/GbF06dKIbiPCb926dSaovv322+ZkTydOnJChQ4ea94frgQcekD/+8Y+yfPlys/6uXbvkpptu4uU5GR3NhfDIyspy7r33Xt/1yspKp2PHjs6MGTPY5TEkLy/PycjI8Hoz4DH9cfvqq6/6rldVVTmpqanOrFmzfMsOHjzoNG/e3Fm6dKlHW4lIvw9Ubm6uM3z4cHZ+jCkrKzPvh3Xr1vn+/2/WrJmzfPly3zoffPCBWaeoqMjDLY1+VGbDpKKiQjZt2mQ+NnTpyR/0elFRUbgeFlFKPzrWjxi7du0qt956qzkZCGLbp59+ak4U4/8zQs9Dru1I/IyIPWvXrjUfPX/zm9+UcePGyb///W+vNwlhdujQIfO1Xbt25qtmBq3W+v9M0Ja0zp078zPhJAizYbJ//36prKz0ncnMpdf1Fxhih4aTRYsWmTPbzZ8/34SYyy67TA4fPuz1psFD7s8BfkZAWwwWL14shYWFMnPmTPPx8jXXXGN+h6Bxqqqqkvvvv18uueQS3xlM9WdCQkKCtG3bNmBdcoMFp7MFGjv9peTq06ePCbddunSR3/3ud3LHHXd4um0AvHfLLbf4/t27d2/zc6Jbt26mWnvVVVd5um0ID+2d3bp1K8dPhAiV2TBJTk6Wpk2b1jgKUa+npqaG62FhAf2r+xvf+IZs377d602Bh9yfA/yMQHXajqS/Q/gZ0Tj96Ec/ktdff13WrFkj55xzTsDPBG1RPHjwYMD65IaTI8yGiX5UkJmZaT428v9YQa8PHDgwXA8LCxw5ckR27NhhxjEhdp177rnml5f/z4jy8nIz1YCfEbHt888/Nz2z/IxoXPT4Pw2yr776qvztb38zPwP8aWZo1qxZwM8EHd2lx1jwM6FutBmEkY7lys3NlX79+klWVpYUFBSYERxjx44N58MiykycONHMmNTWAh2zoqPatGo/atQorzcNEfjDxb+6pv3SmzdvNgd86EEd2jP3s5/9THr06GF+sU2ZMsUcKKjzJxEb7wO9TJs2zcwT1T9u9A/dn/70p9K9e3czpg2Nq7VgyZIl8oc//MHMmnX75vXAT50zrV+19Uyzg74vkpKSZPz48SbIXnTRRV5vfnTzepxCYzdnzhync+fOTkJCghnV9fbbb3u9SYiwkSNHOh06dDDvgbS0NHN9+/btvA4xYM2aNWasTvWLjmJyx3NNmTLFSUlJMSO5rrrqKmfbtm1ebzYi+D44duyYM3ToUOfss882Y5m6dOni3HXXXc6ePXt4HRqZYO8BvSxcuNC3zldffeXcc889zplnnum0aNHCufHGG53du3d7ut02iNP/eB2oAQAAgIagZxYAAADWIswCAADAWoRZAAAAWIswCwAAAGsRZgEAAGAtwiwAAACsRZgFAACAtQizAAAAsBZhFgAsdsUVV5jT4gJArCLMAoBHrr/+ern66quDfu+NN96QuLg42bJlS8S3CwBsQpgFAI/ccccdsnr1avn8889rfG/hwoXSr18/6dOnjyfbBgC2IMwCgEeuu+46Ofvss2XRokUBy48cOSLLly+XnJwcGTVqlKSlpUmLFi2kd+/esnTp0jrvU6u5r732WsCytm3bBjxGaWmpfPe73zXL27VrJ8OHD5eSkpIQPzsAiAzCLAB4JD4+XkaPHm2CpuM4vuUaZCsrK+X73/++ZGZmyooVK2Tr1q3ygx/8QG677TbZsGFDgx/zxIkTkp2dLa1btzatDH//+9+lVatWpt2hoqIiRM8MACKHMAsAHrr99ttlx44dsm7duoAWgxEjRkiXLl1k4sSJ0rdvX+natauMHz/ehM7f/e53DX68ZcuWSVVVlfz61782ld5vfetb5vF27twpa9euDdGzAoDIIcwCgId69uwpF198sSxYsMBc3759u6mYaj+tVmenT59uQqe2A2gFddWqVSZ4NtR7771nHkMrs3p/etH7/vrrr02oBgDbxHu9AQAQ6zS4atV13rx5pkrarVs3GTRokMycOVOeeeYZKSgoMIG2ZcuWZgxXXe0A2jPr37Lgthb49+Nq68KLL75Y47bavwsAtiHMAoDH9GCs++67T5YsWSKLFy+WcePGmVCq/ax6cJb2ziptD/joo4/kvPPOq/W+NJDu3r3bd/3jjz+WY8eO+a5feOGFptWgffv2kpSUFOZnBgDhR5sBAHhMP+ofOXKkTJ482QTRMWPGmOU9evQwo7veeust+eCDD+Tuu++WvXv31nlfV155pcydO1feffdd2bhxo/zwhz+UZs2a+b5/6623SnJysgnJ2s7w6aefml7ZH//4x0FHhAFAtCPMAkCUtBp8+eWXZtJAx44dzbJHHnnEVFJ1mZ7pKzU11Yzrqsvs2bOlU6dOctlll8n3vvc9cwCZjvVy6b/Xr18vnTt3lptuuskcAKaPrT2zVGoB2CjOqd5cBQAAAFiCyiwAAACsRZgFAACAtQizAAAAsBZhFgAAANYizAIAAMBahFkAAABYizALAAAAaxFmAQAAYC3CLAAAAKxFmAUAAIC1CLMAAAAQW/0fmC7oAvnULX4AAAAASUVORK5CYII=", "text/plain": [ "
" ] @@ -651,7 +651,7 @@ "population = np.random.exponential(scale=2, size=100000)\n", "\n", "plt.figure(figsize=(8,4))\n", - "plt.hist(population, bins=50, density=True)\n", + "plt.hist(population, bins=100, density=True)\n", "plt.xlabel(\"Value\")\n", "plt.ylabel(\"Density\")\n", "plt.title(\"Original Population (Skewed)\")\n", @@ -675,7 +675,7 @@ }, { "cell_type": "code", - "execution_count": 30, + "execution_count": 21, "id": "d1dc040d", "metadata": {}, "outputs": [], @@ -694,13 +694,13 @@ }, { "cell_type": "code", - "execution_count": 31, + "execution_count": 22, "id": "d2c74f8f", "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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", 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" ] @@ -720,13 +720,13 @@ }, { "cell_type": "code", - "execution_count": 32, + "execution_count": 23, "id": "10f26d72", "metadata": {}, "outputs": [ { "data": { - "image/png": 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nSq+g6Nm5QMs7tNbet4WZ3tbPjW+HCa3Z1vID7bgB5ASZWRR4eoUvrYXTFkN6OFGzbXpVMA0w9Ive1XpGazddGUNtJ6TZO/0y1MNovtm5YNUc6glZmjHRekc93K79GbVFUHYPv2aVfqFp83Y9IUfXiwZmGoBq5kiD2qxm47RRugZjui5dVwDT2kNtLaRlGxnRXrT6WvqFqLWCWs+pwZ1mc1w1nvpvDTS0dZcGF9r/09ULNCd0nBpga5CjGUxt3q4nS3lminRcrisa6frRzJ6+L8+LQ2R3bHoClmactX2TtofTz5uuO11XGpRlVFucHdrMXi8qoMG5nlymgYaWbGgmUC8okJOromkmUYNg3U/06IE+p9ZOZqf2VoN13Zc0+NQfULqPaWCnmXL9nGirLq1bz45+/fplqUWc1mXr9tQfs5oZ1qBaM9U639WjOC/3ea091QsN6CV4tddxsASrZlbfu5ZZaPmG9gTWvw0axGpgr+UJetTE87OhP1C0r6z2NtYfyXoFMP3bom3h9LPiSYNpDXJ1vwJyxKu3AVAALV261Hnqqaec66+/3rRD0tZX2uJH21QdPXrUa9lPP/3UqV+/vhMdHW1aGo0ZM8aZNm2a31ZY2kbLl7+2R662S2PHjnXP0zY5V1xxhbN3716nbdu2TvHixZ2YmBjTisizjVJ2WnP5G49vqyilbbluu+02037nmmuucUaNGmVa7+hzHjlyJEutklyTrid9jvvuu8+sp3PnzqV7jG9rrvnz55v3XKFCBbMtqlSp4vTu3ds5fPiw1+OmTp1q2iNpCyDPVliB3mtGrbnWr1/vPP30006ZMmXMZ+Dxxx83Lck86Xp/4YUXnHLlypntoe2ZtKWS73NmNDZ/61s/Y9pCSp9X32+9evXMuDL7jLgEao/lSz9LDz/8sHPllVea7dKsWTNn0aJFfp8vK625lLae01ZbOm7Pcbg+v4E+H76mTJlinkfb1pUsWdKsA22R9/PPP19WK7iM3pO2QNP9t06dOuazrttexzBixAgnOTk5aPu8v23uj34OChcubNqG+T5ex5jZfpPbtB2Yts3TdaGt84oUKWJev0ePHgFb9ul2rV27tvl81KxZ05k4caJpMeirefPmzhNPPJEH7wL5VYT+J2dhMIDcopk6zdBlp5F5burfv7/JIOp4Qn2pXCC/0ivBaV28ZjELCs3I68UiduzYkenFTYBAqJkF4MW3B6TWsOrJNHrYnUAWyD3aNUX74xakK2HpFf60lIRAFpeDmlkAXvQELb3Eqtan6mVQ33vvPVPH51kTByD4tDZdT4QqSObMmRPqISAfIJgFkO7Mdy1x0DPd9YQvPQSoAe3tt9/OmgIAhB1qZgEAAGCtkNbMas9GbXmiVwPRDNDChQszXF4vN6qtO7QtkbYu0cOh2kIFAAAABVNIg1ltTK19JxMTE7Mc/Gowq83stSejXrFHg+GdO3fm+lgBAAAQfsKmzEAzswsWLJCOHTtm63HavFmbOOslDLNCL6X3888/m2bkwb4kJgAAAC6fhqenTp0yR+8zu7CL1SeAaWCqb9T3aiKe9PKXnteM1qsR5eTSjQAAAMhbhw4dMleDzLfB7Lhx40wTd70EZSB6mcQRI0b4XTnBvGQgAAAAgkNbQuollLNyWW9rg9nZs2ebIPWTTz7J8HrsQ4YMkYEDB6ZbORrIEswCAACEr6yUhBa2tclyz549Zd68edKmTZsMl42KijITAAAA8h/rLmf74YcfSvfu3c3/27dvH+rhAAAAIIRCmpnVetc9e/a4b+/fv1+++uorc0KXXtZPSwT0hK2ZM2e6Swvi4+Pltddek+bNm8uRI0fM/GLFiknp0qVD9j4AAABQADOz27Ztk0aNGplJaW2r/tvVZuvw4cNy8OBB9/J6ec2LFy9Knz59pGLFiu6pX79+IXsPAAAACJ2w6TObV/QEMM3iJicncwIYAACA5fGadTWzAAAAgAvBLAAAAKxFMAsAAABrEcwCAADAWgSzAAAAsBbBLAAAAKxl5eVsASC7qiUsztFKSxrNlQYBIJyRmQUAAIC1CGYBAABgLYJZAAAAWItgFgAAANYimAUAAIC1CGYBAABgLYJZAAAAWItgFgAAANYimAUAAIC1CGYBAABgLYJZAAAAWKtwqAcAoGCqlrA4R49LGt0+6GMBANiLzCwAAACsRTALAAAAaxHMAgAAwFoEswAAALAWwSwAAACsRTALAAAAaxHMAgAAwFoEswAAALAWwSwAAACsRTALAAAAaxHMAgAAwFoEswAAALAWwSwAAACsRTALAAAAaxHMAgAAwFoEswAAALAWwSwAAACsRTALAAAAaxUO9QAAIDuqJSxmhQEA3MjMAgAAwFoEswAAALBWSIPZDRs2yP333y9XX321REREyMKFCzN9zLp16+Smm26SqKgoqVWrlsyYMSNPxgoAAIDwE9Jg9syZM9KgQQNJTEzM0vL79++X9u3bS+vWreWrr76S/v37S8+ePWX58uW5PlYAAACEn5CeAHbvvfeaKasmT54s1atXl/Hjx5vbN9xwg2zcuFEmTpwocXFxuThSAAAAhCOrama3bNkibdq08ZqnQazODyQ1NVVSUlK8JgAAAOQPVgWzR44ckZiYGK95elsD1N9//93vY0aNGiWlS5d2T5UrV86j0QIAACC35fs+s0OGDJGBAwe6b2vgS0ALBA99XwEAoWRVMBsbGytHjx71mqe3S5UqJcWKFfP7GO16oBMA5GWwnjS6PSscAPKAVWUGLVq0kNWrV3vNW7lypZkPAACAgiekwezp06dNiy2dXK239N8HDx50lwh069bNvfwzzzwj+/btk8GDB8v3338vb731lnz00UcyYMCAkL0HAAAAFNBgdtu2bdKoUSMzKa1t1X8PGzbM3D58+LA7sFXalmvx4sUmG6v9abVF17vvvktbLgAAgAIqwnEcRwoQPQFMuxokJyebWlsAl4cTwPyjZhYA8iZes6pmFgAAALC2mwGA3EOGFQBgIzKzAAAAsBbBLAAAAKxFmQEA5AIutgAAeYPMLAAAAKxFZhYAwggZXQDIHjKzAAAAsBbBLAAAAKxFMAsAAABrEcwCAADAWgSzAAAAsBbBLAAAAKxFMAsAAABrEcwCAADAWgSzAAAAsBbBLAAAAKxFMAsAAABrEcwCAADAWgSzAAAAsBbBLAAAAKxFMAsAAABrEcwCAADAWgSzAAAAsBbBLAAAAKxFMAsAAABrEcwCAADAWgSzAAAAsBbBLAAAAKxFMAsAAABrEcwCAADAWgSzAAAAsFbhUA8AQPBUS1jM6gQAFChkZgEAAGAtMrMAUICz8kmj2wd9LACQl8jMAgAAwFoEswAAALAWwSwAAACsRTALAAAAaxHMAgAAwFohD2YTExOlWrVqEh0dLc2bN5etW7dmuPykSZOkdu3aUqxYMalcubIMGDBAzp07l2fjBQAAQPgIaTA7d+5cGThwoAwfPlx27NghDRo0kLi4ODl27Jjf5WfPni0JCQlm+e+++07ee+898xwvvvhino8dAAAABTyYnTBhgvTq1Uu6d+8uN954o0yePFmKFy8u06ZN87v85s2b5ZZbbpHHHnvMZHPbtm0rXbp0yTSbCwAAgPwpZMHs+fPnZfv27dKmTZv/H0yhQub2li1b/D6mZcuW5jGu4HXfvn2yZMkSadeuXcDXSU1NlZSUFK8JAAAA+UPIrgB24sQJuXTpksTExHjN19vff/+938doRlYfd+utt4rjOHLx4kV55plnMiwzGDVqlIwYMSLo4wcAAEDohfwEsOxYt26d/P3vf5e33nrL1Nh+/PHHsnjxYhk5cmTAxwwZMkSSk5Pd06FDh/J0zAAAAMiHmdly5cpJZGSkHD161Gu+3o6NjfX7mKFDh0rXrl2lZ8+e5na9evXkzJkz8vTTT8tf/vIXU6bgKyoqykwAAADIf0KWmS1atKg0btxYVq9e7Z6XlpZmbrdo0cLvY86ePZsuYNWAWGnZAQAAAAqWkGVmlbblio+PlyZNmkizZs1MD1nNtGp3A9WtWzepVKmSqXtV999/v+mA0KhRI9OTds+ePSZbq/NdQS0AAAAKjpAGs507d5bjx4/LsGHD5MiRI9KwYUNZtmyZ+6SwgwcPemVi//rXv0pERIT5/08//STly5c3gewrr7wSwncBAACAUIlwCtjxeW3NVbp0aXMyWKlSpUI9HCCoqiUsZo0iW5JGt2eNAbA6XrOqmwEAAADgiWAWAAAA1iKYBQAAgLUIZgEAAGAtglkAAABYi2AWAAAA1iKYBQAAgLUIZgEAAGAtglkAAABYi2AWAAAA1iKYBQAAgLUIZgEAAGAtglkAAABYi2AWAAAA1iKYBQAAgLUIZgEAAGAtglkAAABYi2AWAAAA1iKYBQAAgLUIZgEAAGAtglkAAAAUrGB23759wR8JAAAAkBfBbK1ataR169Yya9YsOXfuXE6eAgAAAAhNMLtjxw6pX7++DBw4UGJjY6V3796ydevWyx8NAAAAkNvBbMOGDeW1116Tn3/+WaZNmyaHDx+WW2+9VerWrSsTJkyQ48eP5+RpAQAAgLw7Aaxw4cLy4IMPyrx582TMmDGyZ88eGTRokFSuXFm6detmglwAAAAgLIPZbdu2yXPPPScVK1Y0GVkNZPfu3SsrV640WdsOHToEb6QAAACAj8KSAxq4Tp8+XXbv3i3t2rWTmTNnmv8XKvS/sXH16tVlxowZUq1atZw8PQAAAJB7wezbb78tTz31lDz55JMmK+tPhQoV5L333svJ0wMAAABZEuE4jiPZlJSUJFWqVHFnYl30qQ4dOmTuC1cpKSlSunRpSU5OllKlSoV6OEBQVUtYzBpFnkga3Z41DSAs4rUc1czWrFlTTpw4kW7+yZMnTYkBAAAAkBdyFMwGSuaePn1aoqOjL3dMAAAAQPBrZvUiCSoiIkKGDRsmxYsXd9936dIl+eKLL0wPWgAAACDsgtmdO3e6M7O7du2SokWLuu/Tfzdo0MC05wIAAADCLphdu3at+X/37t3NFcA4gQoAAADWtebSHrMAAACANcGsXrZWL4Sg2Vj9d0Y+/vjjYIwNAAAACE4wq72+9MQv178B5B76xSI/f0bpUQsgJMGsZ2kBZQYAAACwts/s77//LmfPnnXfPnDggEyaNElWrFgRzLEBAAAAwQ9mO3ToIDNnzjT//u2336RZs2Yyfvx4M//tt9/O1nMlJiZKtWrVzMUWmjdvLlu3bs1weX29Pn36SMWKFSUqKkquu+46WbJkSU7eBgAAAApiMLtjxw657bbbzL/nz58vsbGxJjurAe7rr7+e5eeZO3euuRDD8OHDzXNqn9q4uDg5duyY3+XPnz8vd999tyQlJZnX3b17t0ydOlUqVaqUk7cBAACAgtiaS0sMSpYsaf6tpQXa3aBQoUJy8803m6A2qyZMmCC9evUyfWvV5MmTZfHixTJt2jRJSEhIt7zOP3nypGzevFmKFCli5mlWFwAAAAVTjjKztWrVkoULF8qhQ4dk+fLl0rZtWzNfM6pZvZCCZlm3b98ubdq0+f/BFCpkbm/ZssXvYz799FNp0aKFKTOIiYmRunXryt///ndzKd1AUlNTJSUlxWsCAABAAQ5mhw0bZi5bq1lRrXPVANOVpW3UqFGWnuPEiRMmCNWg1JPePnLkiN/H7Nu3z5QX6OO0Tnbo0KGmVvdvf/tbwNcZNWqUaSXmmipXrpyt9woAAIB8Vmbw8MMPy6233iqHDx82da4ud911l3Tq1ElyS1pamlSoUEGmTJkikZGR0rhxY/npp59k7Nixpu7WnyFDhpi6XBfNzBLQAgAAFOBgVulJXzp50q4GWVWuXDkTkB49etRrvt72fV4X7WCgtbL6OJcbbrjBZHK1bKFo0aLpHqMdD3QCQoGLHwAAEIZlBmfOnDGH+Fu2bGnqZ2vUqOE1ZYUGnppZXb16tVfmVW+7yhZ83XLLLbJnzx6znMsPP/xgglx/gSwAAADytxxlZnv27Cnr16+Xrl27mkDSdZnb7NLD//Hx8dKkSROT1dULL2ig7Opu0K1bN9N2S+te1bPPPitvvvmm9OvXT/r27Ss//vijOQHs+eefz9HrAwDsOWLBZXABBC2YXbp0qWmhpZnSy9G5c2c5fvy4OaFMSwUaNmwoy5Ytc58UdvDgQdPhwEVrXbV7woABA6R+/fom0NXA9oUXXriscQAAAMBOEY7jONl9UPXq1U03Aa1XtY2eAKZdDZKTk7PcRgzIKWpmgeAhMwsUHCnZiNdyVDM7cuRIk03ViycAAAAAVpUZaG/XvXv3mnIA7TXruhqXi16aFgAAAAjLYLZjx47BHwkAAACQF8FsoAsUAAAAAHkpRzWz6rfffpN3333XXGHr5MmT7vICvSIXAAAAELaZ2W+++UbatGljzjJLSkqSXr16SdmyZeXjjz827bRmzpwZ/JECAAAAwcjM6sUOnnzySXPRgujoaPf8du3ayYYNG3LylAAAAEDeBLNffvml9O7dO918vYiBXvwAAAAACNtgNioqyjSz9fXDDz9I+fLlgzEuAAAAIHeC2QceeEBefvlluXDhgrkdERFhamX1srIPPfRQTp4SAAAAyJtgVi+acPr0aZOF/f3336VVq1ZSq1YtKVmypLzyyis5eUoAAAAgb7oZaBeDlStXyqZNm+Trr782ge1NN91kOhwAAAAAYRvMpqWlyYwZM0wbLm3LpSUG1atXl9jYWHEcx9wGAAAAwq7MQINVrZft2bOnuThCvXr1pE6dOnLgwAHTqqtTp065N1IAAADgcjKzmpHVPrKrV6+W1q1be923Zs0a6dixo7lgQrdu3bLztAAAAEDuZ2Y//PBDefHFF9MFsurOO++UhIQE+eCDD3I2EgAAACA3g1m9jO0999wT8P57773XnBAGAAAAhF0we/LkSYmJiQl4v97366+/BmNcAAAAQHCD2UuXLknhwoHLbCMjI+XixYvZeUoAAAAgb04A024G2rVAL2frT2pqas5HAgAAAORmMBsfH5/pMnQyAAAAQFgGs9OnT8+9kQAAAAC5WTMLAAAAhBOCWQAAAFiLYBYAAADWIpgFAACAtQhmAQAAYC2CWQAAAFiLYBYAAADWIpgFAACAtQhmAQAAYC2CWQAAAFiLYBYAAADWIpgFAACAtQhmAQAAYC2CWQAAAFiLYBYAAADWIpgFAACAtQhmAQAAYC2CWQAAAFiLYBYAAADWKixhIDExUcaOHStHjhyRBg0ayBtvvCHNmjXL9HFz5syRLl26SIcOHWThwoV5MlYUTNUSFod6CAAAIBwzs3PnzpWBAwfK8OHDZceOHSaYjYuLk2PHjmX4uKSkJBk0aJDcdttteTZWAAAAhJeQB7MTJkyQXr16Sffu3eXGG2+UyZMnS/HixWXatGkBH3Pp0iV5/PHHZcSIEVKjRo0Mnz81NVVSUlK8JgAAAOQPIQ1mz58/L9u3b5c2bdr8/4AKFTK3t2zZEvBxL7/8slSoUEF69OiR6WuMGjVKSpcu7Z4qV64ctPEDAACgAAezJ06cMFnWmJgYr/l6W+tn/dm4caO89957MnXq1Cy9xpAhQyQ5Odk9HTp0KChjBwAAQOiFxQlgWXXq1Cnp2rWrCWTLlSuXpcdERUWZCQBQME/ETBrdPuhjARA+QhrMakAaGRkpR48e9Zqvt2NjY9Mtv3fvXnPi1/333++el5aWZv5fuHBh2b17t9SsWTMPRg4AAAAp6GUGRYsWlcaNG8vq1au9glO93aJFi3TLX3/99bJr1y756quv3NMDDzwgrVu3Nv+mHhYAAKBgCXmZgbblio+PlyZNmpjespMmTZIzZ86Y7gaqW7duUqlSJXMiV3R0tNStW9fr8VdeeaX5v+98AAAA5H8hD2Y7d+4sx48fl2HDhpmTvho2bCjLli1znxR28OBB0+EAAAAA8BXhOI4jBYj2mdUWXdrZoFSpUqEeDizBFcAAe3ECGJC/4zVSngAAALBWyMsMAADITbT0AvI3MrMAAACwFsEsAAAArEUwCwAAAGsRzAIAAMBanACGAoUWWwAA5C9kZgEAAGAtglkAAABYi2AWAAAA1iKYBQAAgLUIZgEAAGAtglkAAABYi2AWAAAA1iKYBQAAgLUIZgEAAGAtglkAAABYi2AWAAAA1iKYBQAAgLUIZgEAAGAtglkAAABYi2AWAAAA1iKYBQAAgLUKh3oAAACEo2oJi3P0uKTR7YM+FgCBkZkFAACAtQhmAQAAYC2CWQAAAFiLYBYAAADWIpgFAACAtQhmAQAAYC2CWQAAAFiLPrMAAAQR/WmBvEVmFgAAANYiM4sClfkAAAD5C5lZAAAAWItgFgAAANYimAUAAIC1CGYBAABgLYJZAAAAWItgFgAAANYKi2A2MTFRqlWrJtHR0dK8eXPZunVrwGWnTp0qt912m5QpU8ZMbdq0yXB5AAAA5F8hD2bnzp0rAwcOlOHDh8uOHTukQYMGEhcXJ8eOHfO7/Lp166RLly6ydu1a2bJli1SuXFnatm0rP/30U56PHQAAAKEV4TiOE8oBaCa2adOm8uabb5rbaWlpJkDt27evJCQkZPr4S5cumQytPr5bt26ZLp+SkiKlS5eW5ORkKVWqVFDeA/IeF00AkN8kjW4f6iEAYSM78VpIM7Pnz5+X7du3m1IB94AKFTK3NeuaFWfPnpULFy5I2bJl/d6fmppqVojnBAAAgPwhpMHsiRMnTGY1JibGa77ePnLkSJae44UXXpCrr77aKyD2NGrUKBPZuybN+gIAACB/CHnN7OUYPXq0zJkzRxYsWGBOHvNnyJAhJkXtmg4dOpTn4wQAAEDuKCwhVK5cOYmMjJSjR496zdfbsbGxGT523LhxJphdtWqV1K9fP+ByUVFRZgIAAED+E9LMbNGiRaVx48ayevVq9zw9AUxvt2jRIuDjXn31VRk5cqQsW7ZMmjRpkkejBQAAQLgJaWZWaVuu+Ph4E5Q2a9ZMJk2aJGfOnJHu3bub+7VDQaVKlUztqxozZowMGzZMZs+ebXrTumprS5QoYSYAAAAUHCEPZjt37izHjx83AaoGpg0bNjQZV9dJYQcPHjQdDlzefvtt0wXh4Ycf9noe7VP70ksv5fn4AQAAUID7zOY1+szmD/SZBZDf0GcWsLDPLAAAAHA5CGYBAABgLYJZAAAAWItgFgAAANYKeTcDFGycyAUAAC4HmVkAAABYi2AWAAAA1iKYBQAAgLUIZgEAAGAtglkAAABYi2AWAAAA1qI1FwAAFrcqTBrdPuhjAWxCZhYAAADWIjMLAIDFyOiioCMzCwAAAGsRzAIAAMBaBLMAAACwFsEsAAAArMUJYAAAIMs44QzhhswsAAAArEUwCwAAAGtRZoCQHnYCAIQGf7eRX5CZBQAAgLUIZgEAAGAtglkAAABYi2AWAAAA1iKYBQAAgLUIZgEAAGAtglkAAABYi2AWAAAA1uKiCfBCE20AQH75Xkoa3T6oY0F4IpgFAAC5jmQJcgvBbD7FHw0AAFAQUDMLAAAAaxHMAgAAwFoEswAAALAWwSwAAACsxQlgAAAgX8rrk6FpBRYaZGYBAABgLYJZAAAAWCssygwSExNl7NixcuTIEWnQoIG88cYb0qxZs4DLz5s3T4YOHSpJSUly7bXXypgxY6Rdu3Z5OmYAAIBglDVQnmB5MDt37lwZOHCgTJ48WZo3by6TJk2SuLg42b17t1SoUCHd8ps3b5YuXbrIqFGj5L777pPZs2dLx44dZceOHVK3bl0JR1zAAAAABDtOIAj+XxGO4zgSQhrANm3aVN58801zOy0tTSpXrix9+/aVhISEdMt37txZzpw5I4sWLXLPu/nmm6Vhw4YmIM5MSkqKlC5dWpKTk6VUqVKSFwhmAQBAuEga3V7CXXbitZBmZs+fPy/bt2+XIUOGuOcVKlRI2rRpI1u2bPH7GJ2vmVxPmslduHCh3+VTU1PN5KIrxbWS8kpa6tk8ey0AAICMVBkwT3Li3yPiJK+44rSs5FxDGsyeOHFCLl26JDExMV7z9fb333/v9zFaV+tveZ3vj5YjjBgxIt18zf4CAAAga0pPkjx36tQpk6EN65rZ3KZZX89MrpYxnDx5Uq666iqJiIiQUNNfHhpYHzp0KM/KHhB8bMf8g22ZP7Ad8we2Y8Hdjo7jmED26quvznTZkAaz5cqVk8jISDl69KjXfL0dGxvr9zE6PzvLR0VFmcnTlVdeKeFGNy7BrP3YjvkH2zJ/YDvmD2zHgrkdS2eSkQ2LPrNFixaVxo0by+rVq70yp3q7RYsWfh+j8z2XVytXrgy4PAAAAPKvkJcZaAlAfHy8NGnSxPSW1dZc2q2ge/fu5v5u3bpJpUqVTO2r6tevn7Rq1UrGjx8v7du3lzlz5si2bdtkypQpIX4nAAAAKHDBrLbaOn78uAwbNsycxKUttpYtW+Y+yevgwYOmw4FLy5YtTW/Zv/71r/Liiy+aiyZoJ4Nw7TGbGS2BGD58eLpSCNiF7Zh/sC3zB7Zj/sB2zB+icjnWCXmfWQAAACCnQlozCwAAAFwOglkAAABYi2AWAAAA1iKYBQAAgLUIZnPZhg0b5P777zdXsNArjmnnhcysW7dObrrpJnPWX61atWTGjBm5PUwEeTvqNtTlfKdAl11G3tAWf02bNpWSJUtKhQoVpGPHjrJ79+5MHzdv3jy5/vrrJTo6WurVqydLlizJk/EieNtR/4767o+6PRE6b7/9ttSvX9/dSF/7xS9dujTDx7Av2r8dZ+TCvkgwm8u0Z26DBg0kMTExS8vv37/f9M9t3bq1fPXVV9K/f3/p2bOnLF++PLeHiiBuRxf9gj18+LB70i9ehM769eulT58+8vnnn5uLrVy4cEHatm1rtm8gmzdvli5dukiPHj1k586dJnDS6d///neejh2Xtx2VftF67o8HDhxgtYbQNddcI6NHj5bt27ebfvF33nmndOjQQb799lu/y7Mv5o/tmCv7orbmQt7Q1b1gwYIMlxk8eLBTp04dr3mdO3d24uLicnl0COZ2XLt2rVnu119/ZcWGsWPHjpnttH79+oDLPPLII0779u295jVv3tzp3bt3HowQwdqO06dPd0qXLs0KDXNlypRx3n33Xb/3sS/mj+04PRf2RTKzYWbLli3Spk0br3lxcXFmPuyjFwGpWLGi3H333bJp06ZQDwc+kpOTzf/Lli0bcN2wT+aP7ahOnz4tVatWlcqVK2eaOULeunTpkrmip2bXA12enn0xf2zH3NgXCWbDjNZUuq5+5qK3U1JS5Pfffw/ZuJA9GsBOnjxZ/vnPf5pJd9g77rhDduzYwaoME2lpaaaM55ZbbsnwCoKB9knqn+3ajrVr15Zp06bJJ598IrNmzTKP0ytK/ve//83T8cLbrl27pESJEuYckWeeeUYWLFggN954o9/VxL6YP7Zj7VzYF0N+OVsgP9KdVScX3VH37t0rEydOlPfffz+kY8P/0ppLrXvduHEjq6QAbEfNEnlminSfvOGGG+Sdd96RkSNH5sFI4Y/+ndTzQzS7Pn/+fImPjzc10YECIdi/HVvkwr5IMBtmYmNj5ejRo17z9LYWSxcrVixk48Lla9asGYFTmPjjH/8oixYtMl0q9OSFnOyTOh/2bEdfRYoUkUaNGsmePXtybXzIXNGiRU3XHtW4cWP58ssv5bXXXjOBjS/2xfyxHXNjX6TMIMzor5XVq1d7zdOzdTOqPYEd9Ferlh8gdPT8PQ2A9BDYmjVrpHr16pk+hn0yf2xHf7V9emiUfTK86CHn1NRUv/exL+aP7Zgr+2JQTydDOqdOnXJ27txpJl3dEyZMMP8+cOCAuT8hIcHp2rWre/l9+/Y5xYsXd/785z873333nZOYmOhERkY6y5YtY+1atB0nTpzoLFy40Pnxxx+dXbt2Of369XMKFSrkrFq1KoTvAs8++6w5i3bdunXO4cOH3dPZs2fdK0e3o25Pl02bNjmFCxd2xo0bZ/bJ4cOHO0WKFDHbFfZsxxEjRjjLly939u7d62zfvt159NFHnejoaOfbb78N0buAbh/tQLF//37nm2++MbcjIiKcFStW+N2G7Iv5YzuOyIV9kWA2l7laNPlO8fHx5n79f6tWrdI9pmHDhk7RokWdGjVqmDYWsGs7jhkzxqlZs6bZQcuWLevccccdzpo1a0L4DqD8bUOdPPcx3Y6u7ery0UcfOdddd53ZJ7V13uLFi1mhlm3H/v37O1WqVDHbMCYmxmnXrp2zY8eOEL0DqKeeesqpWrWq2Sbly5d37rrrLncApNgX8+d27J8L+2KE/ifneV0AAAAgdKiZBQAAgLUIZgEAAGAtglkAAABYi2AWAAAA1iKYBQAAgLUIZgEAAGAtglkAAABYi2AWAAAA1iKYBQBLREREyMKFC0M9DAAIKwSzAPB/jh8/Ls8++6xUqVJFoqKiJDY2VuLi4mTTpk2sIwAIU4VDPQAACBcPPfSQnD9/Xv7xj39IjRo15OjRo7J69Wr55ZdfQj00AEAAZGYBQER+++03+eyzz2TMmDHSunVrqVq1qjRr1kyGDBkiDzzwgHsdTZgwQerVqydXXHGFVK5cWZ577jk5ffq0+/4ZM2bIlVdeKYsWLZLatWtL8eLF5eGHH5azZ8+aILlatWpSpkwZef755+XSpUvux+n8kSNHSpcuXcxzV6pUSRITEzPcNocOHZJHHnnEvF7ZsmWlQ4cOkpSUFHD5devWmVKF5cuXS6NGjaRYsWJy5513yrFjx2Tp0qVyww03SKlSpeSxxx4z43VJS0uTUaNGSfXq1c1jGjRoIPPnz3ffr++jR48e7vv1fb/22mter/3kk09Kx44dZdy4cVKxYkW56qqrpE+fPnLhwgU+fwAuC8EsAIhIiRIlzKQ1qampqYH/aBYqJK+//rp8++23Jjhds2aNDB482GsZDQR1mTlz5siyZctMENmpUydZsmSJmd5//3155513vAJCNXbsWBMo7ty5UxISEqRfv36ycuVKv+PQIFBLIEqWLGmCcC2F0PHfc889JruckZdeeknefPNN2bx5szsgnjRpksyePVsWL14sK1askDfeeMO9vAayM2fOlMmTJ5v3PWDAAHniiSdk/fr17mD3mmuukXnz5sl//vMfGTZsmLz44ovy0Ucfeb3u2rVrZe/eveb/uu408NcJAC6LAwAw5s+f75QpU8aJjo52WrZs6QwZMsT5+uuvM1w78+bNc6666ir37enTpzv6p3XPnj3ueb1793aKFy/unDp1yj0vLi7OzHepWrWqc88993g9d+fOnZ17773XfVufd8GCBebf77//vlO7dm0nLS3NfX9qaqpTrFgxZ/ny5X7HunbtWvMcq1atcs8bNWqUmbd3716v8er41Llz58zYN2/e7PVcPXr0cLp06RJwvfTp08d56KGH3Lfj4+PNe7x48aJ73h/+8AfzHgHgcpCZBQCPmtmff/5ZPv30U5Ph1IzqTTfd5JU9XLVqldx1112mDECzol27djU1tZ6H5bW0oGbNmu7bMTExpoxAM6ee8/TwvqcWLVqku/3dd9/53T5ff/217Nmzx4zBlVXWUoNz586Z7GdG6tev7zUOHa/WCPsbm76Gvre7777b/To6aabW83W0JKJx48ZSvnx5c/+UKVPk4MGDXq9bp04diYyMdN/WcgPfdQAA2cUJYADgITo62gRuOg0dOlR69uwpw4cPNzWfWo963333mY4Hr7zyigkeN27caOpF9dC+BoWqSJEiXutU61T9zdPD8zmldboaPH7wwQfp7tOAMiOeY8lsbK56YC0/0ADek3Z8UFpOMWjQIBk/frwJwDXA1pKJL774IuDr+r4OAOQUwSwAZODGG29093bdvn27Cb40aNPaWeVbF3o5Pv/883S39aQsfzRjPHfuXKlQoYI5aSs3378GrZplbdWqld9ltF63ZcuW5mQ4l8yywwAQLJQZAICIKRXQM/tnzZol33zzjezfv9+c0PTqq6+aLgGqVq1a5sQrPTlq37595kQuPSkqWDQo1Nf74YcfzGF7fX09Ccyfxx9/XMqVK2fGpieA6Xi1LEK7JPz3v/8N2pg0y6pZVz3pS0/a0iB1x44dZh3obXXttdfKtm3bTJcEHbtmtL/88sugjQEAMkJmFgD+r5tB8+bNZeLEiSZg06BVW2/16tXLnJmvtNOAtubS9l3asuv22283Z/p369YtKOvwT3/6kwkKR4wYYbKt+lrascAfLWnYsGGDvPDCC/Lggw/KqVOnTBmA1vMGO1OrLcO0dEHfqwbx2gpMM8Ou9dK7d2/TgaFz586mdEDbi2mWVtt9AUBui9CzwHL9VQAAGdITxPr3728mAEDWUWYAAAAAaxHMAgAAwFqUGQAAAMBaZGYBAABgLYJZAAAAWItgFgAAANYimAUAAIC1CGYBAABgLYJZAAAAWItgFgAAANYimAUAAIDY6n8AaCvXWA8ZXwwAAAAASUVORK5CYII=", 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", 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" ] @@ -746,13 +746,13 @@ }, { "cell_type": "code", - "execution_count": 33, + "execution_count": 24, "id": "f38c622b", "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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b1Zv2Q0bXra+RljjTqiia45ra82pFEl8XIdGcUe2bnPzM62dad7Cz4xLX/sjh1VQSHb31Lt+mt/V94145Q9PGNN/afdt150xLytkl/txpRR0tYZdVo9FwLkZ4AS9PP/20yc3T8kp66FJH7fTqaxqEaDCgaQ1Kc0ntkUctpaSjgPqDqYfsfB2Sy4ocSD2JTEdeNP9SD+1r/Uotj5TRQ73ppT96WgBfTyLSftHgTYNUHYHSwDe9o3paW1MDNu1LDSw0PUFzIbWskqaIpMa+Mpv+aGruouaXagCoo0J2zqn+rcGIli3TAEQPi9q1UjND26lBuAZC+mOrxfD1BC89kdG9XXoS1gMPPGD6R0cIdbu8D61mpG160piOXGvpKv0h1/eb9p32lQZuqeU6Z8SgQYPMhRk0gNcT4jQY0fQQHS3TizKkdOg/NToiqYGyfk50tE3XqXnAGckF1oBeP0saoOpOln7GNPjTEXd9n2iZMg2IMqJPnz7pKo+neeL6euoOr44wa+CtI946367hnJOfeb26nV6sQcttaS3orJKVObz6WbRHzu0AVcvj2UcJ7LKD+t7QnRitu6tBq+5If/fdd+a7RUvi6XvFpkdvtE81CNY6zfr6a/qIlmPs37+/x/PrTqmOVnvX9wV88neZCCDQLFq0yHr88cetatWqmVJQWvZLyxtpia6jR496LPvll19aNWvWtMLDw005pxEjRlhTpkzxWQZMS4h581XyyS459cYbb7jmaYmgq6++2tq9e7fVrFkzq0CBAlapUqVMGSb3ElIZKUvmqz3eZbKUliRr2LChKadUrlw5Ky4uzho3bpxZ55EjR9JVJsqetJ90Hffcc4/ppwsXLiR7jHdZsrlz55ptjoiIMK/Ftddea/Xo0cM6fPiwx+MmT55sSkNp+SP3MmApbWtqZclWrVplPfHEE1bRokXNe6BDhw6mHJs77ffnnnvOKlGihHk9tDSVlpPyXmdqbfPV3/oe0/JZul7d3ho1aph2pfUesaVUGsybvpfatm1rFSlSxLwudevWtb7++muf60tPWTKlZfe0zJi2270d9vs3pfeHt0mTJpn1aMm+ggULmj7Q8oCHDh26ojJ4qW2Tln/Tz2/16tXNe11fe23DsGHDrPj4+Cz7zPt6zX3R90HevHlNyTTvx2sb0/rc5AR9H6dU1szXNurrWrVqVfP+qFSpkvXmm2+a8oreDhw4YN6bWo5QP3/6fbFz506f39X6XL7uA7yF6D++Q2EAgUJH/HSkLyuLwV+Jvn37mpFIbY+/L1sMOJVecU/z9HU0FMnpxUH0KJN9sRQgNaQ0AEiV5jC6n0CkObV6GFMP8RPsAtlHq8FoeoimtGiaBf6PlpH7+uuvPc4vAFJDwAsgVXpSmV7uVvNl9ZK0H3zwgckr1AoJALKP5srb9WfhSb+P9ERGIL0IeAGkeUa/plPoGfx6+PCmm24yQe/tt99OzwEAcgVyeAEAAOBo1OEFAACAoxHwAgAAwNHI4fVBL3V46NAhU+Q9qy9ZCgAAgCunlXXPnDkjZcqUSfOCOQS8PmiwGxUVlQUvBQAAALLTgQMHzJU4U0PA64N9+U7twKy8pCMAAACyhpbI1AHK9Fx2nYDXBzuNQYNdAl4AAIDAlZ70U05aAwAAgKMR8AIAAMDRCHgBAADgaAS8AAAAcDQCXgAAADgaAS8AAAAcjYAXAAAAjkbACwAAAEcj4AUAAICjEfACAADA0Qh4AQAA4Gh5/d0AAEDGRA9akKku2ze8JV0NICgxwgsAAABHI+AFAACAoxHwAgAAwNEIeAEAAOBoBLwAAABwNL8GvHFxcXLLLbdIwYIFJSIiQlq3bi07duxI83Fz5syRatWqSXh4uNSoUUMWLlzocb9lWTJkyBApXbq05M+fX5o2bSo7d+7Mxi0BAABAoPJrwLtq1Srp3bu3bNiwQZYtWyaXLl2SZs2ayblz51J8zLp166R9+/bStWtX2bZtmwmSdfrll19cy4wcOVLGjRsnEydOlI0bN8rVV18tsbGxcuHChRzaMgAAAASKEEuHQwPE8ePHzUivBsK33367z2XatWtnAuKvv/7aNe/WW2+V2rVrmwBXN6dMmTLSv39/GTBggLk/Pj5eSpUqJdOmTZOHH344zXacPn1aChcubB5XqFChLNxCALhy1OEFAMlQvBZQObzaYFWsWLEUl1m/fr1JUXCno7c6X+3du1eOHDnisYx2RkxMjGsZbwkJCabT3CcAAAA4Q8AEvElJSdK3b1+57bbb5IYbbkhxOQ1mdbTWnd7W+fb99ryUlvGVS6xBsT1FRUVlwRYBAAAgEATMpYU1l1fzcNesWZPjzz148GDp16+f67aO8BL0AkgvUgwAILAFRMD71FNPmZzc1atXS7ly5VJdNjIyUo4ePeoxT2/rfPt+e55WaXBfRvN8fQkLCzMTAAAAnMevKQ16gpkGu59//rl8++23UqFChTQfU69ePVm+fLnHPK3woPOVrkODXvdldMRWqzXYywAAACB45PV3GsPHH38sX3zxhanFa+fYah6t1s9VHTt2lLJly5o8W9WnTx9p1KiRjB49Wlq2bCmzZs2SzZs3y6RJk8z9ISEhJhf41VdflSpVqpgA+MUXXzSVG7R8GQAAAIKLXwPeCRMmmP/vuOMOj/lTp06Vzp07m7/3798vefL830B0/fr1TZD8wgsvyPPPP2+C2vnz53uc6DZw4EBTuuyJJ56QU6dOSYMGDWTx4sXmQhUAAAAILgFVhzdQUIcXQCCftMZJcgAgubcOLwAAAJDVCHgBAADgaAFRlgwAglFmUxMAABnDCC8AAAAcjYAXAAAAjkbACwAAAEcj4AUAAICjEfACAADA0Qh4AQAA4GgEvAAAAHA0Al4AAAA4GgEvAAAAHI2AFwAAAI5GwAsAAABHI+AFAACAoxHwAgAAwNEIeAEAAOBoef3dAAAIFNGDFvi7CQCAbMAILwAAAByNgBcAAACORsALAAAARyPgBQAAgKMR8AIAAMDRCHgBAADgaAS8AAAAcDS/BryrV6+We++9V8qUKSMhISEyf/78VJfv3LmzWc57ql69umuZl156Kdn91apVy4GtAQAAQCDya8B77tw5qVWrlowfPz5dy7/11lty+PBh13TgwAEpVqyYPPjggx7LaQDsvtyaNWuyaQsAAAAQ6Px6pbUWLVqYKb0KFy5sJpuOCP/zzz/SpUsXj+Xy5s0rkZGRWdpWAAAA5E65Oof3gw8+kKZNm0r58uU95u/cudOkSVSsWFE6dOgg+/fvT3U9CQkJcvr0aY8JAAAAzpBrA95Dhw7JokWLpFu3bh7zY2JiZNq0abJ48WKZMGGC7N27Vxo2bChnzpxJcV1xcXGu0WOdoqKicmALAAAAkBNybcA7ffp0KVKkiLRu3dpjvqZIaE5vzZo1JTY2VhYuXCinTp2STz/9NMV1DR48WOLj412T5gYDAADAGfyaw5tZlmXJlClT5LHHHpN8+fKluqwGxdddd53s2rUrxWXCwsLMBMAZogct8HcTAAABJFeO8K5atcoEsF27dk1z2bNnz8ru3buldOnSOdI2AAAABBa/BrwajP7www9mUppvq3/bJ5lpqkHHjh19nqymubo33HBDsvsGDBhgAuJ9+/bJunXrpE2bNhIaGirt27fPgS0CAABAoPFrSsPmzZulcePGrtv9+vUz/3fq1MmceKY1dL0rLGiO7WeffWZq8vpy8OBBE9yePHlSSpYsKQ0aNJANGzaYvwEAABB8QixNiIUHLUum1Ro0uC5UqBC9A+Qy5PD6tm94yxx+JQAgMOK1XJnDCwAAAKQXAS8AAAAcjYAXAAAAjkbACwAAAEcj4AUAAICjEfACAADA0Qh4AQAA4GgEvAAAAHA0Al4AAAA4ml8vLQwAcO6V67iyG4BAwQgvAAAAHI2AFwAAAI5GSgMABInMpiYAQG7HCC8AAAAcjYAXAAAAjkZKA4CAxOF3AEBWYYQXAAAAjkbACwAAAEcj4AUAAICjEfACAADA0Qh4AQAA4GhUaQAABFSljX3DW2Z5WwAEN0Z4AQAA4GgEvAAAAHA0vwa8q1evlnvvvVfKlCkjISEhMn/+/FSXX7lypVnOezpy5IjHcuPHj5fo6GgJDw+XmJgY2bRpUzZvCQAAAAKVXwPec+fOSa1atUyAmhE7duyQw4cPu6aIiAjXfbNnz5Z+/frJ0KFDZevWrWb9sbGxcuzYsWzYAgAAAAQ6v5601qJFCzNllAa4RYoU8XnfmDFjpHv37tKlSxdze+LEibJgwQKZMmWKDBo06IrbDAAAgNwlV+bw1q5dW0qXLi133XWXrF271jX/4sWLsmXLFmnatKlrXp48eczt9evXp7i+hIQEOX36tMcEAAAAZ8hVAa8GuTpi+9lnn5kpKipK7rjjDpO6oE6cOCGJiYlSqlQpj8fpbe88X3dxcXFSuHBh16TrBQAAgDPkqjq8VatWNZOtfv36snv3bnnzzTflww8/zPR6Bw8ebPJ+bTrCS9ALAADgDLkq4PWlbt26smbNGvN3iRIlJDQ0VI4ePeqxjN6OjIxMcR1hYWFmAgAAgPPkqpQGX3744QeT6qDy5csnderUkeXLl7vuT0pKMrfr1avnx1YCAAAgKEd4z549K7t27XLd3rt3rwlgixUrJtdee61JNfjrr79kxowZ5v6xY8dKhQoVpHr16nLhwgV5//335dtvv5WlS5e61qGpCZ06dZKbb77ZjP7qY7T8mV21AQAAAMHFrwHv5s2bpXHjxq7bdh6tBqzTpk0zNXb379/vUYWhf//+JgguUKCA1KxZU7755huPdbRr106OHz8uQ4YMMSeqaUWHxYsXJzuRDQAAAMEhxLIsy9+NCDR60ppWa4iPj5dChQr5uzlAUIoetMDfTYCf7Bvekr4HkKXxWq7P4QUAAABSQ8ALAAAARyPgBQAAgKMR8AIAAMDRCHgBAADgaAS8AAAAcDQCXgAAADgaAS8AAAAcjYAXAAAAjkbACwAAAEcj4AUAAICjEfACAADA0Qh4AQAA4GgEvAAAAHA0Al4AAAA4GgEvAAAAHC2vvxsAAIC76EELMtUh+4a3pCMB+MQILwAAAByNgBcAAACORkoDgIA8PA0AQFZhhBcAAACORsALAAAARyPgBQAAgKMR8AIAAMDRCHgBAADgaH4NeFevXi333nuvlClTRkJCQmT+/PmpLj9v3jy56667pGTJklKoUCGpV6+eLFmyxGOZl156yazLfapWrVo2bwkAAAAClV8D3nPnzkmtWrVk/Pjx6Q6QNeBduHChbNmyRRo3bmwC5m3btnksV716dTl8+LBrWrNmTTZtAQAAAAKdX+vwtmjRwkzpNXbsWI/br7/+unzxxRfy1VdfyY033uianzdvXomMjMzStgIAACB3ytU5vElJSXLmzBkpVqyYx/ydO3eaNImKFStKhw4dZP/+/amuJyEhQU6fPu0xAQAAIIgD3j179kggGDVqlJw9e1Yeeugh17yYmBiZNm2aLF68WCZMmCB79+6Vhg0bmsA4JXFxcVK4cGHXFBUVlUNbAAAAgIAMeCtXrmzyZz/66CO5cOGC+MPHH38sw4YNk08//VQiIiJc8zVF4sEHH5SaNWtKbGysyfc9deqUWS4lgwcPlvj4eNd04MCBHNoKAAAABGTAu3XrVhNQ9uvXz+TK9ujRQzZt2iQ5ZdasWdKtWzcTxDZt2jTVZYsUKSLXXXed7Nq1K8VlwsLCTNUH9wkAAABBHPDWrl1b3nrrLTl06JBMmTLFVEJo0KCB3HDDDTJmzBg5fvy4ZJdPPvlEunTpYv5v2bJlmstrysPu3buldOnS2dYmAAAAOPSkNa2GcP/998ucOXNkxIgRZhR1wIABJge2Y8eOJhBOKxj94YcfzKQ031b/tk8y01QDXY97GoPeHj16tMnVPXLkiJk0DcGmz79q1SrZt2+frFu3Ttq0aSOhoaHSvn37K9lUAAAABGPAu3nzZunVq5cZPdWRXQ02dTR12bJlZvS3VatWaT5ey4nZJcU0RUL/HjJkiLmtAbN7hYVJkybJ5cuXpXfv3uY57alPnz6uZQ4ePGiC26pVq5qT2YoXLy4bNmwwF6sAAABA8AmxLMvK6IM0uJ06dars2LFD7r77bpNPq//nyZPHI/CMjo42AWpuo2XJtFqDjhyTzwtcmehBC+hC5Ih9w9NOcwPgHBmJ1zJ14Qkt9/X4449L586dU8yN1coJH3zwQWZWDwAAAGSZTAW8mrJw7bXXeozoKh0s1pJeel++fPmkU6dOWdVOAAAAIOdyeCtVqiQnTpxINv/vv/+WChUqZK4lAAAAQKCM8KaU9qtVF8LDw6+0TQACELm4AICgCHi1ioIKCQkxlRQKFCjgui8xMVE2btxoavQCAAAAuTLg3bZtm2uE9+effzZ5ujb9u1atWqY0GQAAAJArA94VK1aY//VKZ3qlNUp2AQAAwJE5vFqDFwAAAHBUwKuXEJ42bZoZ1dW/UzNv3rysaBsAAACQcwGvXslCT1az/wYAAAAcFfC6pzGQ0gAAAABHX3ji33//lfPnz7tu//nnnzJ27FhZunRpVrYNAAAA8E/A26pVK5kxY4b5+9SpU1K3bl0ZPXq0mT9hwoQrbxUAAADgz4B369at0rBhQ/P33LlzJTIy0ozyahA8bty4rGobAAAA4J+AV9MZChYsaP7WNAat2pAnTx659dZbTeALAAAA5OqAt3LlyjJ//nw5cOCALFmyRJo1a2bmHzt2jItRAAAAIPcHvEOGDDGXEI6OjpaYmBipV6+ea7T3xhtvzOo2AgAAADl7pbW2bdtKgwYN5PDhw1KrVi3X/CZNmkibNm0y3xoAAAAgEAJepSeq6eROqzUAAAAAuT7gPXfunAwfPlyWL19u8naTkpI87t+zZ09WtQ8AAADI+YC3W7dusmrVKnnsscekdOnSrksOAwAAAI4IeBctWiQLFiyQ2267LetbBAAAAPi7SkPRokWlWLFiWdkOAAAAIHAC3ldeecWUJtMLUAAAAACOC3hHjx5tLjhRqlQpqVGjhtx0000eU3qtXr1a7r33XilTpozJA9aLWaRl5cqV5jnCwsLMBTCmTZuWbJnx48ebGsHh4eGmTvCmTZsyvI0AAAAI4hze1q1bZ8mTa7UHreP7+OOPm8sTp2Xv3r3SsmVLefLJJ2XmzJmmSoSeQKcnzsXGxpplZs+eLf369ZOJEyeaYHfs2LHmvh07dkhERESWtBsAAAC5R4hlWZYEAB3h/fzzz1MNpp977jlzstwvv/zimvfwww/LqVOnZPHixea2Brm33HKLvPPOO+a2lkyLioqSp59+WgYNGpSutpw+fVoKFy4s8fHxXCoZ+P+iBy2gL+BI+4a39HcTAGRCRuK1TKU0KA0y33//fRk8eLD8/fffZt7WrVvlr7/+kuyyfv16adq0qcc8Hb3V+erixYuyZcsWj2Xy5MljbtvL+JKQkGA6zX0CAACAM2Qq4P3pp5/kuuuukxEjRsioUaNM8KvmzZtnAuDscuTIEZM37E5va4D677//yokTJyQxMdHnMvrYlMTFxZk9BHvSEWEAAAAEccCrObKdO3eWnTt3mhPDbHfffbc5ES230SBdh8Pt6cCBA/5uEgAAAPx50tr3338v7733XrL5ZcuWTXUk9UpFRkbK0aNHPebpbc3byJ8/v4SGhprJ1zL62JRoxQedAAAA4DyZCng1OPSV5/rHH39IyZIlJbvUq1dPFi5c6DFv2bJlZr7Kly+f1KlTx1RvsE9+05PW9PZTTz2Vbe0CchNOPgMABJtMpTTcd9998vLLL8ulS5dcFRb2799vqig88MAD6V7P2bNn5YcffjCTXXZM/9Z12akGHTt2dC2v5cj27NkjAwcOlN9//13effdd+fTTT+WZZ57xSLeYPHmyTJ8+XbZv3y49e/Y05c+6dOmSmU0FAABAMI7w6oUn2rZta0Zz9WSxRo0amVQGHWl97bXX0r2ezZs3S+PGjT2CVdWpUydzQYnDhw+7gl9VoUIFU5ZMA9y33npLypUrZypF2DV4Vbt27eT48ePmSnDaptq1a5uSZd4nsgEAACA4XFEd3rVr18qPP/5oRmr16mfeJcNyK+rwwslIaQA8UYcXcH68luERXs2J1dFXLUG2b98+k86gI696UpjGznobAAAAyJU5vBrQav6uXs5XLzBRo0YNqV69uvz555+mTFmbNm2yr6UAAABAJmRohFdHdrXOrlY9cM+9Vd9++62pjDBjxgyPE80AAACAXDPC+8knn8jzzz+fLNhVd955pwwaNEhmzpyZle0DAAAAci7g1UsKN2/ePMX7W7RoYU5iAwAAAHJlwPv333+nWt5L7/vnn3+yol0AAABAzge8iYmJkjdvymm/elnfy5cvZ0W7AAAAgJw/aU2rNGg1Br20sC8JCQlZ0yoAAADAHwGvXgEtLVRoAAAAQK4NeKdOnZp9LQEAAACyQYavtAYAgJNcyeW2uSwx4MCT1gAAAIDchoAXAAAAjkbACwAAAEcj4AUAAICjEfACAADA0Qh4AQAA4GgEvAAAAHA0Al4AAAA4GgEvAAAAHI2AFwAAAI5GwAsAAABHI+AFAACAoxHwAgAAwNEIeAEAAOBoARHwjh8/XqKjoyU8PFxiYmJk06ZNKS57xx13SEhISLKpZcuWrmU6d+6c7P7mzZvn0NYAAAAgkOT1dwNmz54t/fr1k4kTJ5pgd+zYsRIbGys7duyQiIiIZMvPmzdPLl686Lp98uRJqVWrljz44IMey2mAO3XqVNftsLCwbN4SAAAABCK/B7xjxoyR7t27S5cuXcxtDXwXLFggU6ZMkUGDBiVbvlixYh63Z82aJQUKFEgW8GqAGxkZma42JCQkmMl2+vTpTG4NAAAAAo1fUxp0pHbLli3StGnT/2tQnjzm9vr169O1jg8++EAefvhhufrqqz3mr1y50owQV61aVXr27GlGglMSFxcnhQsXdk1RUVFXsFUAAAAIJH4NeE+cOCGJiYlSqlQpj/l6+8iRI2k+XnN9f/nlF+nWrVuydIYZM2bI8uXLZcSIEbJq1Spp0aKFeS5fBg8eLPHx8a7pwIEDV7hlAAAACBR+T2m4Ejq6W6NGDalbt67HfB3xten9NWvWlEqVKplR3yZNmiRbj6Y/kOMLAADgTH4d4S1RooSEhobK0aNHPebr7bTyb8+dO2fyd7t27Zrm81SsWNE8165du664zQAAAMhd/Brw5suXT+rUqWNSD2xJSUnmdr169VJ97Jw5c8yJZo8++miaz3Pw4EGTw1u6dOksaTcAAAByD7/X4dWSZJMnT5bp06fL9u3bzQlmOnprV23o2LGjybH1lc7QunVrKV68uMf8s2fPyrPPPisbNmyQffv2meC5VatWUrlyZVPuDAAAAMHF7zm87dq1k+PHj8uQIUPMiWq1a9eWxYsXu05k279/v6nc4E5r9K5Zs0aWLl2abH2aIvHTTz+ZAPrUqVNSpkwZadasmbzyyivk6QIAAAShEMuyLH83ItBoHV4tT6YVGwoVKuTv5gBZKnrQAnoUyCL7hv/fVT4BBG685veUBgAAACA7EfACAADA0Qh4AQAA4GgEvAAAAHA0Al4AAAA4GgEvAAAAHM3vdXgBAAi2Mn+UMwNyFiO8AAAAcDQCXgAAADgaAS8AAAAcjYAXAAAAjkbACwAAAEcj4AUAAICjEfACAADA0Qh4AQAA4GgEvAAAAHA0Al4AAAA4GpcWBoLskqYAAAQbRngBAADgaAS8AAAAcDQCXgAAADgaAS8AAAAcjYAXAAAAjkbACwAAAEcLiIB3/PjxEh0dLeHh4RITEyObNm1Kcdlp06ZJSEiIx6SPc2dZlgwZMkRKly4t+fPnl6ZNm8rOnTtzYEsAAAAQaPxeh3f27NnSr18/mThxogl2x44dK7GxsbJjxw6JiIjw+ZhChQqZ+20a9LobOXKkjBs3TqZPny4VKlSQF1980azzt99+SxYcAwCQW+po7xveMsvbAgQDv4/wjhkzRrp37y5dunSR66+/3gS+BQoUkClTpqT4GA1wIyMjXVOpUqU8Rnc1aH7hhRekVatWUrNmTZkxY4YcOnRI5s+fn0NbBQAAgEDh14D34sWLsmXLFpNy4GpQnjzm9vr161N83NmzZ6V8+fISFRVlgtpff/3Vdd/evXvlyJEjHussXLiwGT1OaZ0JCQly+vRpjwkAAADO4NeA98SJE5KYmOgxQqv0tgatvlStWtWM/n7xxRfy0UcfSVJSktSvX18OHjxo7rcfl5F1xsXFmaDYnjSQBgAAgDP4PaUho+rVqycdO3aU2rVrS6NGjWTevHlSsmRJee+99zK9zsGDB0t8fLxrOnDgQJa2GQAAAEEa8JYoUUJCQ0Pl6NGjHvP1tubmpsdVV10lN954o+zatcvcth+XkXWGhYWZE+HcJwAAADiDXwPefPnySZ06dWT58uWueZqioLd1JDc9NCXi559/NiXIlFZl0MDWfZ2ak7tx48Z0rxMAAADO4feyZFqSrFOnTnLzzTdL3bp1TYWFc+fOmaoNStMXypYta/Js1csvvyy33nqrVK5cWU6dOiVvvPGG/Pnnn9KtWzdXBYe+ffvKq6++KlWqVHGVJStTpoy0bt3ar9sKAACAIAx427VrJ8ePHzcXitCTyjQ3d/Hixa6Tzvbv328qN9j++ecfU8ZMly1atKgZIV63bp0paWYbOHCgCZqfeOIJExQ3aNDArJMavAAAAMEnxNLCtfCgKRBarUFPYCOfF04rXA8g9+LCE0Dm4rVcV6UBAAAAyFUpDQAAIH24JDGQOYzwAgAAwNEIeAEAAOBoBLwAAABwNAJeAAAAOBoBLwAAAByNgBcAAACORsALAAAARyPgBQAAgKMR8AIAAMDRCHgBAADgaAS8AAAAcLS8/m4AEOyiBy3wdxMAAHA0RngBAADgaAS8AAAAcDQCXgAAADgaAS8AAAAcjZPWgCzCyWcAAAQmRngBAADgaAS8AAAAcDQCXgAAADgaObwAADhcZs8x2De8ZZa3BfAHRngBAADgaAER8I4fP16io6MlPDxcYmJiZNOmTSkuO3nyZGnYsKEULVrUTE2bNk22fOfOnSUkJMRjat68eQ5sCQAAAAKN3wPe2bNnS79+/WTo0KGydetWqVWrlsTGxsqxY8d8Lr9y5Upp3769rFixQtavXy9RUVHSrFkz+euvvzyW0wD38OHDrumTTz7JoS0CAABAIPF7wDtmzBjp3r27dOnSRa6//nqZOHGiFChQQKZMmeJz+ZkzZ0qvXr2kdu3aUq1aNXn//fclKSlJli9f7rFcWFiYREZGuiYdDQYAAEDw8WvAe/HiRdmyZYtJS3A1KE8ec1tHb9Pj/PnzcunSJSlWrFiykeCIiAipWrWq9OzZU06ePJniOhISEuT06dMeEwAAAJzBrwHviRMnJDExUUqVKuUxX28fOXIkXet47rnnpEyZMh5Bs6YzzJgxw4z6jhgxQlatWiUtWrQwz+VLXFycFC5c2DVpmgQAAACcIVeXJRs+fLjMmjXLjObqCW+2hx9+2PV3jRo1pGbNmlKpUiWzXJMmTZKtZ/DgwSaP2KYjvAS9AAAAzuDXEd4SJUpIaGioHD161GO+3ta829SMGjXKBLxLly41AW1qKlasaJ5r165dPu/XfN9ChQp5TAAAAHAGvwa8+fLlkzp16niccGafgFavXr0UHzdy5Eh55ZVXZPHixXLzzTen+TwHDx40ObylS5fOsrYDAAAgd/B7lQZNJdDautOnT5ft27ebE8zOnTtnqjaojh07mpQDm+bkvvjii6aKg9bu1Vxfnc6ePWvu1/+fffZZ2bBhg+zbt88Ez61atZLKlSubcmcAAAAILn7P4W3Xrp0cP35chgwZYgJXLTemI7f2iWz79+83lRtsEyZMMNUd2rZt67EereP70ksvmRSJn376yQTQp06dMie0aZ1eHRHW1AUAAAAElxDLsix/NyLQ6ElrWq0hPj6efF5k+7XqAcBp9g1v6e8mIAiczkC85veUBgAAACA7EfACAADA0Qh4AQAA4GgEvAAAAHA0Al4AAAA4mt/LkgGBhmoLAAA4CyO8AAAAcDQCXgAAADgaAS8AAAAcjYAXAAAAjsZJawAAICBO/uWSxMgujPACAADA0Qh4AQAA4GikNMCxqKcLALkLqRDILozwAgAAwNEY4QUAALkaI8NICyO8AAAAcDQCXgAAADgaAS8AAAAcjRxeAAAQlMj9DR6M8AIAAMDRCHgBAADgaAS8AAAAcDRyeJFjuPIZAMAJyP3NfRjhBQAAgKMFRMA7fvx4iY6OlvDwcImJiZFNmzaluvycOXOkWrVqZvkaNWrIwoULPe63LEuGDBkipUuXlvz580vTpk1l586d2bwVAAAACER+T2mYPXu29OvXTyZOnGiC3bFjx0psbKzs2LFDIiIiki2/bt06ad++vcTFxck999wjH3/8sbRu3Vq2bt0qN9xwg1lm5MiRMm7cOJk+fbpUqFBBXnzxRbPO3377zQTJyDzSEgAAyPnf0H3DW9LtVyDE0uFQP9Ig95ZbbpF33nnH3E5KSpKoqCh5+umnZdCgQcmWb9eunZw7d06+/vpr17xbb71VateubYJm3ZwyZcpI//79ZcCAAeb++Ph4KVWqlEybNk0efvjhNNt0+vRpKVy4sHlcoUKFJCfklnwgAl4AAHIeAe+VxWt+HeG9ePGibNmyRQYPHuyalydPHpOCsH79ep+P0fk6IuxOR2/nz59v/t67d68cOXLErMOmnaGBtT7WV8CbkJBgJpt2nN2ROSUp4XymHnftM3OyvC0AACCw5GRMom4YukQy45dhsZLTfZKesVu/BrwnTpyQxMREM/rqTm///vvvPh+jwayv5XW+fb89L6VlvGl6xLBhw5LN15FmAAAAfys8VnKFwn5o55kzZ8zgZkDn8AYCHWF2HzXWtIq///5bihcvLiEhIRKMdK9JA/4DBw7kWFpHbkZ/0V+8vwIHn0f6i/dXcHweLcsywa6msqbFrwFviRIlJDQ0VI4ePeoxX29HRkb6fIzOT215+3+dp1Ua3JfRPF9fwsLCzOSuSJEimdwqZ9E3JwEv/cX7KzDweaS/eH8FDj6PgdFfaY3sBkRZsnz58kmdOnVk+fLlHqOrertevXo+H6Pz3ZdXy5Ytcy2vVRk06HVfRvcuNm7cmOI6AQAA4Fx+T2nQVIJOnTrJzTffLHXr1jVlybQKQ5cuXcz9HTt2lLJly5o8W9WnTx9p1KiRjB49Wlq2bCmzZs2SzZs3y6RJk8z9moLQt29fefXVV6VKlSqusmQ63K3lywAAABBc/B7wapmx48ePmwtF6EllmnawePFi10ln+/fvN5UbbPXr1ze1d1944QV5/vnnTVCrFRrsGrxq4MCBJmh+4okn5NSpU9KgQQOzTmrwpp+meAwdOjRZqgfor6zA+4v+yk68v+gv3l+BIyxA4gm/1+EFAAAAHH9pYQAAACC7EPACAADA0Qh4AQAA4GgEvAAAAHA0At4gtXr1arn33ntNuTYt5aaVLtJr7dq1kjdv3hQv5OFEmemvhIQE+d///ifly5c3Z6dGR0fLlClTJBhkpr9mzpwptWrVkgIFCpiLxjz++ONy8uRJcTotuXjLLbdIwYIFJSIiwpRP3LFjR5qPmzNnjlSrVs1Un6lRo4YsXLhQgkFm+mvy5MnSsGFDKVq0qJmaNm0qmzZtkmCQ2feXTUt/6mc4WMp6Zra/tCJU7969zXeXft9fd911QfGZjMtkf2kJ2qpVq0r+/PnNVdieeeYZuXDhQra2lYA3SGnZNg0uxo8fn6HH6YdaayM3adJEgklm+uuhhx4yF0D54IMPzBfAJ598Yj7gwSCj/aU7Ufq+6tq1q/z6668mmNOApHv37uJ0q1atMj+UGzZsMBfRuXTpkjRr1sz0YUrWrVsn7du3N/21bds28yOj0y+//CJOl5n+WrlypemvFStWyPr1680PrD7mr7/+EqfLTH/Z9u3bJwMGDDA7C8EiM/118eJFueuuu0x/zZ0713zf606WXkPA6VZlor+0tOygQYNMqbLt27eb38jZs2ebUrPZSsuSIbjp2+Dzzz9P17Lt2rWzXnjhBWvo0KFWrVq1rGCUnv5atGiRVbhwYevkyZNWsEtPf73xxhtWxYoVPeaNGzfOKlu2rBVsjh07Zvps1apVKS7z0EMPWS1btvSYFxMTY/Xo0cMKNunpL2+XL1+2ChYsaE2fPt0KNuntL+2j+vXrW++//77VqVMnq1WrVlYwSk9/TZgwwXx/Xbx40Qp2x9LRX71797buvPNOj3n9+vWzbrvttmxtGyO8SLepU6fKnj17zF4ZUvfll1+aqweOHDnS7OXr4S0dKfn333/pOh/0st8HDhwwhwA1Rj569KgZKbn77ruDrr/i4+PN/8WKFUtxGR2l1MPy7mJjY838YJOe/vJ2/vx5MxKVkccEW3+9/PLL5hC1HkUIZunpL/2+1+8wHenUi2bphbBef/11SUxMlGATn47+0guIbdmyxZVWpHGFfvdn9/e936+0htxh586d5hDEd999Z/J3kTr9AK9Zs8bkV37++edy4sQJ6dWrl8lJ1R0HeLrttttMDq9eeVHzuC5fvmxygDOacpPbJSUlmUuja3+4Xz3Sm16V0r4apU1v6/xgkt7+8vbcc8+Z/HLvnQanS29/6XeXHmb+4YcfJJilt7/0+/7bb7+VDh06mMBt165d5vted6qCaYAoKZ399cgjj5jfRL0Krg5w6Pf9k08+me0pDYzwIk26l6pv0GHDhpmRSqTvg68nemgQV7duXbPnOmbMGJk+fTqjvD789ttv0qdPH3OJcd3z10uBaz6cfgkGEx0h0jxcPVEI2dNfw4cPN8vrjmiwXW4+Pf115swZeeyxx0wOaokSJSSYpff9pd/3Oho+adIkqVOnjtlx1xOWJ06cKMGkdzr7S3PqdQT83Xffla1bt8q8efNkwYIF8sorr2RvA7M1YQKOyLH8559/zDKhoaGuKSQkxDVv+fLlVjBJT05qx44drUqVKnnM++2338xj//jjDyuYpKe/Hn30Uatt27Ye87777jvz2EOHDlnBQPPaypUrZ+3ZsyfNZaOioqw333zTY96QIUOsmjVrWsEiI/3lniuuufXff/+9FWzS21/btm3z+X2vk/69a9cuKxhk5P11++23W02aNPGYt3DhQtOPCQkJVjDonYH+atCggTVgwACPeR9++KGVP39+KzExMdvayAgv0lSoUCH5+eefzeEte9KRN604oH/HxMTQi170kM6hQ4fk7Nmzrnl//PGH5MmTR8qVK0d/+cip1L5xFxoaau+UO7q/dPueeuopM+Koh0UrVKiQ5mM0X1ArgLjTM6R1vtNlpr+U5tPrCJIePdD8+mCR0f7SUnfe3/f33XefNG7c2PytFS6cLDPvL/2+1zQGHel1/77XEmX58uUTJ7My0V9++77PtlAaAe3MmTNmT97emx8zZoz5+88//zT3Dxo0yHrsscdSfHywVWnIaH/p8rq3q6OWv/76qzljtUqVKla3bt2sYJDR/po6daqVN29e691337V2795trVmzxrr55putunXrWk7Xs2dPM+q4cuVK6/Dhw67p/PnzrmW0r7TPbGvXrjX9NWrUKGv79u3m83jVVVdZP//8s+V0memv4cOHW/ny5bPmzp3r8Rh9nzpdZvrLWzBVachMf+3fv99U/XjqqaesHTt2WF9//bUVERFhvfrqq5bT9cxEf+n3lfbXJ598YkaEly5dao6IavWZ7ETAG6RWrFhhAhHvSb/YlP7fqFGjFB8fbAFvZvpLA5GmTZuawzQa/GrZFfcvASfLTH9pGbLrr7/e9Ffp0qWtDh06WAcPHrSczlc/6aQ7ATbtK7vvbJ9++ql13XXXmUCuevXq1oIFC6xgkJn+Kl++vM/H6PeY02X2/RWsAW9m+2vdunWmNGBYWJgpUfbaa6+Z0m5OJ5nor0uXLlkvvfSSCXLDw8NNilavXr1M+mR2Cvn/DQYAAAAciRxeAAAAOBoBLwAAAByNgBcAAACORsALAAAARyPgBQAAgKMR8AIAAMDRCHgBAADgaAS8AAAAcDQCXgBwkJCQEJk/f76/mwEAAYWAFwAy4Pjx49KzZ0+59tprJSwsTCIjIyU2NlbWrl1LPwJAgMrr7wYAQG7ywAMPyMWLF2X69OlSsWJFOXr0qCxfvlxOnjzp76YBAFLACC8ApNOpU6fku+++kxEjRkjjxo2lfPnyUrduXRk8eLDcd999ruXGjBkjNWrUkKuvvlqioqKkV69ecvbsWdf906ZNkyJFisjXX38tVatWlQIFCkjbtm3l/PnzJpCOjo6WokWLyn//+19JTEx0PU7nv/LKK9K+fXuz7rJly8r48eNTbfOBAwfkoYceMs9XrFgxadWqlezbty/F5VeuXGnSIpYsWSI33nij5M+fX+688045duyYLFq0SP7zn/9IoUKF5JFHHjHttSUlJUlcXJxUqFDBPKZWrVoyd+5c1/26HV27dnXdr9v91ltveTx3586dpXXr1jJq1CgpXbq0FC9eXHr37i2XLl3iPQrgihDwAkA6XXPNNWbSHNmEhISUv1jz5JFx48bJr7/+agLYb7/9VgYOHOixjAaLusysWbNk8eLFJtBs06aNLFy40EwffvihvPfeex5Bo3rjjTdMMLlt2zYZNGiQ9OnTR5YtW+azHRooarpFwYIFTaCuaRfa/ubNm5tR6tS89NJL8s4778i6detcQfPYsWPl448/lgULFsjSpUvl7bffdi2vwe6MGTNk4sSJZrufeeYZefTRR2XVqlWugLhcuXIyZ84c+e2332TIkCHy/PPPy6effurxvCtWrJDdu3eb/7XvdOdAJwC4IhYAIN3mzp1rFS1a1AoPD7fq169vDR482Prxxx9TfcycOXOs4sWLu25PnTrV0q/fXbt2ueb16NHDKlCggHXmzBnXvNjYWDPfVr58eat58+Ye627Xrp3VokUL121d7+eff27+/vDDD62qVataSUlJrvsTEhKs/PnzW0uWLPHZ1hUrVph1fPPNN655cXFxZt7u3bs92qvtUxcuXDBtX7dunce6unbtarVv3z7Ffundu7f1wAMPuG536tTJbOPly5dd8x588EGzjQBwJRjhBYAM5vAeOnRIvvzySzNSqiOzN910k8co5DfffCNNmjQxKQc6uvrYY4+ZHF/3FABNY6hUqZLrdqlSpUzKgo7Aus/TVAJ39erVS3Z7+/btPtv6448/yq5du0wb7NFpTWu4cOGCGUVNTc2aNT3aoe3VnGVfbdPn0G276667XM+jk474uj+Ppl/UqVNHSpYsae6fNGmS7N+/3+N5q1evLqGhoa7bmtrg3QcAkFGctAYAGRQeHm6CO51efPFF6datmwwdOtTkoGp+7D333GMqObz22msmwFyzZo3JX9U0Ag0c1VVXXeWxTs2b9TVPUwEyS/OGNcCcOXNmsvs06EyNe1vSapudn6ypDhrku9NKFkpTNwYMGCCjR482QboG4ZqesXHjxhSf1/t5ACCzCHgB4Apdf/31rtq3W7ZsMQGaBnaay6u881SvxIYNG5Ld1hPJfNGR59mzZ0tERIQ50Sw7t18DWx2tbdSokc9lNH+4fv365gQ+W1qjzACQVUhpAIB00rQErVjw0UcfyU8//SR79+41J2GNHDnSVD9QlStXNieL6Qlde/bsMSef6YlcWUUDR32+P/74w6QI6PPriWu+dOjQQUqUKGHapietaXs1BUOrPxw8eDDL2qSjtTp6qyeq6YlmGshu3brV9IHeVlWqVJHNmzeb6g/adh0Z//7777OsDQCQGkZ4ASCdNO80JiZG3nzzTRPUaWCrZce6d+9uKg4oraCgZcm0dJmWK7v99ttNBYOOHTtmST/379/fBI7Dhg0zo7b6XFqJwRdNn1i9erU899xzcv/998uZM2dMyoHmF2f1iK+WS9M0Cd1WDfS1DJqOMNv90qNHD1NZol27diZNQUur6WivljoDgOwWomeuZfuzAACumJ7U1rdvXzMBANKPlAYAAAA4GgEvAAAAHI2UBgAAADgaI7wAAABwNAJeAAAAOBoBLwAAAByNgBcAAACORsALAAAARyPgBQAAgKMR8AIAAMDRCHgBAAAgTvb/AHSlC1773JbYAAAAAElFTkSuQmCC", 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" ] @@ -788,7 +788,7 @@ }, { "cell_type": "code", - "execution_count": 34, + "execution_count": 25, "id": "55007845", "metadata": {}, "outputs": [ @@ -796,22 +796,22 @@ "name": "stdout", "output_type": "stream", "text": [ - "Population mean (approx.): 2.0079329836826765\n", - "Population variance (approx.): 4.030341196852308\n", + "Population mean (approx.): 2.0012337957358866\n", + "Population variance (approx.): 3.983317421944735\n", "\n", "For n = 5\n", - "Mean of sample means: 2.001364330224136\n", - "Variance of sample means: 0.78849285045314\n", + "Mean of sample means: 2.001016205586466\n", + "Variance of sample means: 0.7806365493596817\n", "Theoretical variance approx.: 0.8\n", "\n", "For n = 30\n", - "Mean of sample means: 2.0074367218583755\n", - "Variance of sample means: 0.13639464205227103\n", + "Mean of sample means: 2.006761294144693\n", + "Variance of sample means: 0.12896356422754562\n", "Theoretical variance approx.: 0.13333333333333333\n", "\n", "For n = 100\n", - "Mean of sample means: 2.002914768611863\n", - "Variance of sample means: 0.039199397022797754\n", + "Mean of sample means: 2.0015222052034187\n", + "Variance of sample means: 0.040359743223367446\n", "Theoretical variance approx.: 0.04\n" ] } diff --git a/session-7-ols/main.ipynb b/session-7-ols/main.ipynb new file mode 100644 index 0000000..b425bb4 --- /dev/null +++ b/session-7-ols/main.ipynb @@ -0,0 +1,149 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 12, + "id": "0f872066", + "metadata": {}, + "outputs": [], + "source": [ + "# data for the OLS\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "theta0 = 2.6486\n", + "theta1 = 4.98\n", + "m = 50\n", + "disp = 4\n", + "x = np.linspace(0,5,m)\n", + "y = theta0+theta1*x+disp*np.random.rand(m)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "c4906c75", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(x,y, '.k')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "896d7633", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2.5\n", + "17.115760540070784\n" + ] + } + ], + "source": [ + "xSum = 0\n", + "ySum = 0\n", + "\n", + "for i in range(m):\n", + " #print(x[i])\n", + " xSum = xSum + x[i]\n", + " ySum = ySum + y[i]\n", + " pass\n", + "xMean = xSum/m\n", + "yMean = ySum/m\n", + "print(xMean)\n", + "print(yMean)" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "3670b14b", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "theta 0: 4.012173816371986\n", + "theta 1: 5.24143468947952\n" + ] + } + ], + "source": [ + "num = 0\n", + "den = 0\n", + "for i in range(m):\n", + " num = num + x[i]*(yMean-y[i])\n", + " den = den + x[i]*(xMean-x[i])\n", + " pass\n", + "theta1H = num/den\n", + "theta0H = yMean-theta1H*xMean\n", + "print(\"theta 0: \", theta0H)\n", + "print(\"theta 1: \", theta1H)" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "729e6b3b", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "yH = theta0H+theta1H*x\n", + "plt.plot(x, yH, ':r', label=\"Model\")\n", + "plt.plot(x, y, '.k', label=\"Data\")\n", + "plt.legend()\n", + "plt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".venv (3.14.3)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.14.3" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/session-decarb/delete.ipynb b/session-decarb/delete.ipynb new file mode 100644 index 0000000..2b1b7ae --- /dev/null +++ b/session-decarb/delete.ipynb @@ -0,0 +1,86 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 3, + "id": "0254e3fa", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0 60.1290\n", + "1 52.4911\n", + "2 53.6475\n", + "3 52.5073\n", + "4 46.0789\n", + "5 57.7730\n", + "6 68.2315\n", + "7 68.2315\n", + "8 58.9383\n", + "9 57.1548\n", + "10 65.9820\n", + "11 56.5718\n", + "12 78.1363\n", + "Name: Length, dtype: float64" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import pandas as pd\n", + "data = pd.read_csv('example.csv')\n", + "x = data['Length']\n", + "x" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "2eb98515", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "plt.plot(x, 'ok')\n", + "plt.grid()\n", + "plt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".venv (3.14.2)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.14.2" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/session-decarb/results-1.csv b/session-decarb/results-1.csv new file mode 100644 index 0000000..4e19d7f --- /dev/null +++ b/session-decarb/results-1.csv @@ -0,0 +1,16 @@ + ,Area,Mean,Min,Max,Angle,Length +1,33.857,183.689,87.000,224.776,-90.585,57.313 +2,31.121,170.154,34.000,233.000,-90.000,52.632 +3,25.991,181.971,72.000,249.680,-93.053,43.922 +4,26.333,177.569,71.000,221.579,-89.246,44.448 +5,35.566,178.582,59.000,240.709,-88.888,60.245 +6,35.566,182.244,53.029,247.049,-87.221,60.305 +7,40.012,174.999,71.000,241.759,-90.494,67.839 +8,35.908,163.076,52.000,255.000,-90.000,60.819 +9,42.406,190.147,54.000,255.000,-92.328,71.989 +10,42.406,183.133,69.000,255.000,-89.068,71.939 +11,44.116,176.062,49.000,251.000,-92.237,74.911 +12,44.800,192.845,51.000,253.846,-92.203,76.080 +13,36.592,148.907,51.000,228.000,-90.000,61.988 +14,40.012,158.426,75.000,237.517,-90.988,67.846 +15,42.748,169.186,59.000,226.532,-89.538,72.517