lab-sessions-26a/session-6-distributions/main.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "31c8588b",
   "metadata": {},
   "source": [
    "# Week 6 Lab — Commonly Used Distributions and the Central Limit Theorem\n",
    "\n",
    "In this lab, we will:\n",
    "\n",
    "1. work with Bernoulli, Binomial, Poisson, Normal, and Exponential distributions,\n",
    "2. compute probabilities numerically,\n",
    "3. simulate random samples,\n",
    "4. compare theory and simulation,\n",
    "5. visualize the Central Limit Theorem (CLT).\n",
    "\n",
    "We will use Python, NumPy, Matplotlib, and SciPy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "62fc7999",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import binom, poisson, norm, expon\n",
    "\n",
    "np.random.seed(42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "52e8c8bb",
   "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",
    "\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": 7,
   "id": "e8285330",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "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"
     ]
    }
   ],
   "source": [
    "# Now we simulate Bernoulli observations.  \n",
    "#This is equivalent to repeating a success/failure experiment many times.\n",
    "\n",
    "#For example:\n",
    "#- success = component passes,\n",
    "#- failure = component fails.\n",
    "\n",
    "p = 0.7\n",
    "n_samples = 1000\n",
    "\n",
    "bernoulli_data = np.random.binomial(1, p, size=n_samples)\n",
    "\n",
    "print(\"First 20 observations:\")\n",
    "print(bernoulli_data[:20])\n",
    "\n",
    "print(\"Sample mean:\", bernoulli_data.mean())\n",
    "print(\"Sample variance:\", bernoulli_data.var(ddof=1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "02a6d407",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "values, counts = np.unique(bernoulli_data, return_counts=True)\n",
    "\n",
    "plt.figure(figsize=(6,4))\n",
    "plt.bar(values, counts / n_samples, width=0.4)\n",
    "plt.xticks([0, 1])\n",
    "plt.xlabel(\"Outcome\")\n",
    "plt.ylabel(\"Relative frequency\")\n",
    "plt.title(\"Simulated Bernoulli Distribution\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0ce65a2",
   "metadata": {},
   "source": [
    "## Part 3 — Binomial Distribution\n",
    "\n",
    "The Binomial distribution counts the number of successes in `n` independent Bernoulli trials.\n",
    "\n",
    "If `X ~ Binomial(n, p)`, then:\n",
    "\n",
    "- `P(X = k) = C(n,k) p^k (1-p)^(n-k)`\n",
    "- `E[X] = np`\n",
    "- `Var(X) = np(1-p)`\n",
    "\n",
    "Example:\n",
    "Let `X` be the number of defective components in a sample of 20, if the defect probability is `0.08`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "51dd4e92",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P(X=2) = 0.271091\n",
      "Mean = 1.6\n",
      "Variance = 1.4720000000000002\n"
     ]
    }
   ],
   "source": [
    "n = 20\n",
    "p = 0.08\n",
    "\n",
    "k = 2\n",
    "prob_k2 = binom.pmf(k, n, p)\n",
    "\n",
    "print(f\"P(X=2) = {prob_k2:.6f}\")\n",
    "print(\"Mean =\", n * p)\n",
    "print(\"Variance =\", n * p * (1 - p))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "41a6efb0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(0, n + 1)\n",
    "pmf = binom.pmf(x, n, p)\n",
    "\n",
    "plt.figure(figsize=(8,4))\n",
    "plt.bar(x, pmf, width=0.7)\n",
    "plt.xlabel(\"Number of successes\")\n",
    "plt.ylabel(\"Probability\")\n",
    "plt.title(\"Binomial Distribution: n=20, p=0.08\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2da1d97",
   "metadata": {},
   "source": [
    "## Part 4 — Binomial Simulation\n",
    "\n",
    "Now we compare the theoretical Binomial model with simulation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "741ee2d7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Simulated mean: 1.5811\n",
      "Theoretical mean: 1.6\n",
      "Simulated variance: 1.4365664466446644\n",
      "Theoretical variance: 1.4720000000000002\n"
     ]
    }
   ],
   "source": [
    "n = 20\n",
    "p = 0.08\n",
    "n_sim = 10000\n",
    "\n",
    "binom_sim = np.random.binomial(n, p, size=n_sim)\n",
    "\n",
    "print(\"Simulated mean:\", binom_sim.mean())\n",
    "print(\"Theoretical mean:\", n * p)\n",
    "\n",
    "print(\"Simulated variance:\", binom_sim.var(ddof=1))\n",
    "print(\"Theoretical variance:\", n * p * (1 - p))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "bc6f1103",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,4))\n",
    "plt.hist(binom_sim, bins=np.arange(-0.5, n + 1.5, 1), density=True)\n",
    "plt.plot(x, pmf, 'o')\n",
    "plt.xlabel(\"Number of successes\")\n",
    "plt.ylabel(\"Relative frequency / probability\")\n",
    "plt.title(\"Binomial: Simulation vs Theory\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71218a6b",
   "metadata": {},
   "source": [
    "## Part 5 — Poisson Distribution\n",
    "\n",
    "The Poisson distribution models counts of events in a fixed interval.\n",
    "\n",
    "If `X ~ Poisson(λ)`, then:\n",
    "\n",
    "- `P(X=k) = exp(-λ) λ^k / k!`\n",
    "- `E[X] = λ`\n",
    "- `Var(X) = λ`\n",
    "\n",
    "Example:\n",
    "Let `X` be the number of flaws per meter of cable, with average rate `λ = 3`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "d6d2a5f6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P(X=0) = 0.049787068367863944\n",
      "P(X=2) = 0.22404180765538775\n",
      "Mean = 3\n",
      "Variance = 3\n"
     ]
    }
   ],
   "source": [
    "lam = 3\n",
    "\n",
    "print(\"P(X=0) =\", poisson.pmf(0, lam))\n",
    "print(\"P(X=2) =\", poisson.pmf(2, lam))\n",
    "print(\"Mean =\", lam)\n",
    "print(\"Variance =\", lam)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "262e9381",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(0, 15)\n",
    "pmf_poisson = poisson.pmf(x, lam)\n",
    "\n",
    "plt.figure(figsize=(8,4))\n",
    "plt.bar(x, pmf_poisson, width=0.7)\n",
    "plt.xlabel(\"Count\")\n",
    "plt.ylabel(\"Probability\")\n",
    "plt.title(\"Poisson Distribution: lambda = 3\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8033a3c6",
   "metadata": {},
   "source": [
    "## Part 6 — Poisson Simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "f241431b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Simulated mean: 2.9968\n",
      "Theoretical mean: 3\n",
      "Simulated variance: 2.9834881088108816\n",
      "Theoretical variance: 3\n"
     ]
    }
   ],
   "source": [
    "lam = 3\n",
    "n_sim = 10000\n",
    "\n",
    "poisson_sim = np.random.poisson(lam, size=n_sim)\n",
    "\n",
    "print(\"Simulated mean:\", poisson_sim.mean())\n",
    "print(\"Theoretical mean:\", lam)\n",
    "\n",
    "print(\"Simulated variance:\", poisson_sim.var(ddof=1))\n",
    "print(\"Theoretical variance:\", lam)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "2f9e2a0c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,4))\n",
    "plt.hist(poisson_sim, bins=np.arange(-0.5, 15.5, 1), density=True)\n",
    "plt.plot(np.arange(0, 15), poisson.pmf(np.arange(0, 15), lam), 'o')\n",
    "plt.xlabel(\"Count\")\n",
    "plt.ylabel(\"Relative frequency / probability\")\n",
    "plt.title(\"Poisson: Simulation vs Theory\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0583b2a0",
   "metadata": {},
   "source": [
    "## Part 7 — Normal Distribution\n",
    "\n",
    "The Normal distribution is a continuous distribution used widely in science and engineering.\n",
    "\n",
    "If `X ~ N(μ, σ²)`, then:\n",
    "- `μ` is the mean,\n",
    "- `σ` is the standard deviation.\n",
    "\n",
    "Example:\n",
    "Suppose a sensor output is normally distributed with mean `50` and standard deviation `4`.\n",
    "We compute the probability that the output is less than `58`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "c73731b8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Z-score = 2.0\n",
      "P(X < 58) = 0.9772498680518208\n"
     ]
    }
   ],
   "source": [
    "mu = 50\n",
    "sigma = 4\n",
    "\n",
    "prob_less_58 = norm.cdf(58, loc=mu, scale=sigma)\n",
    "z_score = (58 - mu) / sigma\n",
    "\n",
    "print(\"Z-score =\", z_score)\n",
    "print(\"P(X < 58) =\", prob_less_58)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "e28013a8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "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": "markdown",
   "id": "bcf3b558",
   "metadata": {},
   "source": [
    "## Part 8 — Simulating Normal Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "9617ab65",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Simulated mean: 49.950383162899335\n",
      "Theoretical mean: 50\n",
      "Simulated std: 4.0548202451563125\n",
      "Theoretical std: 4\n"
     ]
    }
   ],
   "source": [
    "mu = 50\n",
    "sigma = 4\n",
    "n_sim = 10000\n",
    "\n",
    "normal_sim = np.random.normal(loc=mu, scale=sigma, size=n_sim)\n",
    "\n",
    "print(\"Simulated mean:\", normal_sim.mean())\n",
    "print(\"Theoretical mean:\", mu)\n",
    "\n",
    "print(\"Simulated std:\", normal_sim.std(ddof=1))\n",
    "print(\"Theoretical std:\", sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "f3182d6f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ERERE5NOY8BIRERGRT2PCS0REREQ+jQkvEREREfk0JrxERERE5NOY8BIRERGRT2PCS0REREQ+zfCEd/LkyShXrhxy5cqFxo0bY8uWLSke+88//+CJJ55Qx8ucaxMmTMj0bRIRERGRbzM04Z0/fz6GDRuG0aNHIywsDLVr10a7du1w8eLFZI+Pjo5GhQoVMG7cOBQvXtwjt0lEREREvk3TdV036s6l97Vhw4aYNGmSuux0OtUScYMGDcLw4cNT/VvpwR06dKg6eeo2Ey5VFxwcjMjISK60RkRERJQDpSdfM2xp4bi4OGzfvh0jRoyI32cymdC2bVts3LgxW28zNjZWnRIGkIjIq0jfxYU9wJntwL+HgRuXAEccYLICeYsAhSoA99QB7qkNmLmqPBH5F8Pe9S5dugSHw4GQkJBE++Xy/v37s/U2x44dizFjxmToPomIDHVyE7BzHnDoTyDqzN2PDwwCqncE6vYGSjeWReizo5VERIbi13xA9QhL3W/CHl4pgyAiypGcTuDgMmD9RODU5tv7rXlcSWzRqkD+EMCSG3DEAtcuAJcOAqe3AjFXgfAfXKci9wKtRgLVOzPxJSKfZljCW6RIEZjNZly4cCHRfrmc0oC0rLrNwMBAdSIiyvEu7gN+Gwqc2uS6bA4AanUDqncByj0AWHOlniif3AjsmAP884srCV7wLFCyPvDwR0DZptn2MIiI/GKWhoCAANSvXx+hoaHx+2SAmVxu2rRpjrlNIqIcwR4HhH4ATH3Qlexa8wIPDAOG7gE6TQYqt0092RUmE1DufqDzZOCNA0DLEa7bkbrf6e2BP/4D2G+PZyAi8hWGljRIGUHfvn3RoEEDNGrUSM2re+PGDfTr109d36dPH5QsWVLV2LoHpe3duzd++8yZM9ixYwfy5cuHSpUqpek2iYi8TtRZ4Me+wOlbc4pXeQR45BMguFTGbzMwP9ByOFC/H7DqfVeJw8ZJwNG1wJPfAUWreKz5RER+nfB2794dERERGDVqFM6fP486depg+fLl8YPOTp48qWZZcDt79izq1q0bf/nTTz9VpxYtWmDNmjVpuk0iIq9yfL2r7ODGRSBXMNDxS6B6J8/dvtT6Sg+xJNGLBwEXdgPftAG6zwIqtvbc/RAR+es8vDkV5+ElohxB6mx/fh5w2oFi9wE9fnBNL5ZVZHDbT/2AE+sBkwV4bAJQr3fW3R8Rka/Pw0tERKkI+x74bTCgO109up2nAAF5PRaycsOXJrs/AC/gYyvQBeuBxa/ifz+vw/85Uu9RPj7uUY+1i4jI55YWJiKiZGz+SiWbKtmt1wd4crpHk93UxMGK12wv4wt7Z3X5Let8vGD+jU8TEXk19vASEeUkMmXYsrdc201fBR7+MH6O3JR6ZT1Pw2f2bojVA/Cm9UeMtM6FHRZMc3TIpvsnIvIs9vASEeUUB/8Afn012WTXCJMdnTHR3lVtj7J+j6fMrsHBRETehgkvEVFOcGqLa+ox3QHU6gE89EGOWP3sc/sTmGp/XG3/1/Idmpr+MbpJRETpxoSXiMhokaeBeU8D9ptApYeATpNci0TkCBo+tnfHb44msGoOTLFOQAXtrNGNIiJKl5zyjkpE5J9sMcD83sCNCCCkJtBtJmC2IifRYcIbtoEIc1ZCAe0GvrN+giBcN7pZRERpxoSXiMgoMg360mHA2TAgd0HXPLvZNBtDesUiAAPiXscpZ1GUN13AeOtXKhUmIvIGTHiJiIyybRqwYzagmVxTjxUsl6Ofi38RjIG2oYjVLXjIvB3Pm383uklERGnChJeIyAgX9wF/jHRttx0DVGzlFc/DP3p5fGB3rb423DIX9bUDRjeJiOiumPASERlRt/tTf8Ae4xqk1myQVz0HPzjaYrGjKSyaE18GfAncvGp0k4iIUsWEl4gou60YBVz8B8hbFOj8fzli+rH00TDC9jyOOUNQQrsMLHvb6AYREaWKCS8RUXY6vBLYIgO+AHSeCuQr5pXxv4HceN32Ehy6BuyaB+xdbHSTiIhSxISXiCi7xEQBi4e4thu9CFRu69WxD9PvxVSHa1EKLBkKXL9odJOIiJLFhJeIKLusfA+IOg0UKAu0He0TcZ9ofwIIqQFE/wssec3o5hARJYsJLxFRdjj+N7DtO9d2xy9z7Hy76RUHK9DlK8BkAfYvAfYtMbpJRER3sNy5i4iIPKnK8F+wPOBtlDcBc+ytMfJrWaVsqe8EuXgNoNlg4O/PgN/fBCq0AALzG90qIqJ47OElIspiL1sWq9XJzusFMdb+tG/Gu8VbroUzrp0FVn1odGuIiBJhwktElJX+PYKB5t/U5vu23riGPL4Zb2tu4LHPXdubvwLObDe6RURE8ZjwEhFlFV1Xc9QGajb85aiJ352NfTvWFVsDNbvJAweWvgE4nUa3iIhIYcJLRJRVZBDX4RWI080YbX9WLdjg8x7+EAjID5wNA3bONbo1REQKE14ioqxguwksH6k2v3Y8hmP6Pf4R5/whQIs3b0/DJnMPExEZjAkvEVFW2DQFiDwJBJXEJHtn/4px45eAQhWBGxeBvz4xujVEREx4iYg8TlYcW/eZa7vNaMQg0L+CbAkA2o+9nfhfOmx0i4jIz3EeXiIiT1v9XyDuGlCiLlDzKWDuMp+Ocbnhyc8pPN1aG62wE8smDsRLtruvwnZ83KNZ0DoiIvbwEhF51oW9QNhM13a7/wIm/60ckzmHHbqGDuatqKcdNLo5ROTH/PedmIgoK6wcDehOoFpHoGwzv47xQb00FjhaqO0R1jmu6cqIiAzAhJeIyFNObgIO/QloZqDte4wrgM/tT+KmHoCGpoN4yMTFKIjIGEx4iYg8tchE6Puu7brPAIUrMq5S4YFC+M7RQcXibcs8mOFgXIgo2zHhJSLyhCOrgBPrAXMg0OItxjSBr+yP47KeD5VMZ9HZtJ6xIaJsx4SXiMgTvburPnBtN+wPBJdiTBO4hjyYan9cbQ+2LIQFdsaHiLIVE14iIk8sIXw2HLDmBR4Yxngm43vHQ4jQg1DWdBFdzesYIyLKVkx4iYgyw+kAVn3o2m7yEpCvKOOZjJvIhan2jmp7sOUXWNnLS0TZiAkvEVFm7P4JiNgP5AoGmg1iLFPxg6MtLuoFUEq7hKfMaxkrIso2THiJiDLKYQfW3FpC9/4hQO4CjGUqYhGAyfZOavtVyy8IgI3xIqJswYSXiCij/lkIXDkG5C4ENHqRcUyDeY5WOKcXQgntMrqbVzNmRJQtmPASEWWE0wn89alru+krQGA+xjGdvbyvWH5FIOIYNyLKckx4iYgyYv9vwKUDQGAw0GgAY5gOPzpa4rReBMW1K+zlJaJswYSXiCgj8+66e3cbv+AasEZpFgdr/Ly8L1iWcl5eIspyTHiJiNLr0Arg/C7XvLuNX2L8MmCBo4Wal1dmbOho2sAYElGWYsJLRJTu3t1PXNsNnwPyFmb8MljLO83+iNp+yfIbNDgZRyLKMkx4iYjS4/g64PQWwBwINH2VscvkvLxRem5UNp3BQ6btjCURZRkmvERE6eHu3a3XB8hfnLHLhGvIo5YcFi9bFrt6z4mIsgATXiKitDqzHTj2F2CyuBaaoEybZu+AGN2KOqYjrtgSEWUBJrxERGm14UvXec2ngAKlGTcP+BfBmO9o6brw92eMKRFlCSa8RERpceU4sPdX1zZrdz3qG8djsOsm4OgaVy86EZGHMeElIkqLTVMA3QlUbA0Ur8GYedBpvSh+dTZL3ItORORBTHiJiO4m+jIQNsu13Www45UFvrU/6tqQXvQrJxhjIvKthHfy5MkoV64ccuXKhcaNG2PLli2pHr9gwQJUrVpVHV+zZk38/vvvia6/fv06Xn31VZQqVQq5c+dG9erVMXXq1Cx+FETk07ZNA2zRQEhNoMKtelPyqH16WVdspRd981eMLhH5TsI7f/58DBs2DKNHj0ZYWBhq166Ndu3a4eLFi8kev2HDBvTs2RP9+/dHeHg4OnfurE579uyJP0Zub/ny5fjhhx+wb98+DB06VCXAixcvzsZHRkQ+wxZzOwFrNgjQNKNb5LvctdHSmx4TaXRriMiHGJrwfvbZZxgwYAD69esX3xObJ08eTJs2LdnjJ06ciPbt2+PNN99EtWrV8MEHH6BevXqYNGlSoqS4b9++aNmypeo5fuGFF1QinVrPcWxsLKKiohKdiIiU3T8CNy4CQSWBGl0ZlKxUqS1QtCoQdw0I+56xJiKPscAgcXFx2L59O0aMGBG/z2QyoW3btti4cWOyfyP7pQc3IekRXrRoUfzlZs2aqd7c5557DiVKlMCaNWtw8OBBfP755ym2ZezYsRgzZoxHHhcR+YZyw5eq5W7/DBiHyibgw39b4tv//Gl0s3yb9J43eRn4bTCweSrQeCBgNuxjioh8iGE9vJcuXYLD4UBISEii/XL5/Pnzyf6N7L/b8V9++aXqLZYa3oCAANUjLHXCzZs3T7EtknRHRkbGn06dOpXpx0dE3q+FaZda9laWv53naGV0c/xDre5AniJA5Clg361p4IiIvH3QmqdJwrtp0ybVyys9yOPHj8crr7yClStXpvg3gYGBCAoKSnQiInrW/IcKwo+OlriOPAxIdrDmAhoNcG1vmMTlhonIIwz7rahIkSIwm824cOFCov1yuXjx5Nenl/2pHX/z5k2MHDkSv/zyCx591DXFTa1atbBjxw58+umnqlyCiCgtKmhn0dK8E05dw0zHwwxadmrQH1j3GXA2DDi5CSjblPEnIu/s4ZVyg/r16yM0NDR+n9PpVJebNk3+zU32JzxerFixIv54m82mTlILnJAk1nLbRERp1cfsqtcNddbDKT1xKRVlsXxFgdrdXdubJjPcRJRpho4GkAFoMqNCgwYN0KhRI0yYMAE3btxQszaIPn36oGTJkmpQmRgyZAhatGihyhSkB3fevHnYtm0bvv76a3W9lCLI9TKLg8zBW7ZsWaxduxazZs1SM0IQEaVJTCSeNP+lNqc72jFoRpDBazI92f6lwNVTQIHSfB6IyDsT3u7duyMiIgKjRo1SA8/q1Kmj5tB1D0w7efJkot5amYFhzpw5eOedd1TpQuXKldUMDTVq3F7mU5JgGYTWq1cvXL58WSW9H330EQYOHGjIYyQiLxQ+G/m0GBx0lsQG531Gt8Y/FasGlG8OHPvLtfBH29FGt4iIvJim67pudCNyGpmHNzg4WM3YwAFsRH7G6QC+rAdcOY6Rtv6Y42hjdIv8xvFxt5YXdtv3GzD/GSBPYeC1va4BbUREGcjXfG6WBiKiTDm0QiW7kXoe/OK4n8E00r0dgKBSQPS/wD8L+VwQUYYx4SUiSkgWPJDyKEcr3AR7FA0li0407H/refmKU5QRUYZxCRsiIreL+4GjqwHNhO85FZkhq9slVRD3YFOgFYHndqDLyIkI1ytnrDyCiPwae3iJiNy2uGZ8QZVHcFovyrjkAFcQhMUO19STfS2uhUCIiNKLCS8Rkbh5Fdg51xWLxi8yJjmIe+GPR0ybURRXjW4OEXkhJrxERCL8B8AWDRSrDpR7kDHJQfboFbDdWRkBmgM9zauMbg4ReSEmvEREshLj1m9u9+5qGmOSw8y0u3p5e1lWwgK70c0hIi/DhJeI6OgqNRUZAoOBmk8xHjnQMmdjROjBCNGuop1pm9HNISIvw4SXiGjrNFcM6vQEAvIyHjmQDZb4RUA4eI2I0osJLxH5t8jTwMFlru0GzxndGkrFbHsb2HQzGpkOoLp2nLEiojRjwktE/m37TEB3ugaqFa1idGsoFRdREH84G6rtp82hjBURpRkTXiLyXw4bEDbLtc3eXa8w+1ZZQ2fzeuTFTaObQ0ReggkvEfmv/UuB6+eBvMWAqo8Z3RpKg43O6jjivAf5tBh0Mm9gzIgoTZjwEpH/2vad67xeH8ASYHRrKE00zHG0TlDWoDNuRHRXTHiJyD9dOgQc+wvQTED9Z41uDaXDz47miNWtqGE6jtraEcaOiO6KCS8R+adtt6Yiq/wwUKC00a2hdLiK/FjibKy2e3HwGhGlARNeIvI/cdHAjtmu7Qb9jW4NZcAcu2vw2uPmjQjCDcaQiFLFhJeI/M8/C4GYSKBAGaCSK3Ei77Jdvxf7naWRW4tDF/PfRjeHiHI4JrxE5H+23hqsVr8fYDIb3RrKEC1+irJe5pUcvEZEqWLCS0T+5Ww4cDYMMFmBur2Nbg1lwiLHA4jWA3Gv6QwaaAcYSyJKkSXlq4iIvE+54UtTvf6/lm/xtAX41dYQQz7ckm3tIs+7hjxY7GiKHpY16GUJxTZbVYaZiJLFHl4i8ht5EIOOtxYrmHtrLlfybrMdbdX5I6bNKIgoo5tDRDkUE14i8huPmTeqFbqOOotjk7Oa0c0hD9itV8AuZ3kEanY8YV7HmBJRspjwEpHf6Glerc7nO1qpQU/kG+bcGrwmK69pcBrdHCLKgZjwEpFfqKKdRF3TYdh0s1qpi3zHYkczXNNzo4LpPJqa9hrdHCLKgZjwEpFf6HGrd3eFsz4uIdjo5pAHRSMXfnE8EN/LS0SUFBNeIvJ5gYhD11v1nfNUOQP5allDO9M2FMVVo5tDRDkME14i8nkygj9Yi8ZpvQjWOWsa3RzKAvv1MtjurAyr5sCT5r8YYyJKhAkvEfm8HpZbg9XsLaHzbc9nuXvvu0v5iq4b3RwiykGY8BKRT6uonUFj0344dA0LHC2Mbg5loSWOJmrwWjnTBeA4pygjotuY8BKRT+tuXqPOVzvr4DwKG90cykI3kUvN2KCEzWKsiSgeE14i8lkBsOGJW/Wc87iyml+IH5S4dzEQfdno5hBRDsGEl4h81kOm7SisXcN5vaDq4SXft1svj3+cZQFHLLDrR6ObQ0Q5BBNeIvJZPcyr1LnU7jpgNro5lC00zHX35ofN5OA1IlKY8BKRTyqtXcCD5j1qe76jpdHNoWyk6ngtuYGLe4HT2xh7ImLCS0S+PVjtL0dNnNaLGd0cykZRyAvc1/l2Ly8R+T328BKRzzHDgafMa9U2V1bzU/X6uM73LARirxndGiIyGBNeIvI5rU3hCNGu4pIehBXOBkY3h4xQpilQuDJguwHs+ZnPAZGfY8JLRD6nh6y0BeAnR3PYYDG6OWQETbvdy7udZQ1E/o4JLxH5lOL4Fy1NO9T2fPecrOSf6jwNmKzA2TDg/G6jW0NEBmLCS0Q+pZt5Lcyajk3Oajim32N0c8hIeYsAVR91bXPlNSK/xoSXiHyH04FuFtfsDHPt7N2lBIPXds0HbDcZEiI/xYSXiHzHkdUopV3CVT0vljsbGd0aygkqtAKCywAxka7lhonILzHhJSLfETZDnf3ieACxCDC6NZQTmExAvd6ubc7JS+S3mPASkW+4fhE4sExtxi8tSyTq9AI0E3BiPXDpMGNC5IeY8BKRb9gxG3DaEeashIN6aaNbQzlJcEmg8sOubfbyEvklJrxE5P10PX4UPnt3KdXBazvmAPY4BonIzxie8E6ePBnlypVDrly50LhxY2zZsiXV4xcsWICqVauq42vWrInff//9jmP27duHjh07Ijg4GHnz5kXDhg1x8uTJLHwURGSo4+uAy0eBgPxY4mjCJ4PuVLkdkK84EH0JOOgqfSEi/2Fowjt//nwMGzYMo0ePRlhYGGrXro127drh4sWLyR6/YcMG9OzZE/3790d4eDg6d+6sTnv27Ik/5siRI3jggQdUUrxmzRrs2rUL7777rkqQichHuVfSqvkkboL/1ykZZotrIYqErxci8huarstvgcaQHl3pfZ00aZK67HQ6Ubp0aQwaNAjDhw+/4/ju3bvjxo0bWLJkSfy+Jk2aoE6dOpg6daq63KNHD1itVnz//fcZbldUVJTqHY6MjERQUFCGb4eIskH0ZWB8FcARB7ywBuW+OMuwE46Pu7XgRELyK8AXdeWjDxi6CyhQhpEi8mLpydcM6+GNi4vD9u3b0bZt29uNMZnU5Y0bNyb7N7I/4fFCeoTdx0vCvHTpUtx7771qf7FixVRSvWjRolTbEhsbq4KW8EREXmLnPFeyW7wWUEKSGaIUFKoAlG8uRd9A+A8ME5EfyVDCe/To0Uzf8aVLl+BwOBASEpJov1w+f/58sn8j+1M7Xkohrl+/jnHjxqF9+/b4888/0aVLF3Tt2hVr165NsS1jx45V3xDcJ+llJiJvGax26+fp+n2Nbg15g3q3XieS8DodRreGiHJywlupUiW0atUKP/zwA2JiYpBTSA+v6NSpE1577TVV6iClEY899lh8yUNyRowYobrD3adTp05lY6uJKMNObQEi9gOW3EDNpxhIurtqjwO5CwJRZ4DDoYwYkZ/IUMIrA8xq1aqlBpwVL14cL7744l1nV0iqSJEiMJvNuHDhQqL9clluMzmyP7Xj5TYtFguqV6+e6Jhq1aqlOktDYGCgqv1IeCIiL+Du3a3RFcgVbHRryBtYAoHaPV3bnJOXyG9kKOGVntOJEyfi7NmzmDZtGs6dO6dmRqhRowY+++wzRERE3PU2AgICUL9+fYSGhibqoZXLTZs2TfZvZH/C48WKFSvij5fblEFwBw4cSHTMwYMHUbZs2Yw8VCLKqWIigT0LE/9MTZSeOXllZb5riTtRiMg3ZWrQmvSmSn2szI378ccf4/Dhw3jjjTdUDWyfPn1UIpwa6SH+5ptvMHPmTDV37ksvvaRmYejXr5+6Xm5Dyg3chgwZguXLl2P8+PHYv38/3nvvPWzbtg2vvvpq/DFvvvmmmu5MblfaIzNA/Pbbb3j55Zcz81CJKKfZvQCw3wSKVgVKNzK6NeRNilUDSjUCdIdrhT4i8nmWzPyxJJvSwztv3jy1wIMkuzJH7unTpzFmzBhVS5taqYNMMya9waNGjVIDz6TnWBJa98A0KUOQmRvcmjVrhjlz5uCdd97ByJEjUblyZTUDg/Qsu8kgNanXlYFogwcPRpUqVfDzzz+rHmgi8iHuuVSld1fTjG4N5TDlhi9N9fqnzHXwiXULjq+YilZLK0NPof8n2enNiMg/5uGVsoXp06er0oFHHnkEzz//vDpPmJxK0isrqNntdngbzsNLlMOdDQe+bgmYA4DXDwB5CqU50SESuRGDzYGvIEi7iafjRmKD83bHSUJMeIn8eB7eKVOm4Omnn8aJEydUD6vMgpAw2RUyB+53332XkZsnIkpb7261jomSXaK0khX5fnXcr7Z7mlcxcEQ+LkMlDTJQrEyZMnckudJZLFN6yXUygKxvXw4kISIPi70O7P7Jtc25dykT5jlao7dlJR42bUMhROEyOEMPka/KUA9vxYoV1cIRSV2+fBnly5f3RLuIiJL3zy9A3DWgYHmgLGvzKeP+0cthl7M8AjU7uprXMZREPixDCW9KZb+yylmuXLky2yYiopSFzbo9tVSSX5mIMtLLe7usId1DWojIF0saZBoxoWmamlkhT5488dfJMsGbN29WMy0QEaVHWgeaVdZOY0XgFth0M5otDUHEUg5Qo8xZ7GiK/1h+QEXTOTTUDmCrXpUhJfL3hDc8PDy+h3f37t2qTtdNtmvXrq2mJiMiygruwUWhznqIQAEGmTLtOvLgN0dT9LCsQQ/LKmy1MeElgr8nvKtXr1bnsjCErLTGJXiJKLsEIg5dzH+r7XmOVgw8ebSsQRLeR02bMQZ9EIV8jC6Rj8lQAZzMwctkl4iyUzvTVhTUruO0XgR/OWsx+OQxO/SK2Ocsg1yaDV3M6xlZIn/u4ZUlhGfMmKESXdlOzcKFt9a3JyLykJ5m1y9MC+wt4MzcquhESWiY62iF900z0cO8CjMdD6t9ROSHCa+sZCGD1dzbRETZpZx2Dk3Ne+HQNfzoaMnAk8ctctyPkZY5qGY6hTraEezQKzHKRP6Y8EoZQ3LbRERZrYd5jTpf66yNcyjMgJPHSd3uUmdjPGH+Ww2O3GFnwkvkSzL0u+DNmzcRHR0df1mWGJ4wYQL+/PNPT7aNiAhW2PGEea2KBAerUVaaa3fNyfu4eSPy4fZnHBH5acLbqVMnzJrlmvz96tWraNSoEcaPH6/2T5kyxdNtJCI/1sYUhqJaFC7qBbDKWdfo5pAP26ZXwSFnSeTRYtHRvNHo5hCR0QlvWFgYHnzwQbX9008/oXjx4qqXV5LgL774wpPtIyI/1+PWYLWfHM1hT99MikTppGHerRrxnuZQRo/I3xNeKWfInz+/2pYyBpm1wWQyoUmTJirxJSLyhJKIQHPTLrXNcgbKDgsdDyJWt6Cm6Tju044x6ET+nPBWqlQJixYtwqlTp/DHH3/g4YdlChfg4sWLnJ+XiDymm2UtTJqO9Y77cFIPYWQpy11BEP5wNky0sh8R+WnCO2rUKLWEcLly5dC4cWM0bdo0vre3bl3W2BGRJ96cnHjq1uwM7N2l7DTX4Rq81sm8AYi7weAT+WvC++STT+LkyZPYtm0bli9fHr+/TZs2+Pzzzz3ZPiLyUy1MO1FCu4zLer74Hjei7LDJWQ3HnSHIr90E9nAhJSJfkOHlimSgmvTmSu2um8zWULVqVU+1jYj8mPvnZKmpjIPV6OaQH9FhwnxHK9eFsJlGN4eIPCBDQ55v3LiBcePGITQ0VNXtOp3ORNcfPXrUE20jIj9VHP+q6cgS/rxMlJ1kVpBhlgWwnt4KXNgLhFTnE0Dkbwnv888/j7Vr16J3796455574pccJiLyhB6W1TBrOjY6quOIXpJBpWwXgQJY6ayHDuatrl7eDh/zWSDyt4R32bJlWLp0Ke6//37Pt4iI/JoF9vi5d2c72hjdHPJj8xytXQnvzrlA2/cAa26jm0RE2VnDW7BgQRQqVCij90lElKI2pnAU167gkn57eigiI6xz1gSCywAxkcA/i/gkEPlbwvvBBx+oqclkAQoiIk/qZV6pzn90tISNK6uRgZzyEVm/r+vCtu/4XBD5W0nD+PHjceTIEYSEhKi5eK1W6x1LDxMRpVcZ7QKam3fDqWuY6x4lT2Sken2ANeMAGbx2bhdwTy0+H0T+kvB27tzZ8y0hIr/39K2pyP5y1sIprqxGOUG+YkC1x4F/Frp6eR+faHSLiCi7Et7Ro0dn5M+IiFIUAFv8ymocrEY5SsP+roR31wLgoQ+AXEFGt4iIsmvhiatXr+Lbb7/FiBEjcPny5fhShjNnzmT0JonIj7U3bUFh7RrO6oWwysklyikHKXs/ULQqYLsB7JpvdGuIKLsS3l27duHee+/Fxx9/jE8//VQlv2LhwoUqASYiSq9ellB1Ps/eGg6YGUDKOWSu+QbPuba3fgfoutEtIqLsSHiHDRuGZ599FocOHUKuXLni9z/yyCP466+/MnKTROTHKmun0di0H3ZdlnRtaXRziO5UuwdgzQNE7ANObmSEiPwh4d26dStefPHFO/aXLFkS58+f90S7iMiPPG129e6udNbHBXCOb8qBcgUDNZ+83ctLRL6f8AYGBiIqKuqO/QcPHkTRokU90S4i8hdxN/CEeZ3a5GA1ytEa9Hed7/0VuB5hdGuIKKsT3o4dO+L999+HzWZTlzVNw8mTJ/H222/jiSeeyMhNEpG/2vMzgrRonHAWw9/OGka3hihlJeoAJesDThsQ/j0jReTrCa8sPHH9+nXVm3vz5k20aNEClSpVQv78+fHRRx95vpVE5Lu2TVNncxxtoGd84hii7O3l3T4dcDoYdSJfnoc3ODgYK1aswPr167Fz506V/NarVw9t27b1fAuJyHedCQPOhiNWt2CBo4XRrSG6uxpdgT9GAldPAodDgXsfZtSIfDHhdTqdmDFjhpqC7Pjx46qcoXz58ihevDh0XVeXiYjS07u7zNkIl8HJ/MkLWHMDdXoBmya7Vl5jwkvkFdL1+6EktFK/+/zzz6sFJmrWrIn77rsPJ06cUNOUdenSJetaSkS+JfoysPsntTnbzl+HyIu45+Q9+Ierp5eIfCvhlZ5dmWc3NDQU4eHhmDt3LubNm6fKGlauXIlVq1Zh1qxZWddaIvId4T8A9ptASE1s1asY3RqitCtSCSgvJTg6sH0GI0fkawmvJLgjR45Eq1at7riudevWGD58OGbPnu3J9hGRL5LBPlu/dW03GiBzvRjdIqL0aXhr8FrYLMAex+gR+VLCK0sKt2/fPsXrO3TooHp7iYhSdehP4OoJIFcBoOZTDBZ5nyqPAPnvAW5EuOblJSLfSXgvX76MkJCQFK+X665cueKJdhGRL9vyteu8Xm8gII/RrSFKP7P1di3vlq8YQSJfSngdDgcslpQndjCbzbDb7Z5oFxH5qkuHgCOrXGUM7jlNibxR/WcBcwBweitwZrvRrSEiT01LJrM0yGwMsrRwcmJjY9Nzc0Tkj7Z84zq/tx1QqLzRrSHKuHzFgPu6ArvmAZu/Brqyp5fIJxLevn373vWYPn36ZKY9ROTLYq8BO+a4thu9YHRriO6q3PClqV5fS7sPiwOBuJ0L0GxLC1xCcIrHHh/3KCNO5A0J7/Tp07OuJUTk+3bOA+KuAYUrARXunO2FyNvs0isizFkJ9UyH0dMcii8dXY1uEhElgwvXE1H20PXbg9Wkd9fEtx/yDTPsrtmLnrGshBUcx0KUE/ETh4iyx7G1wKWDQEA+oHZPRp18hiyNfVEvgBDtKtqbthjdHCJKBhNeIsoeMqhH1O4B5Api1Mln2GDBD7eWx37W8ofRzSGizNbwZpXJkyfjk08+wfnz51G7dm18+eWXaNSoUYrHL1iwAO+++y6OHz+OypUr4+OPP8YjjzyS7LEDBw7EV199hc8//xxDhw7NwkdB5F/uNpgnoVJaBNYG/A6zBrT5uwqOrEv73xJ5g7mO1njV8gvqmw6hpnYUu/UKRjeJiHJSD+/8+fMxbNgwjB49GmFhYSrhbdeuHS5evJjs8Rs2bEDPnj3Rv39/hIeHo3Pnzuq0Z8+eO4795ZdfsGnTJpQoUSIbHgkRpaSv+Q+YNR1/O+7DEb0kA0U+JwIFsMTZVG2zl5co5zE84f3ss88wYMAA9OvXD9WrV8fUqVORJ08eTJs2LdnjJ06cqJY3fvPNN1GtWjV88MEHqFevHiZNmpTouDNnzmDQoEGYPXs2rFZrNj0aIkoqH6LR3bxabX/rSP6XGCJfMNP+sDp/zLQRhRFpdHOIKKckvHFxcdi+fTvatm17u0Emk7q8cePGZP9G9ic8XkiPcMLjnU4nevfurZLi++67767tkAUzoqKiEp2IyDO6mdciSLuJI857sNZZm2Eln7VTr4RwZyUEanb0NMtqgkSUUxia8F66dEktVxwSEpJov1yWet7kyP67HS81vbIE8uDBg9PUjrFjxyI4ODj+VLp06Qw9HiJKzAQn+pmXq+3vHI9AN/5HJaIsNd3eTp33saxAAGyMNlEO4XOfPtJjLGUPM2bMgKZpafqbESNGIDIyMv506tSpLG8nkT942LQNpU0RuKLnw0LHA0Y3hyjL/e5sjHN6IRTTrqKjeQMjTpRDGJrwFilSBGazGRcuXEi0Xy4XL1482b+R/akdv27dOjXgrUyZMqqXV04nTpzA66+/jnLlyiV7m4GBgQgKCkp0IqLMe97yuzr/wdEWMQhkSMnn2WHBjFu9vP3N8vrXjW4SERmd8AYEBKB+/foIDQ1NVH8rl5s2dY12TUr2JzxerFixIv54qd3dtWsXduzYEX+SWRqknvePPzg/IlF2qaMdRgPTQcTpZsyyP8TAk19NUXZdz4VqplN40LTb6OYQUU6Yh1emJOvbty8aNGig5t6dMGECbty4oWZtEH369EHJkiVVna0YMmQIWrRogfHjx+PRRx/FvHnzsG3bNnz9tWtS+8KFC6tTQjJLg/QAV6lSxYBHSOSf+t/q3f3N2QwRKGh0c4iyTRTy4kdHSzxnWY4B5qVY56zF6BP5e8LbvXt3REREYNSoUWrgWZ06dbB8+fL4gWknT55UMze4NWvWDHPmzME777yDkSNHqoUnFi1ahBo1ahj4KIgooRK4hA63llj9zt6BwSG/M83RXs0/3dy8G1XtJ7FfL2N0k4j8mqbrOguMkpBpyWS2BhnAxnpeovSvtDbCMhsvWpZiveM+9LL9hyEkvzTJOhGPmTfjJ0dzvGEbiOPjHjW6SUR+m6/53CwNRGSsvLgZPwfpdw727pL/+tbuSnA7mtajGK4Y3Rwiv8aEl4g86qkEC02sdtZhdMlv7dArYYuzCgI0B/paOGiayEhMeInIY8xw4DnzMrU93dGeC02Q3/vW7lpOu5c5FIi74ffxIDIKE14i8phHTZtRxhSBf/X8qm6RyN+tdNbHMWcICmg3gPDZRjeHyG8x4SUiD9Ex0PKb2pppb8eFJohkbnmY1LLayqbJgNPBuBAZgAkvEXlEc9MuVDedwA09ELMcXGiCyE1+7ZDltXHlOLDP9aWQiLIXE14i8oiBZtcH+TxHa1xFfkaV6BZZVjv+S+DfnwGcDZQo2zHhJaJMq60dRjPzXth0c/wgHSK6bYa9HWDNA5zbCRxxTdtHRNmHCS8RZZq7dvdX5/04h8RLexMRcAVBQL2+rlD8/TlDQpTNmPASUaZU0M6inWmb2p5qf4zRJEpJs1cBkxU4vg44tZVxIspGTHiJKFMGmJfCpOlY4aiHw3opRpMoJcGlgFrdb9fyElG2YcJLRBkWgsvoal6ntqfYOzKSRHfzwFAAGnDgd+DCXsaLKJsw4SWiTNXuBmp2bHZWRZh+LyNJdDdFKgPVHndtr5/AeBFlEya8RJQhRXEVPc2u0eZf2LswikRp9eAw1/nun1xz8xJRlmPCS0QZ8rxlKXJpNoQ5K2G9swajSJRWJeoCFVoBugP4m728RNmBCS8Rpd+Nf/GMeWWC3l2NUSRKj+Zvus7DfwCunmLsiLIYE14iSr9Nk5FXi8UuZ3mscdZhBInSq9z9QLkHAaeN8/ISZQMmvESUPjevAJu/VpuT7J3Zu0uUUS2Hu87DvwciTzOORFmICS8Rpc/mr4C4a9jnLI0VzvqMHlFGlXsAKPsA4IhjLy9RFmPCS0RpFxMFbPo/tTnJ3gU630KIMqfl267zsFlA5BlGkyiLMOElorTbNAWIiQSK3ItlzkaMHFFmSR1v2ftdvbycl5coyzDhJaK0ib4MbJzk2m45Ak6+fRBlnqYBLW718m6fCUSdY1SJsgATXiJKmw1fArFRQEgNoLoMViMijyjfHCjTFHDEspaXKIsw4SWiu7seAWye6tpu9R/AxLcOIo/28rYc4drePh24epLBJfIwfmoR0d39/TlgiwZK1AOqdGDEiDytQgtXT6/U8q75mPEl8jAmvESUuqizwNZvXdut33H1RhGR57UZ7TrfOQeIOMgIE3kQE14iSt1fn7pqC8s0Ayq2ZrSIskqpBkCVRwHdCaz+kHEm8iAmvESUsisnXPODCvbuEmU9+X8GDdj7K3A2nBEn8hCLp26IiHzQ6v8CThtQoSVQ7n6jW0Pk1coNX5qm4z6z3o+u5r+xdspg9LXdWn44iePjHvVw64h8G3t4iSh553YCu+a7ttu+xygRZZPP7U/AppvRwrwLjbV9jDuRBzDhJaLkrZABNDpQ40mgRF1GiSibnNJDMM/RSm2/ZZ3n+n9IRJnChJeI7nQ4FDi6GjBZgTbvMkJE2exLexdE64GobzqEDqYtjD9RJjHhJaLEnM5bvbsAGg0ACpZjhIiy2UUUxDcOV53ucMtcWGHnc0CUCUx4iSix3T8CF3YDgcFA8zcZHSKDfGV/DBf1Aihruog+5j/5PBBlAhNeIrrNFgOEfuDafvA1IE8hRofIINHIhfH2p9T2IMsvCMZ1PhdEGcSEl4hu2zwViDoNBJUEGg9kZIgMtsDRAvucpVFAu4HBll+Mbg6R12LCS0Qu1y64VlVzT35vzc3IEBnMCRP+a++ltnub/0RZ7bzRTSLySlx4gsjPpDT5/SeWqXjKcg07nBXQZV5+6PPSNkk+EWWtdc5aWOuopeblfdsyDy/bhjLkROnEHl4iQm3tMJ6y/KUi8Z7tWeh8ayDKUT6y94JD1/CIeQuamPYa3Rwir8OEl8jPaXDiPesstf2z40Hs0CsZ3SQiSuKgXhpzHG3U9hjLDMBhY4yI0oEJL5Gf62L6G3VNh3Fdz4Vxth5GN4eIUvCpvRsu6/lQxXQa2PIN40SUDkx4ifxYXtzEcLV0KTDJ3hkRKGh0k4goBZHIh//Zb30pXTPWNdCUiNKECS+RH3vVsgjFtKs45gzBNEcHo5tDRHfxo6MldjorALFRwMr3GC+iNGLCS+SnKmun8bz5d7X9of0ZxMFqdJOIKA3TlI22Peu6sHMOcHIzY0aUBkx4ifx0oNpH1u9g1RxY4aiPUGd9o5tERGmkBpbW7e268PsbgNPB2BHdBRNeIj/UzbwWjUwHcEMPxGhbX6ObQ0Tp1fY9IFcwcH4XsOVrxo/oLpjwEvmZwojECMsctf2Z/UmcRRGjm0RE6ZW3iCvpFaEfAFdPMoZEqWDCS+Rn/mOdjQLaDfzjLIsZjvZGN4eIMqres0CZZoDtBrD0dUDXGUuinJzwTp48GeXKlUOuXLnQuHFjbNmyJdXjFyxYgKpVq6rja9asid9/dw28ETabDW+//bbanzdvXpQoUQJ9+vTB2bNns+GREOVwR9egq/lvOHUNI2394YDZ6BYRUUaZTMDjEwFzAHDoT2DPz4wlUU5NeOfPn49hw4Zh9OjRCAsLQ+3atdGuXTtcvHgx2eM3bNiAnj17on///ggPD0fnzp3Vac+ePer66OhodTvvvvuuOl+4cCEOHDiAjh07ZvMjI8ph4qKBJcPU5veOttjJFdWIvF/Re4Hmb7q2l70NRF82ukVEOZKm68b+BiI9ug0bNsSkSZPUZafTidKlS2PQoEEYPnz4Hcd3794dN27cwJIlS+L3NWnSBHXq1MHUqVOTvY+tW7eiUaNGOHHiBMqUKXPXNkVFRSE4OBiRkZEICgrK1OMjyjGWjwQ2TcZ5vSAeiv0E15DH6BYRUQYdH/fo7Qv2OOCr5kDEPqBOL6Dz/zGu5Bei0pGvGdrDGxcXh+3bt6Nt27a3G2QyqcsbN25M9m9kf8LjhfQIp3S8kEBomoYCBQoke31sbKwKWsITkU85sRHY5PoQHG57nskukS+xBAAdv1ATDmLHbODIKqNbRJTjGJrwXrp0CQ6HAyEhIYn2y+Xz588n+zeyPz3Hx8TEqJpeKYNIKfsfO3as+obgPkkPM5FPlTL8+jIAHajzDNY46xrdIiLytNKNgEYDXNu/vgrcvMoYE+WkGt6sJAPYunXrBqnamDJlSorHjRgxQvUCu0+nTp3K1nYSZanQ94HLR4H8JYB2HzHYRL5KpikrVAGIOuOq5yWinJHwFilSBGazGRcuXEi0Xy4XL1482b+R/Wk53p3sSt3uihUrUq3tCAwMVNcnPBH5hOPrgc23vux1/BLInXxZDxH5gIC8QOepgGYCds0D9i42ukVEOYahCW9AQADq16+P0NDQ+H0yaE0uN23aNNm/kf0JjxeS0CY83p3sHjp0CCtXrkThwoWz8FEQ5VCx14FfX3FtyzKklRPXvhORDyrTGLh/qGt7yVDgevIzHhH5G8NLGmRKsm+++QYzZ87Evn378NJLL6lZGPr166eulzl0peTAbciQIVi+fDnGjx+P/fv347333sO2bdvw6quvxie7Tz75pNo3e/ZsVSMs9b1ykkFyRH5j2VvAlWNAUCmWMhD5k5YjgJCaQPS/wOLBXJCCSMZ2Gh0FmWYsIiICo0aNUkmpTC8mCa17YNrJkyfVzA1uzZo1w5w5c/DOO+9g5MiRqFy5MhYtWoQaNWqo68+cOYPFi10/48htJbR69Wq0bNkyWx8fkSF2/+QarS0/bXb9CsgVzCeCyJ9mbegyFfimFXBwGRD+PVCvj9GtIvLveXhzIs7DS17tynFg6oNAbBTQ/C2g9X8SXV1u+FLDmkZEWTAPb0r+ngCsHA1Y8wADVgPFqjL85Lf5muE9vETkQQ478PMAV7JbujHQgiO1iXxRWr64aqiImdaaaI7d2D/pSXSOex8xCEx/4kzkAwyv4SUiD1o7Dji9BQgMBrp+A5j5nZbIX+kwYZjtZUTowahqOoXRlllGN4nIMEx4iXzF0bXAX5+6th//HChY1ugWEZHBLiEYQ2yvwKlr6GlZjY6m9UY3icgQTHiJfMHVU8BPMrOJDtR9BqjxhNEtIqIcYoOzBr50dFHb/7V+h3LaOaObRJTtmPASeTtbDPBjH9cURPfUBh651ctLRHTLRHtXbHJWQz4tBlOsE5EbMYwN+RUW+BF5+QCV/1q+wdOWMFzR8+Hx48/h9LursrVtRJTzOWHCkLhXsCTwP6hmOolPrF/hVdtgo5tFlG3Yw0vkxbqZV+Npy2pVnzfY9ipO60WNbhIR5VAXUAgD44YiTjfjMfNmvGzm0sPkP5jwEnmpWtoRfGCZobY/tT+Fdc5aRjeJiHK47XoVvGd/Vm2/YfkROPiH0U0iyhZMeIm8UAlcwrcB4xGo2fCnoz6mODoa3SQi8hJzHG0w294GJk0Hfn4euHTI6CYRZTkmvEReJh+iMS3gExTTrmKfswxes72s5tskIkqr9+x9sdV5r2uRmrk9gOjLDB75NH5KEnkRMxyYbP1CTSJ/QS+A5+LexA3kNrpZRORlbLDgpbjXgKBSwL+Hgbk9XTO+EPkoJrxEXkPHGMsMtDDvQrQeiP5xb+AcChvdKCLy4kUp0GuBa2XGU5uAhQMAp9PoZhFlCSa8RF7iBfMSPGMJVTMyyMpJe/QKRjeJiLxdSHWgx2zAHADsWwz8+R+jW0SUJZjwEnmB7ubVGGmdq7Y/svfCCmcDo5tERL6i/INA5ymu7U3/B2ycbHSLiDyOCS9RTrdnIcZavlWbU+2P4ztHB6NbRES+puaTwEPvu7b/GAmEzza6RUQepem6rnv2Jr1fVFQUgoODERkZiaCgIKObQ/7s4J/AvJ6A066mEfqP/Tn5b2t0q4jIJ+kYZfkez1mWw6FreM32ChY7m6X5r4+PezRLW0eUmXyNPbxEOdXx9cCPvVWy+6ujGd6192OyS0RZSMP79t6YY28Ns6bjM+v/oZ1pCyNOPoEJL1FOdPxvYPZTgD0GuLc9XrcNhJP/XYkoy2nql6SfHM1h0Zz40volWpvCGHfyekx4iXKaI6uAH54EbDeACi2Bp2bADovRrSIiPyEL2bxlewGLHU0RoDkwxTqBSS95PX6KEmWhcsOXpuv4VqZwTLVOUEsGr3LUwUt7n0Xsu6uyrH1ERMmRX5SG2V6CFXZ0MG/FV9bP8brtpXTV9BLlJOzhJcoh2pnkQ+UzlewudzTEi7ZhiEWA0c0iIj8lvywNsg3CL477YdUcmGCdjF7mlUY3iyhDmPAS5QBPm0Pxf9YJ6udD+RnxVdsgtfQnEZHRSa/09M6yPwSTpuMj6zQMNC/mk0JehwkvkYE0OPGWZR7+a/1OjYqeb2+JobZXWLNLRDmqpneU/VlMsndSl4db5+Fdy/cwgcsQk/dgwktkkADYMMH6f3jZ4uot+cz2JN62D+BsDESUA2n41N4dH9meVpf6W5bha+t45MVNoxtGlCZMeIkMUBBRmBUwDp3MG2DTzXg9biC+cHTlPLtElKN943gMr8QNRoxuRVtzOH4KGIMSuGR0s4juigkvUTaroR3Fb4HvoIlpH67pudHP9hZ+djbn80BEXmGpswl6xL2LCD0Y1Uwn8Wvgu6ijHTa6WUSpYsJLlI2eNK/FzwFjUEq7hOPOEDwZNxp/O2vyOSAir7JDr4TOse9jn7M0imqR+DFgDLD5K0DXjW4aUbKY8BJlU73uB5Zp+NT6lZp2bKWjLjrGfYgDehnGn4i80hkUxZNx72GZo6GaYQbL3gIWPAvERBndNKI7MOElymKVtNP4JWAUeltWwqlranDaANvriEJexp6IvNoN5MZLtqEYY+sNmCzA3kXA1y2B83uMbhpRIkx4ibKKrqOP+Q8sCfgP7jOdwGU9H/rb3lCD02SaHyIi36BhuqMD0G85EFQKuHwE+KYV8PcEwOkwunFECj91ibLCtQvAnG543zoTuTQb1jpqoV3sx1jtrMt4E5FvKt0QePEv4N72gCMOWDkamN4B+PeI0S0jYsJL5FFOJ7BtOjC5IXDoT8TqVrxn64NnbW8hAgUZbCLybXkLAz3nAR0nAQH5gVObgakPAJu/Zm8vGYo9vESeEnEAmPEIsGQoEBMJ3FMHj8d9iBmO9ixhICL/oWlAvd7AS+uBcg8Ctmhg2ZvAt22Bs+FGt478FBNeosyKvQaEvg9MuR84uRGw5gXajwMGrMJBvTTjS0T+qWBZoM9i4JFPgcAg4GwY8HUrYOnrwM0rRreO/Iym65w0L6moqCgEBwcjMjISQUFBhjwxZJxyw5em6ThZR76beQ1etyxQ81CKUEddvGvrh7MoksWtJCLyHkVxBSOtc9DFvF5dvqQHYaK9K+Y5WsMGS6Jjj4971KBWki/na4lfZUSUBjqam3ZhhGUOqplOqT3HnCEYa38afzobcHlgIqIkZAzDa7ZX8KOjJd63zEBl0xl8YJ2B/uZl+NTeDUudjVn6RVmKCS9ROhPdIZaFqG86pPZc1fOqXoofHA/d0UtBRESJbXTehw5xY9HDvFq9l5YzXcCkgC8xwLlUvZeu4kw2lEX4CU10VzpamnaqN+e6Jtd68TG6Fd87HsIke2dEIh9jSESURnZYVCfBQseD6G/+HS9alqC26SimBXyKfc4ywJ5YoHpnwGRmTMljWMObDNbw+jd3DW8uxKKL+W88Z16ufn4TN/UA/OBoi6/tjyECBQxuKRGR9yuMSAyw/I5nzCuQT4tx7SxUAWjyMlC7BxCY3+gmkg/ka0x4MxlA8j0PjpiGnubV6GlehYLadbXvmp4bcx2tVaJ7CcFGN5GIyOcE4Tr6mv/E60Ght2dxkLl86/QEGj4PFK1idBMph2HCm40BJB9huwnsXQyEfw8cXxe/+6SzKKY72mOBowWuI4+hTSQi8gfHx7QAdswGtnwD/OsaL6GUvR+o3ROo3gnIxc9mAhPezGLC6yccNuDoWuCfX4B9vwGxrqnFnLqGv501MNvRFiuc9eHkdNVERNkmfloymTX16Bpg67fAgd8B3enab8kFVH0MqNUNqNASsATy2fFTUZyWjCgFcdGuHlxJcPcvSTz5eYEyQJ1n8MDy4pxHl4goJ6zYVrGV6xR5Btg1H9g5F7h0ENjzk+skC1rc2w6o9jhQqS0QkNfoVlMOxRreZLCH15cWjNBRRruophNrbQpHM9M/yKXZ4q+N0IOwzNEYSx1NsEWvwnkgiYgMlurCE9LrKyu27ZznKkO7fv72deZAoGxToGJr1ymkhitpJp/FGt5sDCDltIRXRzntPJqY9qGxaZ86v0e7nOi4M3phrHLUxe/OxtjsrMaSBSIiL6TBibraYbQ3b0V70xaUMUUkuj5CD0bR2u1dtb+lGwNF7gVMJsPaS57HhDcbA0gGu/EvcC4cOBuOP1YsRx3TYYRoVxMdEqebEa5XxhpHHaxy1sEBvTRXQyMi8ik6Kmpn1a95D5j2oKlpL/JosYkPyRUMlGroSn5LNQCK1wbyFjaqweQBTHizMYCUTeyxwL+HgYv7gIgDQMQ+4NxO4OrJOw6N1S3YoVfCJmc11YMb5qyMGHBQAxGRvwiADfVMhzCvzU3g5GbgzHbAfvPOA/Pf4yp9KF7DdV6sOlCoPGDNbUSzKZ04aI28su42L26itBaBMtoFdV5au6jOpUShrHYBFu3WCN0kjjqLY7deAbuc5bHbWQE79YqIRUA2PgoiIspJ4mDFJmd1oM2jt2flubAHOLXFdZIE+Mox4No51+nwisQ3EFQKKFwBKFwJKFQRKFwRKFgOCCrhGijH2mCvkyOWFp48eTI++eQTnD9/HrVr18aXX36JRo0apXj8ggUL8O677+L48eOoXLkyPv74YzzyyCPx1+u6jtGjR+Obb77B1atXcf/992PKlCnqWMpmMsAg9hpwIwK4fsF1uibn54HrFzHTuhvFtKsI0S6j0K1FHlISpefBQb0UDjlL4pBeCvv10tjjLI8ocFQuERGlwmwFStR1nRq/6Nonn00X9gIXdgPn97gSYpkBIiYSiDrtOh37687bCsgHBJV0Jb/Bcl4SyFcMyFMEyFvk9nnuglweOQcxfJaG+fPno0+fPpg6dSoaN26MCRMmqIT2wIEDKFas2B3Hb9iwAc2bN8fYsWPx2GOPYc6cOSrhDQsLQ40aNdQxclmunzlzJsqXL6+S4927d2Pv3r3IlSvXXdvk9yUN8pJw2oG4G4At2nXuPqnL113Te6nLt/bfvArEXHVN83Xz1rm6fBXQHWl+PVzW8+GkXgyn9WLq/JReVJ0fcpbCRbWUL0fcEhFRVtFRENdQXjuvTuVMcn4Oj5WMBq6ecn2upZnmSnpV8lvItViGLJMcmPT81kmut+YFrLkAS+47zzngzrtreCXJbdiwISZNmqQuO51OlC5dGoMGDcLw4cPvOL579+64ceMGlixZEr+vSZMmqFOnjkqa5eGUKFECr7/+Ot544w11vQQiJCQEM2bMQI8ePXJewrv7JyD6X9ek2k6HK0FU506M/2MfzJoTGnSY4VQnkzrp8duucz1+O+nxVthVPVOrSgUAR5zrZL917oh1/dQjNbLx10mhv2dfFtF6IC7qBRCBYHV+US+ICDlHAXV+QS+I03oRrmZGREQ5Vm7EoLh2Bfdo/+IeXHada5dRRItEIS0KhXANhbUoFNBuePy+ZXyKlOvFyEm3qu3KxQsAZgtgsrp6sU2ybbm1bU1ynTnBtpxMgJb0ZE6wrbnO5e+SHmfNA9TrDaN5TQ1vXFwctm/fjhEjRsTvM5lMaNu2LTZu3Jjs38j+YcOGJdrXrl07LFq0SG0fO3ZMlUbIbbhJMCSxlr9NLuGNjY1VJzcJnDuQ2WL5WOByguUTExjgwbuJ2p/+v7HrJkQjENHIhWhd/qO5tm/qAWr/TbmsByIKeRCp58W1W+dRel5EwnV+FXkRl+aa2uj0N5KIiCgbSBp7BMHqBFRI8TgzHCiA6yioXUMh7RqCcQN5tZvIhxjkw03k1WKQF9HIr92+nB/RyI045NLkEzMOuWBDgJbwF1KZQ96GXLgB92/VUadOwwiX9CC0/D75X8z3jGmXbe1w52lp6bs1NOG9dOkSHA6H6n1NSC7v3598dibJbHLHy3739e59KR2TlJQ/jBkz5o790tNMRERERAldA9ANyQmegGx37do11bmZ4wetGU16mBP2GktZxeXLl1G4cGFoXjQSU77pSJJ+6tQpTqfG2HoNvm4ZW2/E1y3j6m2ifDBHkJ5dSXallPVuDE14ixQpArPZjAsXLiTaL5eLFy+e7N/I/tSOd5/LvnvuuSfRMVLnm5zAwEB1SqhAARkg5Z3khewrL+achrFlbL0RX7eMrbfha5axTau79ey6GbrGXkBAAOrXr4/Q0NBEvatyuWnTpsn+jexPeLxYsWJF/PEyK4MkvQmPkW81mzdvTvE2iYiIiMh3GV7SIKUEffv2RYMGDdTcuzItmczC0K9fP3W9TFlWsmRJVWcrhgwZghYtWmD8+PF49NFHMW/ePGzbtg1ff/21ul5KEIYOHYoPP/xQzbvrnpZMurs7d+5s6GMlIiIiIj9MeGWasYiICIwaNUoNKpOyg+XLl8cPOjt58qSaucGtWbNmau7dd955ByNHjlRJrczQ4J6DV7z11lsqaX7hhRfUwhMPPPCAus20zMHrzaQsQxbcSFqeQYxtTsbXLWPrjfi6ZVy9TaCf5wiGz8NLRERERJSVDK3hJSIiIiLKakx4iYiIiMinMeElIiIiIp/GhJeIiIiIfBoTXi8zZcoU1KpVK35SbplbeNmyZfHXt2zZUk3NlvA0cOBAQ9vsrcaNGxc/zZ1bTEwMXnnlFbUKX758+fDEE0/csRAKpT+ufN1m3HvvvXfH//mqVavyNZsNseXrNnPOnDmDZ555Rr2f5s6dGzVr1lTTjLrJmHqZwUkWkZLr27Zti0OHDmXyXv3D3WL77LPP3vHabt++PXyZ4dOSUfqUKlVKJQwyHZu8GcycOROdOnVCeHg47rvvPnXMgAED8P7778f/TZ48eRjmdNq6dSu++uor9eUioddeew1Lly7FggUL1Oour776Krp27Yr169czxpmIK1+3mSP/91euXBl/2WK5/dbO12zWxVbw/TZjrly5gvvvvx+tWrVSnTZFixZVyWzBggXjj/nf//6HL774Qn3OuefUb9euHfbu3evz04xmdWyFJLjTp0+Hm69PV8aE18s8/vjjiS5/9NFHqtd306ZN8QmvJLgpLc1Md3f9+nX06tUL33zzjVrAxC0yMhLfffedmge6devWap+8WVSrVk3Fv0mTJgxvBuLqxtdtxkkSltz/eb5msy62bnzdZszHH3+M0qVLJ0q4JKl1kw4dWYhK5tyXTh0xa9YsNUe/zL3fo0ePDN6z77tbbBMmuP6UK7CkwYs5HA610pwsspFw2eTZs2ejSJEiajGOESNGIDo62tB2ehspWZBV/OTns4S2b98Om82WaL/8vFmmTBls3LjRgJb6Rlzd+LrNOOm9kdUkK1SooL5UyII9gq/ZrIutG1+3GbN48WK1wupTTz2FYsWKoW7duurLsNuxY8fUYlQJ3y/kV7XGjRvz/TaTsXVbs2aNur5KlSp46aWX8O+//8KXsYfXC+3evVsluFJPKnWkv/zyC6pXr66ue/rpp1G2bFn1Br1r1y68/fbbOHDgABYuXGh0s72CfIEICwtTP70nJW++AQEBKFCgQKL90uMg11HG4ir4us04SQBmzJihPrTOnTuHMWPG4MEHH8SePXv4ms3C2ObPn5+v20w4evSo+nVy2LBhatVUeW8YPHiweo/t27dv/Huqe9VVN77fZj627nIGKceTnt8jR46o4zp06KC+TJjNZvgkWWmNvEtsbKx+6NAhfdu2bfrw4cP1IkWK6P/880+yx4aGhspKevrhw4ezvZ3e5uTJk3qxYsX0nTt3xu9r0aKFPmTIELU9e/ZsPSAg4I6/a9iwof7WW29la1t9Ka7J4es2465cuaIHBQXp3377LV+zWRjb5PB1m3ZWq1Vv2rRpon2DBg3SmzRporbXr1+vPrvOnj2b6JinnnpK79atWwaePf9xt9gm58iRIyreK1eu1H0VSxq8kHxLq1SpEurXr4+xY8eidu3amDhxYoo9FOLw4cPZ3ErvIz//Xrx4EfXq1VN1e3Jau3atGjQh29KzEBcXh6tXryb6O5mlwZ/qoDwdVynNSYqv24yTXyDuvfde9X9eXpd8zWZNbJPD123aycwL7l8m3WQ8hLtkxP2emnQWHL7fZj62yZGSHSmF9OVcgQmvD3A6nYiNjU32uh07dsT/B6DUtWnTRpWLSMzcJ6mDkro997bVakVoaGj830i5iLyJJKyhpvTFNbmfz/i6zdzgQPmJUv7Py5divmazJrbJ4es27WQWAXn/TOjgwYOqJE/IT+2S9CZ8v42KisLmzZv5fpvJ2Cbn9OnTqobXp3MFo7uYKX2khGHt2rX6sWPH9F27dqnLmqbpf/75pypbeP/991Wpg1z/66+/6hUqVNCbN2/OMGdQ0p/eBw4cqJcpU0ZftWqVirP8bJT0pyNKX1z5us2c119/XV+zZo36Py8/A7dt21aVOV28eJGv2SyMLV+3mbNlyxbdYrHoH330kSrRk5KxPHny6D/88EP8MePGjdMLFCigPsvk865Tp056+fLl9Zs3b2b2qfXr2F67dk1/44039I0bN6rXtpQx1KtXT69cubIeExOj+yomvF7mueee08uWLatqSYsWLaq3adNGJbvuWklJbgsVKqQHBgbqlSpV0t988009MjLS6Gb7TMIrb7Qvv/yyXrBgQfUG0qVLF/3cuXOGttHb48rXbeZ0795dv+eee9R7QsmSJdXlhDX7fM1mTWz5us283377Ta9Ro4b6vKpatar+9ddfJ7re6XTq7777rh4SEqKOkc+7AwcOeOCe/Tu20dHR+sMPP6xyCKn3lZxiwIAB+vnz53Vfpsk/RvcyExERERFlFdbwEhEREZFPY8JLRERERD6NCS8RERER+TQmvERERETk05jwEhEREZFPY8JLRERERD6NCS8RERER+TQmvERERETk05jwEhH5uJYtW2Lo0KFGN4OIyDBMeImIcrDHH38c7du3T/a6devWQdM07Nq1K9vbRUTkTZjwEhHlYP3798eKFStw+vTpO66bPn06GjRogFq1ahnSNiIib8GEl4goB3vsscdQtGhRzJgxI9H+69evY8GCBejcuTN69uyJkiVLIk+ePKhZsybmzp2b6m1Kr/CiRYsS7StQoECi+zh16hS6deum9hcqVAidOnXC8ePHPfzoiIiyBxNeIqIczGKxoE+fPioZ1XU9fr8kuw6HA8888wzq16+PpUuXYs+ePXjhhRfQu3dvbNmyJcP3abPZ0K5dO+TPn1+VTaxfvx758uVTpRVxcXEeemRERNmHCS8RUQ733HPP4ciRI1i7dm2icoYnnngCZcuWxRtvvIE6deqgQoUKGDRokEpMf/zxxwzf3/z58+F0OvHtt9+qHuNq1aqp+zt58iTWrFnjoUdFRJR9mPASEeVwVatWRbNmzTBt2jR1+fDhw6rnVep7pZf3gw8+UImplB5IT+wff/yhktOM2rlzp7oP6eGV25OT3HZMTIxKvImIvI3F6AYQEdHdSXIrvbeTJ09Wva0VK1ZEixYt8PHHH2PixImYMGGCSnrz5s2rpiBLrfRAangTlke4yxgS1gdLmcTs2bPv+FupJyYi8jZMeImIvIAMIBsyZAjmzJmDWbNm4aWXXlKJq9TXyoAyqeUVUopw8OBBVK9ePcXbkqT13Llz8ZcPHTqE6Ojo+Mv16tVTZQ3FihVDUFBQFj8yIqKsx5IGIiIvIGUF3bt3x4gRI1Sy+uyzz6r9lStXVtOWbdiwAfv27cOLL76ICxcupHpbrVu3xqRJkxAeHo5t27Zh4MCBsFqt8df36tULRYoUUYm0lE4cO3ZM1e4OHjw42enRiIhyOia8REReVNZw5coVNYNCiRIl1L533nlH9cjKPllRrXjx4mqqstSMHz8epUuXxoMPPoinn35aDXqTKc3cZPuvv/5CmTJl0LVrVzVoTe5banjZ40tE3kjTkxZyERERERH5EPbwEhEREZFPY8JLRERERD6NCS8RERER+TQmvERERETk05jwEhEREZFPY8JLRERERD6NCS8RERER+TQmvERERETk05jwEhEREZFPY8JLRERERD6NCS8RERERwZf9P7KkntGXgJL2AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,4))\n",
    "plt.hist(normal_sim, bins=30, density=True)\n",
    "plt.plot(x, pdf)\n",
    "plt.xlabel(\"Value\")\n",
    "plt.ylabel(\"Density\")\n",
    "plt.title(\"Normal: Simulation vs Theory\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc269da3",
   "metadata": {},
   "source": [
    "## Part 9 — Exponential Distribution\n",
    "\n",
    "The Exponential distribution is often used to model waiting times.\n",
    "\n",
    "If `X ~ Exponential(λ)`, then:\n",
    "- mean = `1/λ`\n",
    "\n",
    "Example:\n",
    "Suppose machine failures occur at rate `λ = 0.5` failures per hour.\n",
    "Then the average waiting time until the next failure is `1/0.5 = 2` hours."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "8917aabe",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean waiting time = 2.0\n",
      "P(X < 2) = 0.6321205588285577\n"
     ]
    }
   ],
   "source": [
    "lam = 0.5\n",
    "\n",
    "print(\"Mean waiting time =\", 1 / lam)\n",
    "print(\"P(X < 2) =\", expon.cdf(2, scale=1/lam))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "37a5afbd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0, 12, 400)\n",
    "pdf_exp = expon.pdf(x, scale=1/lam)\n",
    "\n",
    "plt.figure(figsize=(8,4))\n",
    "plt.plot(x, pdf_exp)\n",
    "plt.xlabel(\"Waiting time\")\n",
    "plt.ylabel(\"Density\")\n",
    "plt.title(\"Exponential Distribution\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "34e1dc63",
   "metadata": {},
   "source": [
    "## Part 10 — Central Limit Theorem\n",
    "\n",
    "The Central Limit Theorem states that the sampling distribution of the sample mean becomes approximately normal as the sample size increases.\n",
    "\n",
    "This is true even when the original population is not normal, provided the sample size is sufficiently large.\n",
    "\n",
    "We will demonstrate this using a strongly skewed population."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "cd561dd9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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SSy81Lcr0pq9Nf0b159KftmPTx1511VUBy++8806zXPd3SZ5//nknMTHRjLdRo0bO+eefb9p8aYs3l7b/mjRpku9n9vLLL3e2bt1q9lXR1lyzZ8926tevH/B6AZQuQv9TntALAJWls1ba3F+vxKSzwjWdnoiks9xbt271eighTT+e19lUnckMtUsbe0nfK/oz9Ic//MHroQBWoGYWQJXS+sKitOxAuw34nzwDPPzww6atlpZW4L+07lfDvZZGACgfamYBVCltkaQnr2i3AT2rXOsC9ab1ia1atWJvI6A1ltuLFf+ltcoa8AGUH2EWQJXSE7JWrFhhPkLWX8p6EQRtRv/oo4+ypwEAVY6aWQAAAFiLmlkAAABYizALAAAAa4VdzaxeGUYvM6mNs6uqgTsAAACqjnaOPXLkiLnQi3bDKUvYhVkNspxRDQAAEPpyc3PlrLPOKnOdsAuzOiPr7hy95CEAAABCS15enpl8dHNbWcIuzLqlBRpkCbMAAAChqzwloZwABgAAAGsRZgEAAGAtwiwAAACsRZgFAACAtQizAAAAsBZhFgAAANYizAIAAMBahFkAAABYizALAAAAaxFmAQAAYC3CLAAAAKwV6fUAwkH82MwKrZ+Tnhq0sQAAANQkzMwCAADAWoRZAAAAWIswCwAAAGsRZgEAAGAtwiwAAACsRZgFAACAtQizAAAAsBZhFgAAANYizAIAAMBahFkAAABYizALAAAAaxFmAQAAYC3CLAAAAKxFmAUAAIC1CLMAAACwFmEWAAAA1iLMAgAAwFqEWQAAAFiLMAsAAABrEWYBAABgLcIsAAAArEWYBQAAgLUIswAAALAWYRYAAADWIswCAADAWoRZAAAAWCskwuysWbMkPj5e6tWrJz179pR169aV63GvvfaaREREyKBBg4I+RgAAAIQez8Ps4sWLZfTo0TJx4kTZuHGjJCQkSEpKiuzbt6/Mx+Xk5MiYMWOkV69e1TZWAAAAhBbPw+yMGTNk5MiRMmLECOncubPMmTNH6tevL3Pnzi31MQUFBXLLLbfIpEmTpF27dtU6XgAAAIQOT8Nsfn6+bNiwQfr27fu/AdWqZe5nZWWV+rgnnnhCmjVrJnfccccpn+PEiROSl5cXcAMAAEDN4GmYPXDggJlljY2NDViu9/fs2VPiY95//3156aWX5IUXXijXc0yZMkUaN27su7Vq1apKxg4AAADveV5mUBFHjhyR2267zQTZmJiYcj1m3LhxcvjwYd8tNzc36OMEAABA9YgUD2kgrV27tuzduzdgud6Pi4srtv6OHTvMiV8DBgzwLSssLDRfIyMjJTs7W9q3bx/wmLp165obAAAAah5PZ2ajoqIkMTFRVq5cGRBO9X5ycnKx9Tt16iRbtmyRTZs2+W7XXnut9OnTx/ybEgIAAIDw4unMrNK2XGlpadK9e3dJSkqSjIwMOXbsmOluoIYNGyYtW7Y0ta/ah7ZLly4Bj2/SpIn5WnQ5AAAAaj7Pw+yQIUNk//79MmHCBHPSV7du3WTZsmW+k8J27txpOhwAAAAARUU4juNIGNHWXNrVQE8Gi46OrpbnjB+bWaH1c9JTgzYWAACAmpTXmPIEAACAtQizAAAAsBZhFgAAANYizAIAAMBahFkAAABYizALAAAAaxFmAQAAYC3CLAAAAKxFmAUAAIC1CLMAAACwFmEWAAAA1iLMAgAAwFqEWQAAAFiLMAsAAABrEWYBAABgLcIsAAAArEWYBQAAgLUIswAAALAWYRYAAADWIswCAADAWoRZAAAAWIswCwAAAGsRZgEAAGCtSK8HgOLix2aWe7fkpKeyCwEAQNhiZhYAAADWIswCAADAWoRZAAAAWIswCwAAAGsRZgEAAGAtwiwAAACsRZgFAACAtQizAAAAsBZhFgAAANYizAIAAMBahFkAAABYizALAAAAaxFmAQAAYC3CLAAAAKxFmAUAAIC1CLMAAACwFmEWAAAA1iLMAgAAwFqEWQAAAFiLMAsAAABrEWYBAABgLcIsAAAArEWYBQAAgLUIswAAALAWYRYAAADWIswCAADAWoRZAAAAWIswCwAAAGsRZgEAAGAtwiwAAACsRZgFAACAtUIizM6aNUvi4+OlXr160rNnT1m3bl2p67755pvSvXt3adKkiTRo0EC6desmL7/8crWOFwAAAKHB8zC7ePFiGT16tEycOFE2btwoCQkJkpKSIvv27Stx/aZNm8qjjz4qWVlZsnnzZhkxYoS5LV++vNrHDgAAAG9FOI7jeDkAnYnt0aOHzJw509wvLCyUVq1ayahRo2Ts2LHl2saFF14oqampMnny5FOum5eXJ40bN5bDhw9LdHS0VIf4sZlB23ZOemrQtg0AAOCFiuQ1T2dm8/PzZcOGDdK3b9//DahWLXNfZ15PRXP4ypUrJTs7Wy677LIS1zlx4oTZIf43AAAA1AyehtkDBw5IQUGBxMbGBizX+3v27Cn1cZrSGzZsKFFRUWZG9rnnnpNf/OIXJa47ZcoUk+zdm876AgAAoGbwvGa2Mho1aiSbNm2Sjz76SJ588klTc7t69eoS1x03bpwJv+4tNze32scLAACA4IgUD8XExEjt2rVl7969Acv1flxcXKmP01KEDh06mH9rN4Nt27aZGdjLL7+82Lp169Y1NwAAANQ8ns7MaplAYmKiqXt16Qlgej85Obnc29HHaG0sAAAAwounM7NKSwTS0tJM79ikpCTJyMiQY8eOmXZbatiwYdKyZUsz86r0q67bvn17E2Dfffdd02d29uzZHr8SAAAAhF2YHTJkiOzfv18mTJhgTvrSsoFly5b5TgrbuXOnKStwadC999575dtvv5XTTjtNOnXqJK+88orZDgAAAMKL531mqxt9ZgEAAEKbNX1mAQAAgJ+DMAsAAABrEWYBAABgLcIsAAAArEWYBQAAgLU8b82Fnyd+bGa5181JT2V3AwCAGoWZWQAAAFiLMAsAAABrEWYBAABgLcIsAAAArEWYBQAAgLUIswAAALAWYRYAAADhFWa/+uqrqh8JAAAAUB1htkOHDtKnTx955ZVX5KeffqrMJgAAAABvwuzGjRula9euMnr0aImLi5O77rpL1q1b9/NHAwAAAAQ7zHbr1k2eeeYZ2bVrl8ydO1d2794tl156qXTp0kVmzJgh+/fvr8xmAQAAgOo7ASwyMlKuu+46WbJkiUydOlW2b98uY8aMkVatWsmwYcNMyAUAAABCMsyuX79e7r33XmnevLmZkdUgu2PHDlmxYoWZtR04cGDVjRQAAAAoIlIqQYPrvHnzJDs7W66++mpZsGCB+Vqr1n+zcdu2bWX+/PkSHx9fmc0DAAAAwQuzs2fPlttvv12GDx9uZmVL0qxZM3nppZcqs3kAAAAgeGFWywhat27tm4l1OY4jubm55ntRUVGSlpZWmc0DAAAAwauZbd++vRw4cKDY8oMHD5oSAwAAACBkw6zOwJbk6NGjUq9evZ87JgAAAKDqywz0IgkqIiJCJkyYIPXr1/d9r6CgQP7973+bHrQAAABAyIXZjz/+2Dczu2XLFlMX69J/JyQkmPZcAAAAQMiF2VWrVpmvI0aMMFcAi46ODta4AAAAgOB0M9AeswAAAIA1YVYvW6sXQtDZWP13Wd58882qGBsAAABQNWG2cePG5sQv998AAACANWHWv7SAMgMAAABY22f2xx9/lOPHj/vuf/PNN5KRkSF///vfq3JsAAAAQNWH2YEDB8qCBQvMvw8dOiRJSUkyffp0s3z27NmV2SQAAABQPWF248aN0qtXL/Pv119/XeLi4szsrAbcZ599tjKbBAAAAKonzGqJQaNGjcy/tbRAuxvUqlVLLrroIhNqAQAAgJANsx06dJClS5dKbm6uLF++XPr162eW79u3jwspAAAAILTD7IQJE8xla+Pj46Vnz56SnJzsm6W94IILqnqMAAAAQNVdAez666+XSy+9VHbv3i0JCQm+5VdeeaX88pe/rMwmAQAAgOoJs0pP+tKbP+1qAAAAAIR0mD127Jikp6fLypUrTZ1sYWFhwPe/+uqrqhofAAAAULVh9s4775Q1a9bIbbfdJs2bN/dd5hYAAAAI+TD7t7/9TTIzM+WSSy6p+hEBAAAAwQyzp59+ujRt2rQyD4WH4sdmVmj9nPTUoI0FAADAs9ZckydPNu259OIJAAAAgFUzs9OnT5cdO3ZIbGys6TVbp06dYpe7BQAAAEIyzA4aNKjqRwIAAABUR5idOHFiZR4GAAAAeF8zqw4dOiQvvviijBs3Tg4ePOgrL/juu++qcnwAAABA1c7Mbt68Wfr27SuNGzeWnJwcGTlypOlu8Oabb8rOnTtlwYIFldksAAAAEPyZ2dGjR8vw4cPlyy+/lHr16vmWX3311bJ27drKbBIAAAConjD70UcfyV133VVsecuWLWXPnj2V2SQAAABQPWG2bt26kpeXV2z5F198IWeeeWZlNgkAAABUT5i99tpr5YknnpCTJ0+a+xEREaZW9re//a0MHjy4MpsEAAAAqifM6kUTjh49amZhf/zxR+ndu7d06NBBGjVqJE8++WRlNgkAAABUT5jVLgYrVqyQzMxMefbZZ+X++++Xd999V9asWSMNGjSo8PZmzZplriSmJ5P17NlT1q1bV+q6L7zwgvTq1UtOP/10c9OuCmWtDwAAgJqrwq25CgsLZf78+aYNl7bl0hKDtm3bSlxcnDiOY+5XxOLFi013hDlz5pggm5GRISkpKZKdnS3NmjUrtv7q1atl6NChcvHFF5vwO3XqVOnXr598+umn5gQ0AAAAhI8IRxNoOemqAwYMMLOwCQkJ0qlTJ7Ns27ZtsmXLFlNLu3Tp0goNQANsjx49ZObMmb6w3KpVKxk1apSMHTv2lI8vKCgwM7T6+GHDhp1yfT1xTWeWDx8+LNHR0VId4sdmio1y0lO9HgIAAAhDeRXIaxWamdUZWe0ju3LlSunTp0/A9/75z3/KoEGDzAUTyhMqVX5+vmzYsMFcRcxVq1YtUzqQlZVVrm0cP37cnIimF20oyYkTJ8zNVVIXBgAAAIRBzeyiRYvkkUceKRZk1RVXXGFmUl999dVyb+/AgQNmZjU2NjZgud4vb79a7aDQokULE4BLMmXKFJPs3ZvO+gIAACAMw6xexrZ///6lfv+qq66STz75RKpLenq6vPbaa/LWW28FXInMn8766hS1e8vNza228QEAACC4KlRmcPDgwWKzqP70ez/88EO5txcTEyO1a9eWvXv3BizX+3pCWVmefvppE2b/8Y9/SNeuXcu8wIPeAAAAEOYzs1oSEBlZev7VYPqf//yn3NuLioqSxMREU4Pr0hPA9H5ycnKpj3vqqadk8uTJsmzZMunevXsFXgEAAADCdmZWOxcMHz681JlO/xOtykvbcqWlpZlQmpSUZFpzHTt2TEaMGGG+ryeTacstrX1V2oprwoQJsnDhQtOb1q2tbdiwobkBAAAgfFQozGroPJXydjJwDRkyRPbv328CqgbTbt26mRlXt5xBL5OrHQ5cs2fPNl0Qrr/++oDtTJw4UR5//PEKPTcAAADCqM9sTUCf2fKjzywAAAj1vFapy9kCAAAAoYAwCwAAAGsRZgEAAGAtwiwAAACsRZgFAACAtQizAAAAsBZhFgAAANYizAIAACA8rgCG8BI/NrPc63KBBQAA4AVmZgEAAGAtwiwAAACsRZgFAACAtQizAAAAsBZhFgAAANYizAIAAMBahFkAAABYizALAAAAaxFmAQAAYC3CLAAAAKxFmAUAAIC1CLMAAACwFmEWAAAA1iLMAgAAwFqEWQAAAFiLMAsAAABrEWYBAABgLcIsAAAArEWYBQAAgLUIswAAALAWYRYAAADWivR6AKgZ4sdmlnvdnPTUoI4FAACED2ZmAQAAYC3CLAAAAKxFmAUAAIC1CLMAAACwFmEWAAAA1iLMAgAAwFqEWQAAAFiLMAsAAABrEWYBAABgLcIsAAAArEWYBQAAgLUIswAAALAWYRYAAADWIswCAADAWoRZAAAAWIswCwAAAGsRZgEAAGAtwiwAAACsRZgFAACAtQizAAAAsBZhFgAAANaK9HoACD/xYzPLvW5OempQxwIAAOzGzCwAAACsRZgFAACAtTwPs7NmzZL4+HipV6+e9OzZU9atW1fqup9++qkMHjzYrB8RESEZGRnVOlYAAACEFk/D7OLFi2X06NEyceJE2bhxoyQkJEhKSors27evxPWPHz8u7dq1k/T0dImLi6v28QIAACC0eBpmZ8yYISNHjpQRI0ZI586dZc6cOVK/fn2ZO3duiev36NFDpk2bJjfddJPUrVu32scLAACA0OJZmM3Pz5cNGzZI3759/zeYWrXM/aysrCp7nhMnTkheXl7ADQAAADWDZ2H2wIEDUlBQILGxsQHL9f6ePXuq7HmmTJkijRs39t1atWpVZdsGAABAmJ8AFmzjxo2Tw4cP+265ubleDwkAAAC2XzQhJiZGateuLXv37g1Yrver8uQura2lvhYAAKBm8mxmNioqShITE2XlypW+ZYWFheZ+cnKyV8MCAACARTy9nK225UpLS5Pu3btLUlKS6Rt77Ngx091ADRs2TFq2bGnqXt2Txj777DPfv7/77jvZtGmTNGzYUDp06ODlSwEAAEC4hdkhQ4bI/v37ZcKECeakr27dusmyZct8J4Xt3LnTdDhw7dq1Sy644ALf/aefftrcevfuLatXr/bkNQAAAMA7EY7jOBJGtDWXdjXQk8Gio6Or5Tnjx2ZWy/NAJCc9ld0AAEAY5bUa380AAAAANRdhFgAAANYizAIAAMBahFkAAABYizALAAAAaxFmAQAAYC3CLAAAAKxFmAUAAIC1CLMAAACwFmEWAAAA1iLMAgAAwFqEWQAAAFgr0usBAFUpfmxmudfNSU9l5wMAYDlmZgEAAGAtwiwAAACsRZgFAACAtQizAAAAsBZhFgAAANYizAIAAMBahFkAAABYiz6zCFv0pAUAwH7MzAIAAMBahFkAAABYizALAAAAaxFmAQAAYC3CLAAAAKxFmAUAAIC1CLMAAACwFmEWAAAA1uKiCUA5cIEFAABCEzOzAAAAsBZhFgAAANYizAIAAMBahFkAAABYizALAAAAa9HNAPCw84HKSU/lGAAAUEnMzAIAAMBahFkAAABYizALAAAAaxFmAQAAYC1OAAM8xqVyAQCoPGZmAQAAYC3CLAAAAKxFmAUAAIC1qJkFLEJ9LQAAgZiZBQAAgLUIswAAALAWZQZADVWRkgSVk54atLEAABAszMwCAADAWszMAjA4uQwAYCNmZgEAAGAtZmYBVBizuACAUMHMLAAAAKzFzCyAoGIWFwAQTIRZACGDdmIAACvD7KxZs2TatGmyZ88eSUhIkOeee06SkpJKXX/JkiUyfvx4ycnJkY4dO8rUqVPl6quvrtYxA/Aes74AAM/D7OLFi2X06NEyZ84c6dmzp2RkZEhKSopkZ2dLs2bNiq3/wQcfyNChQ2XKlClyzTXXyMKFC2XQoEGyceNG6dKliyevAUDNm/UtLy42AQDeinAcx/FyABpge/ToITNnzjT3CwsLpVWrVjJq1CgZO3ZssfWHDBkix44dk3feece37KKLLpJu3bqZQHwqeXl50rhxYzl8+LBER0eLzb9EAdRsBGUA4SqvAnnN05nZ/Px82bBhg4wbN863rFatWtK3b1/Jysoq8TG6XGdy/elM7tKlS0tc/8SJE+bm0p3i7qTqUnjieLU9F4Cao/XDS7wegrW2TkrxeggAfgY3p5VnztXTMHvgwAEpKCiQ2NjYgOV6//PPPy/xMVpXW9L6urwkWo4wadKkYst19hcAUDM1zvB6BACqwpEjR8wMbUjXzAabzvr6z+RqGcPBgwfljDPOkIiIiGr5y0KDc25ubrWVNcAbHOvwwvEOHxzr8MGxDh06I6tBtkWLFqdc19MwGxMTI7Vr15a9e/cGLNf7cXFxJT5Gl1dk/bp165qbvyZNmkh10yBLmA0PHOvwwvEOHxzr8MGxDg2nmpENiSuARUVFSWJioqxcuTJg5lTvJycnl/gYXe6/vlqxYkWp6wMAAKDm8rzMQEsA0tLSpHv37qa3rLbm0m4FI0aMMN8fNmyYtGzZ0tS+qgcffFB69+4t06dPl9TUVHnttddk/fr18vzzz3v8SgAAABB2YVZbbe3fv18mTJhgTuLSFlvLli3zneS1c+dO0+HAdfHFF5veso899pg88sgj5qIJ2skgVHvMaonDxIkTi5U6oObhWIcXjnf44FiHD461nTzvMwsAAABUlqc1swAAAMDPQZgFAACAtQizAAAAsBZhFgAAANYizAbZrFmzJD4+XurVqyc9e/aUdevWBfspUc0ef/xxczU5/1unTp04DjXA2rVrZcCAAeYKNHpctXOKPz1/VjuxNG/eXE477TTp27evfPnll56NF8E71sOHDy/2Pu/fvz+73ELa6rNHjx7SqFEjadasmQwaNEiys7MD1vnpp5/kvvvuM1cLbdiwoQwePLjYBZsQOgizQbR48WLTR1dbc23cuFESEhIkJSVF9u3bF8ynhQfOO+882b17t+/2/vvvcxxqAO15re9b/aO0JE899ZQ8++yzMmfOHPn3v/8tDRo0MO9x/UWImnWslYZX//f5okWLqnWMqBpr1qwxQfXDDz80F106efKk9OvXz/wMuB5++GH561//KkuWLDHr79q1S6677joOQajS1lwIjqSkJOe+++7z3S8oKHBatGjhTJkyhV1eg0ycONFJSEjwehgIMv3f5VtvveW7X1hY6MTFxTnTpk3zLTt06JBTt25dZ9GiRRyPGnSsVVpamjNw4EDPxoTg2bdvnznma9as8b2P69Sp4yxZssS3zrZt28w6WVlZHIoQxMxskOTn58uGDRvMx44uvfiD3s/KygrW08Ij+tGyfjzZrl07ueWWW8zFPlCzff311+ZCL/7vcb2OuJYT8R6vmVavXm0+lj7nnHPknnvuke+//97rIaEKHD582Hxt2rSp+aq/u3W21v+9raVjrVu35r0dogizQXLgwAEpKCjwXcnMpff1FyBqDg0v8+fPN1eumz17tgk5vXr1kiNHjng9NASR+z7mPR4etMRgwYIFsnLlSpk6dar56Pmqq64y/5+HvQoLC+Whhx6SSy65xHclUX1vR0VFSZMmTQLW5fd36PL8craA7fQXmqtr164m3LZp00b+8pe/yB133OHp2ABUjZtuusn37/PPP9+819u3b29ma6+88kp2s6W0dnbr1q2c52A5ZmaDJCYmRmrXrl3s7Ee9HxcXF6ynRQjQv+bPPvts2b59u9dDQRC572Pe4+FJS4r0//O8z+11//33yzvvvCOrVq2Ss846K+C9raWChw4dClif39+hizAbJPoRRWJiovlIyv/jDL2fnJwcrKdFCDh69Kjs2LHDtGtCzdW2bVvzS8//PZ6Xl2e6GvAer/m+/fZbUzPL+9w+eo6fBtm33npL/vnPf5r3sj/93V2nTp2A97a27tJzIXhvhybKDIJI23KlpaVJ9+7dJSkpSTIyMkzrjxEjRgTzaVHNxowZY/pTammBtm/RVmw6Kz906FCORQ34w8R/5k3roTdt2mROFNGTQbTW7ne/+5107NjR/EIcP368ORFQ+1ai5hxrvU2aNMn0GtU/YPSP1d/85jfSoUMH04oN9pUWLFy4UN5++23Ta9atf9cTOLVftH7VEjH9Ha7HPjo6WkaNGmWC7EUXXeT18FESr9sp1HTPPfec07p1aycqKsq06vrwww+9HhKq2JAhQ5zmzZubY9yyZUtzf/v27eznGmDVqlWmHU/Rm7ZpcttzjR8/3omNjTUtua688konOzvb62Gjio/18ePHnX79+jlnnnmmadnUpk0bZ+TIkc6ePXvY1xYq6Tjrbd68eb51fvzxR+fee+91Tj/9dKd+/frOL3/5S2f37t2ejhuli9D/lJhyAQAAgBBHzSwAAACsRZgFAACAtQizAAAAsBZhFgAAANYizAIAAMBahFkAAABYizALAAAAaxFmAQAAYC3CLABY7PLLLzeX1QWAcEWYBQCPDBgwQPr371/i99577z2JiIiQzZs3V/u4AMAmhFkA8Mgdd9whK1askG+//bbY9+bNmyfdu3eXrl27ejI2ALAFYRYAPHLNNdfImWeeKfPnzw9YfvToUVmyZIkMGjRIhg4dKi1btpT69evL+eefL4sWLSpzmzqbu3Tp0oBlTZo0CXiO3NxcufHGG83ypk2bysCBAyUnJ6eKXx0AVA/CLAB4JDIyUoYNG2aCpuM4vuUaZAsKCuTWW2+VxMREyczMlK1bt8qvfvUrue2222TdunWVfs6TJ09KSkqKNGrUyJQy/Otf/5KGDRuacof8/PwqemUAUH0IswDgodtvv1127Ngha9asCSgxGDx4sLRp00bGjBkj3bp1k3bt2smoUaNM6PzLX/5S6edbvHixFBYWyosvvmhmes8991zzfDt37pTVq1dX0asCgOpDmAUAD3Xq1EkuvvhimTt3rrm/fft2M2Oq9bQ6Ozt58mQTOrUcQGdQly9fboJnZX3yySfmOXRmVrenN932Tz/9ZEI1ANgm0usBAEC40+Cqs66zZs0ys6Tt27eX3r17y9SpU+WZZ56RjIwME2gbNGhg2nCVVQ6gNbP+JQtuaYF/Pa6WLrz66qvFHqv1uwBgG8IsAHhMT8Z68MEHZeHChbJgwQK55557TCjVelY9OUtrZ5WWB3zxxRfSuXPnUrelgXT37t2++19++aUcP37cd//CCy80pQbNmjWT6OjoIL8yAAg+ygwAwGP6Uf+QIUNk3LhxJogOHz7cLO/YsaNp3fXBBx/Itm3b5K677pK9e/eWua0rrrhCZs6cKR9//LGsX79e7r77bqlTp47v+7fccovExMSYkKzlDF9//bWplX3ggQdKbBEGAKGOMAsAIVJq8MMPP5hOAy1atDDLHnvsMTOTqsv0Sl9xcXGmXVdZpk+fLq1atZJevXrJzTffbE4g07ZeLv332rVrpXXr1nLdddeZE8D0ubVmlplaADaKcIoWVwEAAACWYGYWAAAA1iLMAgAAwFqEWQAAAFiLMAsAAABrEWYBAABgLcIsAAAArEWYBQAAgLUIswAAALAWYRYAAADWIswCAADAWoRZAAAAiK3+H3sbjceOP6n6AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "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.xlabel(\"Value\")\n",
    "plt.ylabel(\"Density\")\n",
    "plt.title(\"Original Population (Skewed)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "74402ec4",
   "metadata": {},
   "source": [
    "## Part 11 — Sampling Distribution of the Mean\n",
    "\n",
    "We now repeatedly draw samples and compute their means.\n",
    "\n",
    "We will compare:\n",
    "- sample size `n = 5`\n",
    "- sample size `n = 30`\n",
    "- sample size `n = 100`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "d1dc040d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def sample_means(population, sample_size, n_reps=5000):\n",
    "    means = []\n",
    "    for _ in range(n_reps):\n",
    "        sample = np.random.choice(population, size=sample_size, replace=True)\n",
    "        means.append(sample.mean())\n",
    "    return np.array(means)\n",
    "\n",
    "means_5 = sample_means(population, 5)\n",
    "means_30 = sample_means(population, 30)\n",
    "means_100 = sample_means(population, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "d2c74f8f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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0XOj8n665QPND26kBW0OOjmD+/e9/NwdL6UGBnu3SA5p0MnjtHx3Z08eVcRdqXtqmB2DpiLNO36Qf/Pp6077TvtJQ5q8zJ8XHx5uTCmg414PL9KA+LdnQkTM9oUB+zoqmI4kagvV9onsP9Da17jYvtbca1vW9pOFTv0Dpe0yDnY6U6+tEp+rSuvW8GDZsWK6miNO6bH0+9cusjgxrqNaRal3vmqO4MN/zeta1Z555xszfqlNf+Yu/amb1S5fWJevBiq7T12o/6Zd+DbLa/ox1x7rXQafuAvwq1/MeAMXIBx984AwePNhp3LixmQ5Jp77SKX50mqqMU8q8++67TosWLZzw8HAzpdGYMWOcmTNn+pwKS6fRysjXtEeuaZfGjRvnXqdT3pQtW9bZs2eP061bN6dMmTJORESEmYrIcxqlvEzN5as9GaeKUjotV8eOHc2UQldddZWTlJTkvPLKK+Y2Dx06lKupklyL9pPeRo8ePUw/nT9/PtN1Mk7NtWjRIvOYa9SoYZ6LOnXqOEOHDnUOHjzodb0ZM2aY6ZF0SjXPqbCyeqzZTc21bt065/e//71TuXJl8xoYMGCAmZLMk/a7TktUrVo183zo9Ew6pVLG28yubb76W19jOoWU3q4+3ubNm5t25fQacclqeqyM9LXUt29fp1KlSuZ5iY6OdpYsWeLz9nIzNZfSqed0qi1tt2c7XK/frF4fGU2fPt3cjk5bV758edMHOkXegQMHLmsquOwek06Bpu/fpk2bmte6PvfahlGjRjmnTp3y23ve13Pui74OSpYsaaYNy3h9bWNO75uCptPq3XvvveZvo77+tc+0XTr9lq9pDKdMmWK2c00vB/hLiP7j33gMoCDoSJ2O0OV2IvOC9thjj5kRRG1PoE+VCxRVeiY4rYv/6KOPxHY6iqsnBNED5QB/omYWQI60ZjBjDaseTKO73QmyQMHRWVN0flzX2e5speVRWiqiZxEE/I2aWQA50gM2dERF61P1NKivvvqqqePTmQQAFBytTdcDrWynNbTBslcJRQ9hFkCujnzXEgc90l0P+NLzxWugvfHGG+k9AEBAUTMLAAAAa1EzCwAAAGsRZgEAAGCtYlczq6eIPHDggJl43N+nvwQAAMDl05lj9QxzV155ZY4ncSl2YVaDbO3atQPdDAAAAOQgJSXFnPkxO8UuzLpOBamd48/TAwIAAMA/dPpHHXzMzSm8i12YdZUWaJAlzAIAAASv3JSEcgAYAAAArEWYBQAAgLUIswAAALAWYRYAAADWIswCAADAWoRZAAAAWIswCwAAAGsRZgEAAGAtwiwAAACsFRRhdvLkyRIVFSXh4eHSvn172bx5c5bbzp4925wNwnPR6wEAAKD4CXiYXbBggQwfPlwSExNl27Zt0rJlS4mNjZUjR45keR09De3Bgwfdy759+wq1zQAAAAgOJQPdgAkTJsiQIUNk0KBB5vLUqVNl6dKlMnPmTImPj/d5HR2NjYyMLOSWoiiIil+ar+vtHd3d720BAACWj8xeuHBBtm7dKl27dv21QSVKmMubNm3K8npnzpyRunXrSu3ataVnz57y5ZdfZrltWlqapKamei0AAAAoGgIaZo8dOyaXLl2SiIgIr/V6+dChQz6v06hRIzNq+84778i8efMkPT1dOnToID/++KPP7ZOSkqRixYruRQMwAAAAioaA18zmVUxMjAwcOFBatWolnTp1ksWLF0v16tVl2rRpPrdPSEiQU6dOuZeUlJRCbzMAAACKYM1stWrVJDQ0VA4fPuy1Xi/ntib2iiuukNatW8vu3bt9/j4sLMwsAAAAKHoCOjJbqlQpadOmjaxevdq9TssG9LKOwOaGlil88cUXUrNmzQJsKQAAAIJRwGcz0Gm54uLipG3bthIdHS3Jycly9uxZ9+wGWlJQq1YtU/uqnn/+ebnuuuukYcOGcvLkSRk3bpyZmuvBBx8M8CMBAABAsQuz/fr1k6NHj8rIkSPNQV9aC7ts2TL3QWH79+83Mxy4nDhxwkzlpdtWrlzZjOxu3LhRmjRpEsBHgfxiqiwAAHA5QhzHcaQY0am5dFYDPRhMT76A4hVmCc8AABStvGbdbAYAAACAC2EWAAAA1iLMAgAAwFqEWQAAAFiLMAsAAABrEWYBAABgLcIsAAAArEWYBQAAgLUIswAAALBWwE9nCxTmmbwAAEDRwsgsAAAArEWYBQAAgLUIswAAALAWYRYAAADWIswCAADAWoRZAAAAWIswCwAAAGsRZgEAAGAtwiwAAACsxRnAgAI849je0d3pXwAAChAjswAAALAWYRYAAADWIswCAADAWoRZAAAAWIswCwAAAGsRZgEAAGAtwiwAAACsRZgFAACAtQizAAAAsBZhFgAAANYizAIAAMBahFkAAABYizALAAAAaxFmAQAAYC3CLAAAAKxFmAUAAIC1CLMAAACwFmEWAAAA1iLMAgAAwFqEWQAAAFiLMAsAAABrEWYBAABgLcIsAAAArEWYBQAAgLVKBroBQFEWFb80X9fbO7q739sCAEBRxMgsAAAArEWYBQAAgLWCIsxOnjxZoqKiJDw8XNq3by+bN2/O1fXmz58vISEh0qtXrwJvIwAAAIJPwMPsggULZPjw4ZKYmCjbtm2Tli1bSmxsrBw5ciTb6+3du1dGjBghHTt2LLS2AgAAILgEPMxOmDBBhgwZIoMGDZImTZrI1KlTpUyZMjJz5swsr3Pp0iUZMGCAjBo1SurXr1+o7QUAAEDwCGiYvXDhgmzdulW6du36a4NKlDCXN23alOX1nn/+ealRo4Y88MADOd5HWlqapKamei0AAAAoGgIaZo8dO2ZGWSMiIrzW6+VDhw75vM7HH38sr776qsyYMSNX95GUlCQVK1Z0L7Vr1/ZL2wEAABB4AS8zyIvTp0/LfffdZ4JstWrVcnWdhIQEOXXqlHtJSUkp8HYCAACgGJw0QQNpaGioHD582Gu9Xo6MjMy0/Z49e8yBX7fffrt7XXp6uvm/ZMmSsmvXLmnQoIHXdcLCwswCAACAoiegI7OlSpWSNm3ayOrVq73CqV6OiYnJtH3jxo3liy++kB07driXO+64Qzp37mx+poQAAACgeAn46Wx1Wq64uDhp27atREdHS3Jyspw9e9bMbqAGDhwotWrVMrWvOg9ts2bNvK5fqVIl83/G9QAAACj6Ah5m+/XrJ0ePHpWRI0eag75atWoly5Ytcx8Utn//fjPDAQAAAJBRiOM4jhQjOjWXzmqgB4NVqFAh0M0p9qLilxb7PvBl7+ju9AsAoNhKzUNeY8gTAAAA1iLMAgAAwFqEWQAAAFiLMAsAAABrEWYBAABgLcIsAAAArEWYBQAAgLUCftIEFA3MFwsAAAKBkVkAAABYizALAAAAaxFmAQAAYC3CLAAAAKxFmAUAAIC1mM0AKEKzQ+wd3d3vbQEAIJgxMgsAAABrEWYBAABgLcIsAAAArEWYBQAAgLUIswAAALAWYRYAAADWIswCAADAWoRZAAAAWIswCwAAAGsRZgEAAGAtwiwAAACsRZgFAACAtQizAAAAsBZhFgAAANYizAIAAMBahFkAAABYizALAAAAaxFmAQAAYC3CLAAAAKxFmAUAAIC1CLMAAACwFmEWAAAA1iLMAgAAwFqEWQAAAFiLMAsAAABrEWYBAABgLcIsAAAArEWYBQAAgLUIswAAALAWYRYAAADWIswCAADAWoRZAAAAWIswCwAAAGuVDHQDEFyi4pcGugkI0PO3d3R3+h4AYJ2gGJmdPHmyREVFSXh4uLRv3142b96c5baLFy+Wtm3bSqVKlaRs2bLSqlUrmTt3bqG2FwAAAMEh4GF2wYIFMnz4cElMTJRt27ZJy5YtJTY2Vo4cOeJz+ypVqsgzzzwjmzZtks8//1wGDRpkluXLlxd62wEAAGBhmP3+++/91oAJEybIkCFDTCBt0qSJTJ06VcqUKSMzZ870uf1vf/tb6d27t1xzzTXSoEEDGTZsmLRo0UI+/vhjv7UJAAAARTjMNmzYUDp37izz5s2T8+fP5/vOL1y4IFu3bpWuXbv+2qASJcxlHXnNieM4snr1atm1a5fceOONPrdJS0uT1NRUrwUAAADFOMxqOYCOhmp5QGRkpAwdOjTbOtesHDt2TC5duiQRERFe6/XyoUOHsrzeqVOnpFy5clKqVCnp3r27TJw4UW6++Waf2yYlJUnFihXdS+3atfPcTgAAABShMKsHXb388sty4MABUw5w8OBBueGGG6RZs2ambODo0aNSkMqXLy87duyQLVu2yIsvvmhC9dq1a31um5CQYMKva0lJSSnQtgEAAMCSA8BKliwpd955pyxcuFDGjBkju3fvlhEjRpjRz4EDB5qQm51q1apJaGioHD582Gu9XtYR3ywbXaKEKXXQUP3EE09I3759zQisL2FhYVKhQgWvBQAAAEXDZYXZzz77TB566CGpWbOmGZHVILtnzx5ZuXKlGbXt2bNnttfXMoE2bdqYuleX9PR0czkmJibX7dDraG0sAAAAipd8nTRBg+usWbPMgVe33XabzJkzx/yvI6aqXr16Mnv2bDN3bE60RCAuLs7MHRsdHS3Jycly9uxZM7uB0hHeWrVquUde9X/dVmcy0AD7/vvvm3lmp0yZkp+HAgAAgOIWZjU4Dh48WO6//34zKutLjRo15NVXX83xtvr162dqbEeOHGkO+tLSgWXLlrkPCtu/f787JCsNujoa/OOPP0rp0qWlcePGZlYFvR0AAAAULyGOzm+VR3v37pU6dep4hUylN6UHWOnvgpVOzaWzGujBYNTPZsbpbIsvTmcLALAxr+WrZlZ38eu0WhkdP37clBgAAAAAhSFfYTarwdwzZ85IeHj45bYJAAAA8H/NrB6spUJCQkyNq5521kVPfvDpp5+amlcAAAAg6MLs9u3b3SOzX3zxhZlay0V/btmypZmeCwAAAAi6MLtmzRrzv06bpWcA4wAqAAAAWDc1l84xCwAAAFgTZvW0tXoiBB2N1Z+zs3jxYn+0DQAAAPBPmNW5vvTAL9fPAAAAgDVh1rO0gDIDAAAAWDvP7H/+8x85d+6c+/K+ffskOTlZVqxY4c+2AQAAAP4Psz179pQ5c+aYn0+ePCnR0dEyfvx4s37KlCn5uUkAAACgcMLstm3bpGPHjubnRYsWSWRkpBmd1YD7yiuv5OcmAQAAgMIJs1piUL58efOzlhbo7AYlSpSQ6667zoRaAAAAIGjDbMOGDeXtt9+WlJQUWb58uXTr1s2sP3LkCCdSAAAAQHCH2ZEjR5rT1kZFRUn79u0lJibGPUrbunVrf7cRAAAA8N8ZwPr27Ss33HCDHDx4UFq2bOle36VLF+ndu3d+bhIAAAAonDCr9KAvXTzprAYAAABAUIfZs2fPyujRo2X16tWmTjY9Pd3r999//72/2gcAAAD4N8w++OCDsm7dOrnvvvukZs2a7tPcAgAAAEEfZj/44ANZunSpXH/99f5vEQAAAFCQsxlUrlxZqlSpkp+rAgAAAIENsy+88IKZnktPngAAAABYVWYwfvx42bNnj0RERJi5Zq+44opMp7sFAAAAgjLM9urVy/8tAQAAAAojzCYmJubnagAAAEDga2bVyZMn5R//+IckJCTI8ePH3eUFP/30kz/bBwAAAPh3ZPbzzz+Xrl27SsWKFWXv3r0yZMgQM7vB4sWLZf/+/TJnzpz83CwAAABQ8COzw4cPl/vvv1++++47CQ8Pd6+/7bbbZP369fm5SQAAAKBwwuyWLVtk6NChmdbXqlVLDh06lJ+bBAAAAAonzIaFhUlqamqm9d9++61Ur149PzcJAAAAFE6YveOOO+T555+XixcvmsshISGmVvapp56SPn365OcmAQAAgDwLcRzHyeuVTp06JX379jXlBmfOnJErr7zSlBfExMTI+++/L2XLlpVgpSPKeuCaPoYKFSoEujlBJyp+aaCbAMvsHd090E0AABQxeclr+ZrNQG985cqVsmHDBtm5c6cJtNdee62Z4QAAAAAoLHkOs+np6TJ79mwzDZdOy6UlBvXq1ZPIyEjRQV69DAAAAARdzayGVa2XffDBB83JEZo3by5NmzaVffv2mam6evfuXXAtBQAAAC5nZFZHZHUe2dWrV0vnzp29fvfhhx9Kr169zAkTBg4cmJebBQAAAAp+ZPaNN96Qp59+OlOQVTfddJPEx8fLa6+9lr+WAAAAAAUZZvU0trfcckuWv7/11lvNAWEAAABA0IXZ48ePS0RERJa/19+dOHHCH+0CAAAA/Fsze+nSJSlZMuurhIaGyi+//JKXmwRQTOcmZn5aAEChh1mdzUBnLdDT2fqSlpbml0YBAAAAfg+zcXFxOW7DTAYAAAAIyjA7a9asgmsJAAAAUJAHgAEAAADBhDALAAAAaxFmAQAAYC3CLAAAAKwVFGF28uTJEhUVJeHh4dK+fXvZvHlzltvOmDFDOnbsKJUrVzZL165ds90eAAAARVfAw+yCBQtk+PDhkpiYKNu2bZOWLVtKbGysHDlyxOf2a9eulf79+8uaNWtk06ZNUrt2benWrZv89NNPhd52AAAABFaIo2dCCCAdiW3Xrp1MmjTJXE5PTzcB9ZFHHpH4+PhcnZVMR2j1+rmZ4zY1NVUqVqwop06dkgoVKvjlMRQl+T2bE5BXnAEMAOCPvBbQkdkLFy7I1q1bTamAu0ElSpjLOuqaG+fOnZOLFy9KlSpVsjwrmXaI5wIAAICiIaBh9tixY2ZkNSIiwmu9Xj506FCubuOpp56SK6+80isQe0pKSjLJ3rXoqC8AAACKhoDXzF6O0aNHy/z58+Wtt94yB4/5kpCQYIaoXUtKSkqhtxMAAABBcDpbf6tWrZqEhobK4cOHvdbr5cjIyGyv+9JLL5kwu2rVKmnRokWW24WFhZkFAAAARU9AR2ZLlSolbdq0kdWrV7vX6QFgejkmJibL640dO1ZeeOEFWbZsmbRt27aQWgsAAIBgE9CRWaXTcsXFxZlQGh0dLcnJyXL27FkZNGiQ+b3OUFCrVi1T+6rGjBkjI0eOlNdff93MTeuqrS1XrpxZAAAAUHwEPMz269dPjh49agKqBtNWrVqZEVfXQWH79+83Mxy4TJkyxcyC0LdvX6/b0Xlqn3vuuUJvPwAAAIrxPLOFjXlms8c8sygszDMLALB+nlkAAADgchBmAQAAYC3CLAAAAKxFmAUAAIC1CLMAAACwFmEWAAAA1iLMAgAAwFqEWQAAAFiLMAsAAABrEWYBAABgLcIsAAAArEWYBQAAgLUIswAAALBWyUA3AAUjKn4pXQsAAIo8RmYBAABgLcIsAAAArEWYBQAAgLWomQVgVV333tHd/d4WAIC9GJkFAACAtQizAAAAsBZhFgAAANYizAIAAMBahFkAAABYizALAAAAaxFmAQAAYC3CLAAAAKxFmAUAAIC1CLMAAACwFmEWAAAA1iLMAgAAwFqEWQAAAFiLMAsAAABrEWYBAABgLcIsAAAArEWYBQAAgLUIswAAALAWYRYAAADWKhnoBgBAXkTFL81Xh+0d3Z2OBoAiiJFZAAAAWIswCwAAAGsRZgEAAGAtwiwAAACsRZgFAACAtQizAAAAsBZhFgAAANYizAIAAMBahFkAAABYK+BhdvLkyRIVFSXh4eHSvn172bx5c5bbfvnll9KnTx+zfUhIiCQnJxdqWwEAABBcAhpmFyxYIMOHD5fExETZtm2btGzZUmJjY+XIkSM+tz937pzUr19fRo8eLZGRkYXeXgAAAASXgIbZCRMmyJAhQ2TQoEHSpEkTmTp1qpQpU0Zmzpzpc/t27drJuHHj5J577pGwsLBCby8AAACCS8DC7IULF2Tr1q3StWvXXxtTooS5vGnTJr/dT1pamqSmpnotAAAAKBoCFmaPHTsmly5dkoiICK/1evnQoUN+u5+kpCSpWLGie6ldu7bfbhsAAADF/ACwgpaQkCCnTp1yLykpKYFuEgAAAPykpARItWrVJDQ0VA4fPuy1Xi/78+Aura2lvhYAAKBoCtjIbKlSpaRNmzayevVq97r09HRzOSYmJlDNAgAAgEUCNjKrdFquuLg4adu2rURHR5t5Y8+ePWtmN1ADBw6UWrVqmbpX10FjX331lfvnn376SXbs2CHlypWThg0bBvKhAAAAoLiF2X79+snRo0dl5MiR5qCvVq1aybJly9wHhe3fv9/McOBy4MABad26tfvySy+9ZJZOnTrJ2rVrA/IYAAAAEDghjuM4Uozo1Fw6q4EeDFahQgUpqqLilwa6CUBQ2Tu6e6CbAAAogLxW5GczAAAAQNEV0DIDACiqeysYCQaAwsHILAAAAKxFmAUAAIC1CLMAAACwFmEWAAAA1iLMAgAAwFrMZhDkmC8WAAAga4zMAgAAwFqEWQAAAFiLMAsAAABrEWYBAABgLcIsAAAArEWYBQAAgLUIswAAALAWYRYAAADWIswCAADAWoRZAAAAWIswCwAAAGsRZgEAAGAtwiwAAACsRZgFAACAtQizAAAAsFbJQDcAAIqiqPil+bre3tHd/d4WACjKGJkFAACAtQizAAAAsBZhFgAAANYizAIAAMBahFkAAABYi9kMACCIMAsCAOQNYRYAigBCMIDiijIDAAAAWIswCwAAAGsRZgEAAGAtwiwAAACsxQFgQXxgBgAAALLHyCwAAACsRZgFAACAtQizAAAAsBY1swBQjHGyBQC2I8wCAAr1wNa9o7vT4wD8hjIDAAAAWIswCwAAAGsRZgEAAGAtwiwAAACsRZgFAACAtQizAAAAsBZTcwEArMCcuACCdmR28uTJEhUVJeHh4dK+fXvZvHlzttsvXLhQGjdubLZv3ry5vP/++4XWVgAAAASPgI/MLliwQIYPHy5Tp041QTY5OVliY2Nl165dUqNGjUzbb9y4Ufr37y9JSUnSo0cPef3116VXr16ybds2adasWUAeAwCgcE64YANGkIHCFeI4jiMBpAG2Xbt2MmnSJHM5PT1dateuLY888ojEx8dn2r5fv35y9uxZWbJkiXvdddddJ61atTKBOCepqalSsWJFOXXqlFSoUEEKQ1H/ww0AuHycGQ3IX14L6MjshQsXZOvWrZKQkOBeV6JECenatats2rTJ53V0vY7ketKR3Lffftvn9mlpaWZx0U5xdVJhSU87V2j3BQCwU53HF0pR9u9Rsfm6XrPE5YV+n0Vds3z2aWH2pyun5WbMNaBh9tixY3Lp0iWJiIjwWq+Xv/nmG5/XOXTokM/tdb0vWo4watSoTOt19BcAABSOisnF4z6LsooB6M/Tp0+bEdqgrpktaDrq6zmSq2UMx48fl6pVq0pISEiO3wo09KakpBRaSYJN6B/6htcO7yv+7gQP/ibTP0XptaMjshpkr7zyyhy3DWiYrVatmoSGhsrhw4e91uvlyMhIn9fR9XnZPiwszCyeKlWqlKd26hMbLE9uMKJ/6BteO7yv+LsTPPibTP8UlddOTiOyQTE1V6lSpaRNmzayevVqr5FTvRwTE+PzOrrec3u1cuXKLLcHAABA0RXwMgMtAYiLi5O2bdtKdHS0mZpLZysYNGiQ+f3AgQOlVq1apvZVDRs2TDp16iTjx4+X7t27y/z58+Wzzz6T6dOnB/iRAAAAoNiFWZ1q6+jRozJy5EhzEJdOsbVs2TL3QV779+83Mxy4dOjQwcwt+3//93/y9NNPy9VXX21mMiiIOWa1PCExMTFTmQLoH147vLcKCn936B9eO7y3CluY5Xkn4PPMAgAAAFafzhYAAADID8IsAAAArEWYBQAAgLUIswAAALAWYTYbkydPlqioKAkPD5f27dvL5s2bC++ZCWLr16+X22+/3ZyVQ8+iprNJ4L90Crl27dpJ+fLlpUaNGtKrVy/ZtWsX3SMiU6ZMkRYtWrgn5da5oT/44AP6JgujR48276/HHnus2PfRc889Z/rCc2ncuHGx7xdPP/30k9x7773m7JalS5eW5s2bm2krIeZzPOPrR5eHH3642HfPpUuX5Nlnn5V69eqZ102DBg3khRdeMGffsglhNgsLFiwwc+DqVBXbtm2Tli1bSmxsrBw5ckSKO50HWPtDwz68rVu3zvyB/OSTT8zJPC5evCjdunUzfVbcXXXVVSagbd261XzI3nTTTdKzZ0/58ssvA920oLNlyxaZNm2aCf/4r6ZNm8rBgwfdy8cff0zX/M+JEyfk+uuvlyuuuMJ8Qfzqq6/MXOyVK1emj/73fvJ87ejfZnXXXXcV+/4ZM2aMGWiYNGmSfP311+by2LFjZeLEiVb1DVNzZUFHYnWETZ9g15nJ9LzFjzzyiMTHxxfmcxTU9NvtW2+9ZUYgkZnOoawjtBpyb7zxRroogypVqsi4cePkgQceoG/+58yZM3LttdfK3//+d/nLX/5i5t7Wk8kU95FZ3QO0Y8eOQDclKOln0oYNG+Sjjz4KdFOsoHs7lixZIt999535DCvOevToYeb1f/XVV93r+vTpY0Zp582bJ7ZgZNaHCxcumNGjrl27/tpRJUqYy5s2bSrM5weWO3XqlDu0wXvXlp69T0esORW1Nx3Z17Mbev79gZjgoaVN9evXlwEDBpgT6uC/3n33XXMWTR1p1C/PrVu3lhkzZtA9WXy+a0gbPHhwsQ+yrhNRrV69Wr799ltzeefOnWavx6233io2CfgZwILRsWPHzIet6yxkLnr5m2++CVi7YBcdzdcRAN39VxBnqLPRF198YcLr+fPnpVy5cmZUv0mTJoFuVtDQgK9lTbpbFN57ymbPni2NGjUyu4lHjRolHTt2lH//+9+mPr24+/77782uYi2N0zNj6uvn0UcflVKlSpnTxeNXOsJ/8uRJuf/+++kW+e+ofmpqqqlBDw0NNdnnxRdfNF8YbUKYBQpwhE0/bKnt+5WGEd1VrCPWixYtMh+0WoJBoBVJSUmRYcOGmXo+PegUv/IcJdI6Yg23devWlTfffJMSlf99cdaR2b/+9a+mj3RkVv/2TJ06lTCbge5O19eTjvJDzHvotddek9dff93UpevfZx2E0f6x6YsQYdaHatWqmW8ohw8f9lqvlyMjIwvruYHF/vSnP5maLJ35QQ98wn/pSFHDhg3Nz23atDEjSC+//LI52Km409ImPcBU62VddJREX0Nau5+Wlmb+LkGkUqVK8pvf/EZ2795Nd4hIzZo1M30hvOaaa+Rf//oX/eNh3759smrVKlm8eDH98j9//vOfzejsPffcYy7rLBjaTzozj01hlprZLD5w9YNW60g8v/nqZer7kB2dzkSDrO4+//DDD810J8iavq80pEGkS5cupgxDR0Zci4626e4+/Zkg632Q3J49e0yIg5hSpoxTAGoNpI5e41ezZs0yNcVak47/OnfunDkmyJP+rdG/zTZhZDYLWnuk30r0wyQ6OtocTawHqwwaNEiKO/0g8RwR+eGHH8yHrR7kVKdOHSnupQW6u+add94xtXyHDh0y6ytWrGiODi3OEhISzO49fY2cPn3a9NPatWtl+fLlgW5aUNDXS8ba6rJly5p5Q4t7zfWIESPM3NYazg4cOGCmTNQP3P79+we6aUHh8ccfNwfyaJnB3XffbeZEnz59ulnwXxrONMzq53rJkkQfF31faY2s/l3WMoPt27fLhAkTzAFyVnGQpYkTJzp16tRxSpUq5URHRzuffPIJveU4zpo1a3Q25UxLXFxcse8fX/2iy6xZs4p93wwePNipW7eueT9Vr17d6dKli7NixYpi3y/Z6dSpkzNs2LBi30f9+vVzatasaV47tWrVMpd3795d7PvF03vvvec0a9bMCQsLcxo3buxMnz6d/vGwfPly87d4165d9IuH1NRU8zdGs054eLhTv35955lnnnHS0tIcmzDPLAAAAKxFzSwAAACsRZgFAACAtQizAAAAsBZhFgAAANYizAIAAMBahFkAAABYizALAAAAaxFmAQAAYC3CLABYIiQkRN5+++1ANwMAggphFgD+5+jRo/LHP/7RnKc8LCxMIiMjJTY2VjZs2EAfAUCQKhnoBgBAsOjTp49cuHBB/vnPf0r9+vXl8OHDsnr1avn5558D3TQAQBYYmQUAETl58qR89NFHMmbMGOncubPUrVtXoqOjJSEhQe644w53H02YMEGaN28uZcuWldq1a8tDDz0kZ86ccf9+9uzZUqlSJVmyZIk0atRIypQpI3379pVz586ZkBwVFSWVK1eWRx99VC5duuS+nq5/4YUXpH///ua2a9WqJZMnT872uUlJSZG7777b3F+VKlWkZ8+esnfv3iy3X7t2rSlVWL58ubRu3VpKly4tN910kxw5ckQ++OADueaaa6RChQryu9/9zrTXJT09XZKSkqRevXrmOi1btpRFixa5f6+P44EHHnD/Xh/3yy+/7HXf999/v/Tq1UteeuklqVmzplStWlUefvhhuXjxIq8/AJeFMAsAIlKuXDmzaE1qWlpa1n80S5SQV155Rb788ksTTj/88EN58sknvbbRIKjbzJ8/X5YtW2ZCZO/eveX99983y9y5c2XatGlegVCNGzfOBMXt27dLfHy8DBs2TFauXOmzHRoCtQSifPnyJoRrKYS2/5ZbbjGjy9l57rnnZNKkSbJx40Z3IE5OTpbXX39dli5dKitWrJCJEye6t9cgO2fOHJk6dap53I8//rjce++9sm7dOnfYveqqq2ThwoXy1VdfyciRI+Xpp5+WN9980+t+16xZI3v27DH/a99p8NcFAC6LAwAwFi1a5FSuXNkJDw93OnTo4CQkJDg7d+7MtncWLlzoVK1a1X151qxZjv5p3b17t3vd0KFDnTJlyjinT592r4uNjTXrXerWrevccsstXrfdr18/59Zbb3Vf1tt96623zM9z5851GjVq5KSnp7t/n5aW5pQuXdpZvny5z7auWbPG3MaqVavc65KSksy6PXv2eLVX26fOnz9v2r5x40av23rggQec/v37Z9kvDz/8sNOnTx/35bi4OPMYf/nlF/e6u+66yzxGALgcjMwCgEfN7IEDB+Tdd981I5w6onrttdd6jR6uWrVKunTpYsoAdFT0vvvuMzW1nrvltbSgQYMG7ssRERGmjEBHTj3X6e59TzExMZkuf/311z6fn507d8ru3btNG1yjylpqcP78eTP6mZ0WLVp4tUPbqzXCvtqm96GP7eabb3bfjy46Uut5P1oS0aZNG6levbr5/fTp02X//v1e99u0aVMJDQ11X9Zyg4x9AAB5xQFgAOAhPDzcBDddnn32WXnwwQclMTHR1HxqPWqPHj3MjAcvvviiCY8ff/yxqRfVXfsaCtUVV1zh1adap+prne6ezy+t09Xw+Nprr2X6nQbK7Hi2Jae2ueqBtfxAA7wnnfFBaTnFiBEjZPz48SaAa8DWkolPP/00y/vNeD8AkF+EWQDIRpMmTdxzu27dutWELw1tWjurMtaFXo5PPvkk02U9KMsXHTFesGCB1KhRwxy0VZCPX0OrjrJ26tTJ5zZar9uhQwdzMJxLTqPDAOAvlBkAgIgpFdAj++fNmyeff/65/PDDD+aAprFjx5pZAlTDhg3NgVd6cNT3339vDuTSg6L8RUOh3t+3335rdtvr/etBYL4MGDBAqlWrZtqmB4Bpe7UsQmdJ+PHHH/3WJh1l1VFXPehLD9rSkLpt2zbTB3pZXX311fLZZ5+ZWRK07TqivWXLFr+1AQCyw8gsAPxvNoP27dvL3/72NxPYNLTq1FtDhgwxR+YrnWlAp+bS6bt0yq4bb7zRHOk/cOBAv/ThE088YULhqFGjzGir3pfOWOCLljSsX79ennrqKbnzzjvl9OnTpgxA63n9PVKrU4Zp6YI+Vg3xOhWYjgy7+mXo0KFmBoZ+/fqZ0gGdXkxHaXW6LwAoaCF6FFiB3wsAIFt6gNhjjz1mFgBA7lFmAAAAAGsRZgEAAGAtygwAAABgLUZmAQAAYC3CLAAAAKxFmAUAAIC1CLMAAACwFmEWAAAA1iLMAgAAwFqEWQAAAFiLMAsAAACx1f8D29Sj+et8A5UAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,4))\n",
    "plt.hist(means_5, bins=40, density=True)\n",
    "plt.xlabel(\"Sample mean\")\n",
    "plt.ylabel(\"Density\")\n",
    "plt.title(\"Sampling Distribution of the Mean (n = 5)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "10f26d72",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,4))\n",
    "plt.hist(means_30, bins=40, density=True)\n",
    "plt.xlabel(\"Sample mean\")\n",
    "plt.ylabel(\"Density\")\n",
    "plt.title(\"Sampling Distribution of the Mean (n = 30)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "f38c622b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,4))\n",
    "plt.hist(means_100, bins=40, density=True)\n",
    "plt.xlabel(\"Sample mean\")\n",
    "plt.ylabel(\"Density\")\n",
    "plt.title(\"Sampling Distribution of the Mean (n = 100)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1a99848c",
   "metadata": {},
   "source": [
    "## Part 12 — Numerical Check of the CLT\n",
    "\n",
    "For an exponential population with scale = 2:\n",
    "\n",
    "- population mean should be about 2,\n",
    "- population variance should be about 4,\n",
    "- variance of the sample mean should be about `4/n`.\n",
    "\n",
    "We compare this with simulation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "55007845",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Population mean (approx.): 2.0079329836826765\n",
      "Population variance (approx.): 4.030341196852308\n",
      "\n",
      "For n = 5\n",
      "Mean of sample means: 2.001364330224136\n",
      "Variance of sample means: 0.78849285045314\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",
      "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",
      "Theoretical variance approx.: 0.04\n"
     ]
    }
   ],
   "source": [
    "print(\"Population mean (approx.):\", population.mean())\n",
    "print(\"Population variance (approx.):\", population.var())\n",
    "\n",
    "print(\"\\nFor n = 5\")\n",
    "print(\"Mean of sample means:\", means_5.mean())\n",
    "print(\"Variance of sample means:\", means_5.var(ddof=1))\n",
    "print(\"Theoretical variance approx.:\", 4/5)\n",
    "\n",
    "print(\"\\nFor n = 30\")\n",
    "print(\"Mean of sample means:\", means_30.mean())\n",
    "print(\"Variance of sample means:\", means_30.var(ddof=1))\n",
    "print(\"Theoretical variance approx.:\", 4/30)\n",
    "\n",
    "print(\"\\nFor n = 100\")\n",
    "print(\"Mean of sample means:\", means_100.mean())\n",
    "print(\"Variance of sample means:\", means_100.var(ddof=1))\n",
    "print(\"Theoretical variance approx.:\", 4/100)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a8dadb5",
   "metadata": {},
   "source": [
    "## Part 13 — Final Questions\n",
    "\n",
    "Answer the following after running the notebook:\n",
    "\n",
    "1. What is the difference between a Bernoulli and a Binomial random variable?\n",
    "2. When is the Poisson model appropriate?\n",
    "3. Why is the Normal model so important in applications?\n",
    "4. What does a Z-score represent?\n",
    "5. What does the Central Limit Theorem say precisely?\n",
    "6. Does the CLT apply to raw data or to sample means?"
   ]
  }
 ],
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   "pygments_lexer": "ipython3",
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