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": 2,
   "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": 3,
   "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": 4,
   "id": "e8285330",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "First 20 observations:\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"
     ]
    }
   ],
   "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": 5,
   "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": 6,
   "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": 7,
   "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": 8,
   "id": "741ee2d7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Simulated mean: 1.5818\n",
      "Theoretical mean: 1.6\n",
      "Simulated variance: 1.4380525652565255\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": 9,
   "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": 10,
   "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": 11,
   "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": 12,
   "id": "f241431b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Simulated mean: 3.0051\n",
      "Theoretical mean: 3\n",
      "Simulated variance: 3.0315771477147715\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": 13,
   "id": "2f9e2a0c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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00qRWM9Fc+rQWUAFyMlIaAAAIQlrmTHOpdTKcTmLUXGEAnhHwAgAAwNLI4QUAAIClEfACAADA0pi05oHWn9T1yLUofkaW2wQAAIBvaGVdrZGuta/TWvCGgNcDDXa1mDkAAAACmy6zrosapYaA1wMd2XUcQF0qEgAAAIElPj7eDFA64rbUEPB64Ehj0GCXgBcAACBwpSf9lElrAAAAsDQCXgAAAFgaAS8AAAAsjYAXAAAAlkbACwAAAEsj4AUAAIClEfACAADA0gh4AQAAYGkEvAAAALA0VlpDzmRLFDm8TuTiKZFCpUUqNhQJzeXvXgVuvwAACGIEvMh5dn8psnyQSPyJv9sKh4s8NFYksg39AgDAYkLsdrvd350INPHx8VKkSBE5f/68FC5c2N/dQRIRMcsyfUxahG6S6XkmmeuhLktv2/76LeiZ0FdW2KIyte9DY1pnLQhfEC0iSX8d/+pkh7n+DcYBAAjieI0cXuQYoWKTYXnmJgt2XW8Py/Oh2c7naQw64pws2JW/25bH3NgOAABkGAEvcoyo0D0SHnIuWbDroO3hIb+b7XxKc3Zd0yuSsYvEH7+xHQAAyDACXuQYpSTOq9t5jU5Q8+Z2AADADQEvcozTEubV7bxGqzF4czsAAOCGKg3IMTbZqskJezEpI57TGnTiWqwUN9v5cjKd5gz/kC/tfjV6J05sssy3k+kAALAARniRY9gkVIYnRLtVZXDe99ft4QldzXb0CwAA6yDgRY6iJce09FisFHNr1xHUrJQks2q/AACwAlIakONo8Ljyah1TjUEnqGnOrqYx+HpkN1j6BQBAsCPgRY6kQeQGW6QEmkDtFwAAwYyhIwAAAFgaAS8AAAAsjYAXAAAAlkbACwAAAEsj4AUAAIClEfACAADA0gh4AQAAYGkEvAAAALA0Al4AAABYGgEvAAAALI2AFwAAAJZGwAsAAABLI+AFAACApRHwAgAAwNIIeAEAAGBpBLwAAACwNAJeAAAAWBoBLwAAACyNgBcAAACWRsALAAAASwuIgHfatGkSEREh+fPnl3r16smmTZtS3HbWrFly3333SdGiRc2lWbNmyba32+0ydOhQKVu2rBQoUMBss2/fPh+8EgAAAAQavwe88+fPl/79+8uwYcNky5Ytctddd0mLFi3k9OnTHrf/9ttvpXPnzrJmzRpZv369lC9fXpo3by7Hjx93bjNu3DiZMmWKzJgxQzZu3CgFCxY0+7xy5YoPXxkAAAACQYhdh0MzoFu3bvLMM89I48aNvdIBHdGtW7euTJ061dy22WwmiO3du7fExMSk+fjExEQz0quPj46ONqO74eHhMmDAABk4cKDZ5vz581K6dGn54IMPpFOnTmnuMz4+XooUKWIeV7hwYS+8SnhTRMwyDmgGHBrTmuMFALCcjMRrGR7h1Z1qikDVqlVl1KhRbiOrGXXt2jX56aefzP6cHQoNNbd19DY9Ll++LAkJCVKsWDFz++DBgxIbG+u2Tz0YGlintM+rV6+ag+Z6AQAAgDVkOOBdvHixCXJ79uxp0hE097Zly5aycOFCE3hmxNmzZ80IrY6+utLbGrSmx6BBg8yIriPAdTwuI/scPXq0CYodFx1hBgAAQA7O4S1ZsqTJu92+fbvJka1SpYp07drVBJ79+vXz2QSxMWPGyLx58+Tzzz83E94ya/DgwWbk2nE5evSoV/sJAACAIJ20dvLkSVm5cqW55MqVS1q1aiU7d+6UyMhImThxYpqPL1GihHncqVOn3Nr1dpkyZVJ97JtvvmkC3q+//lpq1qzpbHc8LiP7zJcvn8n9cL0AAAAghwa8mrawaNEiefjhh6VixYry6aefSt++feXEiRMyZ84cWbVqlSxYsEBGjBiR5r7y5s0rtWvXltWrVzvbdNKa3m7QoEGKj9MqDK+//rosX75c6tSp43ZfpUqVTGDruk/NydWR6NT2CQAAAGvKndEHaG1bDUq1NJjWv61Vq1aybR544AEJCwtL1/40NUIrP2jgGhUVJZMmTZJLly5J9+7dzf1aeaFcuXImz1aNHTvW1Nj9+OOPTf6wIy+3UKFC5hISEmIC8JEjR5qJdRoAv/rqqybdol27dhl9uQAAAMhpAa+mKrRv3z7VnFkNdrVaQnp07NhRzpw5Y4JYDV41gNaRW8eksyNHjpjKDQ7Tp0831R0ef/xxt/1oHd/XXnvNXH/ppZdM0Pzcc89JXFycNGrUyOwzK3m+AAAAyCF1eJ9++mmZPHmy3HzzzW7tGmBq7dz3339fgh11eAMbdXgzhjq8AAArytY6vJqn++effyZr17a5c+dmdHcAAABAYKQ0aBStg8F6uXDhglt6gNbS/eqrr6RUqVLZ1U8AAAAgewNezcvVCWF6ue2225Ldr+3Dhw/PXC8AAAAAfwe8a9asMaO7Dz74oClL5ljK11FeTEuUaSUEAAAAICgD3iZNmpj/tfpChQoVzIguAAAAYImAd8eOHVK9enVTHkxnwulqailxXfUMAAAACIqAV2vjao1cnZSm13V011M1M23XCWwAAABAUAW8msZQsmRJ53UAAADAUgGvTkjzdB0AAACwRMD75ZdfpnuHbdq0yUp/AAAAAN8HvO3atUvXzsjhBQAAQFAGvDabLft7AgAAAGSD0OzYKQAAABBUI7xTpkyR5557TvLnz2+up+aFF17wVt8AAAAA3wS8EydOlC5dupiAV6+nlsNLwAsAAICgrMPr6ToAAABg6RxeXW3N04prAAAAQFAHvO+9955Ur17dpDjoRa+/++673u8dAAAA4IuUBldDhw6VCRMmSO/evaVBgwambf369dKvXz85cuSIjBgxIqt9AgAAAPwX8E6fPl1mzZolnTt3dltdrWbNmiYIJuAFAABAUKc0JCQkSJ06dZK1165dW65fv+6tfgEAAAD+CXi7du1qRnmTmjlzpildBgAAAARdSkP//v3dau3qBLWvv/5a6tevb9o2btxo8nejo6Ozr6cAAABAdgW8W7duTZa+oH777Tfzf4kSJczl559/zkwfAAAAAP8GvGvWrMm+HgAAAACBuvAEAAAAYLmyZGrz5s2yYMECk7d77do1t/s+++wzb/UNAAAA8P0I77x586Rhw4byyy+/yOeff27KlGnu7jfffCNFihTJeo8AAAAAfwa8o0aNkokTJ8qSJUskb968MnnyZNmzZ4906NBBKlSo4M2+AQAAAL4PeLUyQ+vWrc11DXgvXbpkSpXp0sJaixcAAAAI6oC3aNGicuHCBXO9XLlysmvXLnM9Li5OLl++7P0eAvAvW6LIwbUiOxfe+F9vAwBg5UlrjRs3lpUrV0qNGjWkffv20qdPH5O/q21NmzbNnl4C8I/dX4osHyQSf+LvtsLhIg+NFYlsw08FAGDNgHfq1Kly5coVc/2VV16RPHnyyLp16+Sxxx6TIUOGZEcfAfgr2F2gqyfa3dvjT95o7zCXoBcAYM2At1ixYs7roaGhEhMT4+0+AfA3TVvQkd2kwa6hbSEiy2NEqrUWCc3lhw4CAJDNdXgTExNNSTItTaYiIyOlbdu2kjt3pnYHINAcXueexpCMXST++I3tKt3nw44BAJBxGY5QteZumzZtJDY2Vm6//XbTNnbsWClZsqQpVVa9evVMdANAQLl4yrvbAQAQTFUann32Wbnzzjvl2LFjsmXLFnM5evSo1KxZU5577rns6SUA3ypU2rvbAQAQTCO827ZtM0sLa3kyB73+xhtvSN26db3dPwD+ULHhjWoMOkHNYx5vyI37dTsAAKwW8N52221y6tQpM8rr6vTp01KlShVv9g2AF0TELMvU41qEdpDpeSaZ66Ehf7fbTPxrl55n28uKl5dnat+HxtxYvAYAgIBJaYiPj3deRo8eLS+88IIsXLjQpDXoRa/37dvX5PICsIYVtijpmdBXYuXvyiwqVoqbdr0fAADLjPCGhYWZ5YMd7Ha7dOjQwdmmt9UjjzxiKjgAsAYNalderSNRoXuklMTJaQmTTbZqYst4+j8AAIEd8K5Zsyb7ewIgIGlwu8EW6e9uAACQvQFvkyZNMv8MAAAAgB9laqWIuLg4ee+995wLT+gEtqefflqKFCni7f4BAAAAWZLhRDwtSXbrrbfKxIkT5dy5c+YyYcIE06Y1eQEAAICgHuHt16+fWWlt1qxZzqWEr1+/bhak0EoN33//fXb0EwAAAPBNwKsjvK7BrtlJ7tzy0ksvSZ06dTLXCwAAACBQUhoKFy4sR44cSdauywvffPPN3uoXAAAA4J+At2PHjvLMM8/I/PnzTZCrl3nz5pmUhs6dO3unVwAAAIC/UhrefPNNs+BEdHS0yd1VefLkkZ49e8qYMWO81S8AAADA9wGvrqK2YcMGee2118wSw7/99ptp1woNN910k3d6BAAAAPgr4M2VK5c0b97c1N+tVKmS1KhRw5t9AQAAAPyfw1u9enU5cOCA93sCAAAABELAO3LkSBk4cKAsXbpUTp48KfHx8W4XAAAAIKgD3latWsn27dvN4hO33HKLFC1a1FzCwsLM/xk1bdo0iYiIkPz580u9evVk06ZNKW77888/y2OPPWa214lzkyZNSraN5hfrfa6XatWqZbhf8CJbosjBtSI7F974X28DAAAEapWGNWvWeO3JtbRZ//79ZcaMGSbY1QC2RYsWsnfvXilVqlSy7S9fviyVK1eW9u3bmxXfUnLnnXfKqlWrnLddF8mAj+3+UmT5IJH4E3+3FQ4XeWisSGQbfhwAACDbZTgSbNKkideefMKECdKjRw/p3r27ua2B77Jly+T999+XmJiYZNvXrVvXXJSn+10D3DJlynitn8hCsLsgWkTs7u3xJ2+0d5hL0AsAALJdpoY+//jjD3nvvfdMtQYVGRlpgtZixYqlex/Xrl2Tn376SQYPHuxsCw0NlWbNmsn69eslK/bt2yfh4eEmTaJBgwamhFqFChVS3P7q1avm4kAushdo2oKO7CYNdg1tCxFZHiNSrbVIaC5vPCMAAIB3At7vv/9eHnnkESlSpIjUqVPHtE2ZMkVGjBghS5YskcaNG6drP2fPnjV1fUuXLu3Wrrf37NkjmaWpER988IHcfvvtZlLd8OHD5b777pNdu3aluPSxBsS6HZKLiFmWqcNSP3S3zMvrksaQjF0k/rh0GjJBNtgiOfQAACBwAt5evXqZ5YWnT59u6vIqDVz/9a9/mft27twp/tSyZUvn9Zo1a5oAuGLFirJgwQKzJLInOsqsucSuI7zly5f3SX+tqpTEeXU7AAAAnwW8+/fvl4ULFzqDXaXXNWCcO3duuvdTokQJ87hTp065tettb+bfavWI2267zfQ7Jfny5TMXeM9pCfPqdgAAAD4rS3bPPfc4c3ddadtdd92V7v3kzZtXateuLatXr3a22Ww2c1vzbr3l4sWLZgnksmXLem2fSNsmWzU5YS8mNk8pvPqztoucsBc32wEAAATUCO8LL7wgffr0MSOm9evXN20bNmww9XTHjBkjO3bscEspSI2OCnfr1s3kAkdFRZmyZJcuXXJWbYiOjpZy5cqZHFvHRLfdu3c7rx8/fly2bdsmhQoVkipVqph2XRRDc4w1jeHEiRMybNgwM5LcuXPnjL5UZIFNQmV4QrRMzzPJBLehIS73/RUED0/oarYDAADITiF2uz2FMTjPtJJCqjsMCRHdpf6vub1pmTp1qowfP15iY2OlVq1aZgKc5t2q+++/3ywyoZPQ1KFDh6RSpUoeS6V9++235nqnTp3MxLrff/9dSpYsKY0aNZI33nhDbr311nS/Rs3h1Ul558+fl8KFC0tOltlJaw4tQjfJsDxzJTzknLNNR3Y12F1hi/JCDxGMDo1p7e8uAACCXEbitQwHvIcPH073tjrKGowIeL0X8KpQsUlU6B4zQU1zdjWNgZHdnI2AFwDgy3gtwykNwRrEwn80uKX0GAAA8BcSKAEAAGBpBLwAAACwNAJeAAAAWFq6A94DBw5kb08AAAAAfwa8WlO3evXq8vLLL8vGjRuzoy8AAACA/wLes2fPmgUgTp8+LW3btjUrl/Xo0UOWLFkiV65c8X7PAAAAAF8GvPnz5zcrmL377rty8uRJWbRokRQvXlwGDRokJUqUkHbt2sn7778vZ86c8Ua/AAAAAP9NWtNV1Bo2bGiWEtalfrdu3Sr33XefWRHtlltuMcsMAwAAAIEgwwtPeFK1alUZMGCAueiSvufO/b2MLAAAABD0Aa8rTXPQCwAAABAIqMMLAAAASyPgBQAAgKUR8AIAAMDSMhzwduvWTb7//vvs6Q0AAADg74D3/Pnz0qxZM1OZYdSoUXL8+HFv9wkAAADwX8C7ePFiE+T27NlT5s+fLxEREdKyZUtZuHChJCQkeK9nAAAAgL9yeEuWLCn9+/eX7du3y8aNG6VKlSrStWtXCQ8Pl379+sm+ffu80TcAAADAv5PWdInhlStXmkuuXLmkVatWsnPnTomMjJSJEydmvXcAAACArwNeTVtYtGiRPPzww1KxYkX59NNPpW/fvnLixAmZM2eOrFq1ShYsWCAjRozIat8AAAAA36+0VrZsWbHZbNK5c2fZtGmT1KpVK9k2DzzwgISFhWW9dwAAAICvA15NVWjfvr3kz58/xW002D148GBW+wYAAAD4PqWhTZs2cvny5WTt586dk/j4+Kz3CAAAAPBnwNupUyeZN29esnbN29X7AAAAgKAOeLUMmeboJnX//feb+wAAAICgDnivXr0q169f91i94c8///RWvwAAAAD/BLxRUVEyc+bMZO0zZsyQ2rVre6dXAAAAgL+qNIwcOVKaNWtmVllr2rSpaVu9erX8+OOP8vXXX3urXwAAAIB/RnjvvfdeWb9+vZQvX95MVFuyZIlZWnjHjh1y3333eadXAAAAgL9GeJUuNvHRRx95qw8AAABAYAW8utLa/v375fTp0+a6q8aNG3urbwAAAIDvA94NGzbIE088IYcPHxa73e52X0hIiCQmJma9VwAAAIC/At7nn39e6tSpI8uWLZOyZcuaIBcAAACwTMC7b98+WbhwoZmoBgAAAFiuSkO9evVM/i4AAABgyRHe3r17y4ABAyQ2NlZq1KghefLkcbu/Zs2a3uwfAAAA4NuA97HHHjP/P/300842zePVCWxMWgMAAEDQB7wHDx7Mnp4AAAAAgRDwVqxYMTv6AQAAAATGpDX14YcfmiWGw8PDTT1eNWnSJPniiy+83T8AAADAtwHv9OnTpX///tKqVSuJi4tzLjQRFhZmgl4AAAAgqAPet99+W2bNmiWvvPKK5MqVy9mui1Hs3LnT2/0DAAAAfBvw6qS1u+++O1l7vnz55NKlS1nrDQAAAODvgLdSpUqybdu2ZO3Lly+XO+64w1v9AgAAAPxTpUHzd3v16iVXrlwxtXc3bdokn3zyiYwePVreffdd7/QKAAAA8FfA++yzz0qBAgVkyJAhcvnyZXniiSdMtYbJkydLp06dvNUvAAAAwD8Br+rSpYu5aMB78eJFKVWqlHd6AwAAAARCwOtw0003mQsAAABgmYBXJ62FhISkeP+BAwey2icAAADAfwFv37593W4nJCTI1q1bTZWGF1980Xs9AwAAAPwR8Pbp08dj+7Rp02Tz5s3e6BMAAADgvzq8KWnZsqUsWrTIW7sDAAAA/D9pzdXChQulWLFi3todAKTOlihyeJ3IxVMihUqLVGwoEvr3cucAAGQ64NVlhV0nreniE7GxsXLmzBn5z3/+k9HdAUDG7f5SZPkgkfgTf7cVDhd5aKxIZBuOKAAgaykN7dq1k7Zt2zovjz76qAwbNkx27dolzz33XEZ3Z3J/IyIiJH/+/FKvXj2zcltKfv75Z3nsscfM9hp0T5o0Kcv7BBCEwe6CaPdgV8WfvNGu9wMAkJURXg1uvWX+/PlmqeIZM2aYwFQD2BYtWsjevXs9LmahC11UrlxZ2rdvL/369fPKPgH4XkTMskw9LlRs8kO+PlJG7BKarDqiXWx2kdj5faXR1RCxZWKKwqExrTPVLwBAYMvwX4T4+Ph0X9IyYcIE6dGjh3Tv3l0iIyNNkKoLWbz//vset69bt66MHz/eLGGcL18+r+wTQPCICt0j4SHnPAS7N2h7eMjvZjsAADI9whsWFpbqwhOOvF7dJjExMcVtrl27Jj/99JMMHjzY2RYaGirNmjWT9evXZ7RbWdrn1atXzcUhPcE6AN8rJXFe3Q4AkDNkOOCdPXu2xMTEyFNPPSUNGjQwbRpMzpkzR0aPHm1yZ9Pj7NmzJiAuXbq0W7ve3rMnc6Mzmd2n9nv48OGZek4AvnNawry6HQAgZ8hwwDt37lyTNtC5c2dnW5s2baRGjRoyc+ZM+fbbbyXY6Iiw5v26jvCWL1/er30CkNwmWzU5YS8mZcRzWoPJ4ZXiZjsAADKdw6ujuXXq1EnWrm0ZqYZQokQJyZUrl5w6dcqtXW+XKVMmo93K0j41H7hw4cJuFwCBRyeiDU+IvnHdnuS+v24PT+iaqQlrAADryvBfBR35nDVrVrL2d999N0Ojonnz5pXatWvL6tWrnW02m83cdqRKZFR27BNAYFlhi5KeCX0lVtwXutGRXW3X+wEAyFJKw8SJE00t3P/+97+m7JfSkd19+/ZleGlhTSPo1q2bGR2OiooyJcQuXbpkKiyo6OhoKVeunMmxdUxK2717t/P68ePHZdu2bVKoUCGpUqVKuvYJIPhpULvyah1TjUEnqGnOrqYxMLILAPBKwNuqVSv59ddfZfr06c6JYI888og8//zzGc577dixo1mhbejQoWa1tlq1asny5cudk86OHDliqiw4nDhxwqz05vDmm2+aS5MmTZy5w2ntE4A1aHC7wRbp724AAIJAiF1riMGNTlorUqSInD9/Psfn82Z2gQAgGLHwBABYM17L1MyOtWvXypNPPikNGzY0aQXqww8/lB9++CFzPQYAAACySYYDXs3T1aV6CxQoIFu2bHEu2KDR9ahRo7KjjwAAAIDvAt6RI0ea5Xq1UkOePHmc7ffee68JgAEAAICgDnj37t0rjRs3TtauORRxcSznCQAAgCAPeHUBh/379ydr1/zdypUre6tfAAAAgH8C3h49ekifPn1k48aNEhISYkqFffTRRzJw4EDp2bOnd3oFAAAA+KsOb0xMjFm9rGnTpnL58mWT3qBL82rA27t3b2/1CwAAAPB9wJuYmCj/+9//pFevXvLiiy+a1IaLFy9KZGSkWe0MAAAACOqAN1euXNK8eXP55ZdfJCwszAS6AAAAgKVyeKtXry4HDhzInt4AAAAAgVCHV/N1ly5dKidPnjTLurleAAAAgKCetNaqVSvzf5s2bUyVBge73W5ua54vAAAAELQB75o1a7KnJwAAAIC/At5HH31UPvjgAylcuLAcPnxYOnbsaEqRAQAAAJbI4dV83UuXLpnr3bt3l/Pnz2d3vwAAAADfjfBWq1ZNBg8eLA888IDJ1V2wYIEZ7fUkOjraOz0DAAAAfBXwzpgxQ/r37y/Lli0zE9OGDBniNmHNQdsIeAEAABB0AW/Dhg1lw4YN5npoaKj8+uuvUqpUqezuGwAAAOD7OrwHDx6UkiVLZv2ZAQAAgEAsS1axYsXs6QkAAAAQCCO8AAAAQDAh4AUAAIClEfACAADA0jIV8F6/fl1WrVol77zzjly4cMG0nThxQi5evOjt/gEAAAC+nbSmSws/9NBDcuTIEbl69ar84x//kJtvvlnGjh1rbmvNXgAAACBoR3j79OkjderUkT/++EMKFCjgbP/nP/8pq1ev9nb/AAAAAN+O8K5du1bWrVsnefPmdWuPiIiQ48ePZ603AAAAgL9HeG02myQmJiZrP3bsmEltAAAAAII64G3evLlMmjTJeTskJMRMVhs2bJi0atXK2/0DAAAAfJvS8NZbb0mLFi0kMjJSrly5Ik888YTs27dPSpQoIZ988knWegMAAAD4O+C95ZZbZPv27TJv3jzZsWOHGd195plnpEuXLm6T2AAAAICgDHh1VDd//vzy5JNPZk+PAAAAAH/m8JYqVUq6desmK1euNBPYAAAAAEsFvHPmzJHLly9L27ZtpVy5ctK3b1/ZvHlz9vQOAAAA8HXAqwtMfPrpp3Lq1CkZNWqU7N69W+rXry+33XabjBgxIqv9AQAAAPwb8Dpozd3u3bvL119/bSavFSxYUIYPH+7d3gEAAAD+Cnh18tqCBQukXbt2cs8998i5c+fkxRdfzGp/AAAAAP9WaVixYoV8/PHHsnjxYsmdO7c8/vjjZpS3cePG3u0ZAAAA4I+AV3N4H374YZk7d65ZWS1Pnjze6AcAAAAQGAGvTlbT/F0AAADAMgFvfHy8FC5c2Fy32+3mdkoc2wEAAABBE/AWLVpUTp48aRadCAsLk5CQkGTbaCCs7YmJidnRTwAAACD7At5vvvlGihUrZq6vWbMmc88EAAAABGrA26RJE+f1SpUqSfny5ZON8uoI79GjR73fQwAAAMCXdXg14D1z5kyydq3Dq/cBAAAAQR3wOnJ1k7p48aLkz5/fW/0CAAAAfFuWrH///uZ/DXZfffVVuemmm5z36US1jRs3Sq1atbzTKwAAAMDXAe/WrVudI7w7d+6UvHnzOu/T63fddZcMHDjQW/0CAAAAfBvwOqozdO/eXSZPnky9XQAAAFhzpbXZs2dnT08AAACAQAh41ebNm2XBggVy5MgRuXbtmtt9n332mbf6BgAAAPi+SsO8efOkYcOG8ssvv8jnn38uCQkJ8vPPP5vFKYoUKZL1HgEAAABelOGAd9SoUTJx4kRZsmSJmaym+bx79uyRDh06SIUKFbzZNwAILrZEkYNrRXYuvPG/3gYABF9Kw2+//SatW7c21zXgvXTpkilV1q9fP3nwwQdl+PDh2dFPpIf+cT28TuTiKZFCpUUqNhQJzcWxA3xh95ciyweJxJ/4u61wuMhDY0Ui2/AzAIBgGuEtWrSoXLhwwVwvV66c7Nq1y1yPi4uTy5cvZ6oT06ZNk4iICLNwRb169WTTpk2pbv/pp59KtWrVzPY1atSQr776yu3+p556ygThrpeHHnpILP/HdlJ1kTkPiyx65sb/elvbAWT/79+CaPdgV8WfvNHO7yEABFfA27hxY1m5cqW53r59e+nTp4/06NFDOnfuLE2bNs1wB+bPn28WtRg2bJhs2bLF1PNt0aKFnD592uP269atM8/1zDPPmNrA7dq1MxdH4O2gAe7Jkyedl08++UQsiz+2gH/PrOjIrtg93PlX2/IY0hsAwI9C7LqSRAacO3dOrly5IuHh4WKz2WTcuHEmCK1ataoMGTLEjABnhI7o1q1bV6ZOnWpu6z7Lly8vvXv3lpiYmGTbd+zY0aRRLF261NlWv359s8rbjBkznCO8OuK8ePFiyYz4+HgzAe/8+fOBX29Y/9jqSG7SkSWnkBunVfvuzFR6Q0TMsix3EbCy+qG7ZV7ekWlu1+naENlgi8zw/g+NuZFCBgDIfLyW4RzeYsWKOa+HhoZ6DErTS0ua/fTTTzJ48GC3fTZr1kzWr1/v8THa7ljm2EFHhJMGt99++62UKlXKBOCaWzxy5EgpXry4x31evXrVXFwPYNDQnN0Ug11lF4k/fmO7Svf5sGNAzlBK4ry6HQDA+9IV8GYkAMzIiOjZs2clMTFRSpcu7daut7XygyexsbEet9d213SGRx99VCpVqmQm2b388svSsmVLEyznypV8lHP06NHBO9lOJ6h5czsAGXJawry6HQDATwFvWFiYmfiVGs2M0G00gPW3Tp06Oa/rpLaaNWvKrbfeakZ9PeUZ6wiz66ixBviaVhEUtBqDN7cDkCGbbNXkhL2YlJFzEurhY9JmF4mV4mY7AEAAB7xr1qzJlicvUaKEGXE9dcp99FFvlylTxuNjtD0j26vKlSub59q/f7/HgDdfvnzm4k+ZzZUNFZv8kC/tP7aN3okTm5CPC3ibTUJleEK0TM8zyfy+uf4e6m01PKGr2Q4AEMABb5MmTbLlybWOb+3atWX16tWm0oJj0pre/ve//+3xMQ0aNDD39+3b19mmVSO0PSXHjh2T33//XcqWLStWwx9bwP9W2KKkZ0JfGZZnroTLOWe7ftnUYFfvBwD4T4Ynram1a9fKO++8IwcOHDA1cbUe74cffmhyZhs1apShfWkqQbdu3aROnToSFRUlkyZNMlUYunfvbu6Pjo42+9c8W6Vl0DQAf+utt8wCGLrU8ebNm2XmzJnm/osXL5p83Mcee8yM+moO70svvSRVqlQxk9usiD+2QGD8Hq68WkeiQveYCWqas6tpDIzsAkAQBryLFi2Srl27SpcuXUzdXEd1Ay0JocsOJ10EIi1aZuzMmTMydOhQM/FMy4stX77cOTHtyJEjpnKDQ8OGDeXjjz82JdB0MpqWQ9MKDdWrVzf3a4rEjh07ZM6cOaY0mZZPa968ubz++ut+T1vITvyxBfxPg9vMlB4DAARYHd67777bLCOsI68333yzbN++3eTI6iIQWgnBtVpCsPJHHV7q3QLwhDq8AJD1eC3Dsyj27t1rVltLSp9QR1QBAACAQJLhgFfzYrXaQVI//PCDGekFAAAAgjrg7dGjh5k4tnHjRlN398SJE/LRRx/JwIEDpWfPntnTSwAAAMBXk9Z0KWEtHab1bC9fvmzSG3QymAa8vXv3zmw/AAAAgMAIeHVU95VXXpEXX3zRpDZoGbDIyEgpVKiQ/Pnnn1KgQIHs6SkAAACQCaFZWTRCA12tnZsnTx6ZMGGCqcMLAAAABGXAq/V2Bw8ebBaI0Fq4WvtWzZ492wS6EydONOXKAAAAgKBMadCFIXR1tWbNmsm6deukffv2ZjW0DRs2mNFdva2LPgAAAABBGfDqEsJz586VNm3ayK5du6RmzZpy/fp1s/CE5vUCAAAAQZ3ScOzYMaldu7a5rsv4amUGTWEg2AUAAIAlAt7ExEQzUc0hd+7cpjIDAAAAYImUBrvdLk899ZQZ2VVXrlyR559/XgoWLOi23Weffeb9XgIAAADZHfB269bN7faTTz6Z2ecEAAAAAi/g1fJjAAAAQI5ZeAIAAAAIBgS8AAAAsDQCXgAAAFgaAS8AAAAsjYAXAAAAlkbACwAAAEsj4AUAAIClEfACAADA0gh4AQAAYGkEvAAAALA0Al4AAABYWm5/dwAAkM1siSKH14lcPCVSqLRIxYYiobk47AByDAJeALCy3V+KLB8kEn/i77bC4SIPjRWJbOPPngGAz5DSAABWDnYXRLsHuyr+5I12vR8AcgACXgCwahqDjuyK3cOdf7Utj7mxHQBYHAEvAFiR5uwmHdl1YxeJP35jOwCwOHJ4ASCARcQsy9Tj2oSukyl5097uhVnL5UtbfIb3f2hM60z1CwD8gRFeALCg0xLm1e0AIJgR8AKABW2yVZMT9mJis6eQ4msXOWEvbrYDAKsj4AUAC7JJqAxPiL5xPUnQ67g9PKGr2Q4ArI5POgCwqBW2KOmZ0FdipZhbe6wUN+16PwDkBExaAwAL06B25dU6EhW6R0pJnMnZ1TQGRnYB5CQEvABgcRrcbrBF+rsbAOA3pDQAAADA0gh4AQAAYGkEvAAAALA0Al4AAABYGgEvAAAALI0qDQAA/7AlihxeJ3LxlEih0iIVG4qE5uKnAcDrCHgBAL63+0uR5YNE4k/83VY4XOShsSKRbfiJAPAqUhoAAL4PdhdEuwe7Kv7kjXa9HwC8iIAXAODbNAYd2RW7hzv/alsec2M7APASAl4AgO9ozm7SkV03dpH44ze2AwAvIeAFAPiOTlDz5nYAkA5MWgMAZFhEzLJMHbX6oQdlXt60t+v0yUHZ8FHGnuPQmNaZ6hMA6yPgBQD4zCZbNTlhLyZl5JyEhiS/32YXiZXiZju/oFQaYEkEvAAAn7FJqAxPiJbpeSaZ4NY16NXbanhCV7Odz1EqDbAscngBAD61whYlPRP6SqwUc2vXkV1t1/t9jlJpgKUxwgsA8DkNalderSNRoXuklMTJaQkzaQx+GdlNs1RayI1SadVa+28luEBMtQjEPgEpIOAFAPiFBrcbbJHBVSqt0n3ic4GYahGIfQrkQDwQ+xTI/bJqwDtt2jQZP368xMbGyl133SVvv/22REWlfErr008/lVdffVUOHTokVatWlbFjx0qrVq2c99vtdhk2bJjMmjVL4uLi5N5775Xp06ebbQEA1pTZyhFtQtfJlHRUjnhh1nL50haf4f1nqXqEI9Ui6eizY1W6DnN9H2AGYp8CORAPxD4Fcr+smsM7f/586d+/vwlQt2zZYgLeFi1ayOnTpz1uv27dOuncubM888wzsnXrVmnXrp257Nq1y7nNuHHjZMqUKTJjxgzZuHGjFCxY0OzzypUrPnxlAIBgoOkU3tzO0qvSBWKfAjkPOxD7FMj9ykYhdh0O9aN69epJ3bp1ZerUqea2zWaT8uXLS+/evSUmJibZ9h07dpRLly7J0qVLnW3169eXWrVqmQBXX054eLgMGDBABg4caO4/f/68lC5dWj744APp1KlTmn2Kj4+XIkWKmMcVLlxYAnlkAgCQNaFikx/yvZBmqbRGVyf7NMe4fuhumZd3ZJrbdbo2JFOpIZkaeT64VmTOw2lv122pb9M/NMCeVD2V1JSQG6OXfXf67pR9IPYpkPuVCRmJ1/ya0nDt2jX56aefZPDgwc620NBQadasmaxfv97jY7RdR4Rd6ejt4sWLzfWDBw+a1Ajdh4MeDA2s9bGeAt6rV6+ai4MeOMeB9BXb1cs+ey4AgMvnr4i8ktBRJub5j7ntqVTaKwkd5LrNt2cJw0JPSXw6xqTCrp0Smy0iw/uv0O/TDD+mVehGGZc37T69NPUL+coWm+H97xreQjLl0DqRM8dT2cAucuaYyK6VIhENM/ccVuhTIPcrExxxWnrGbv0a8J49e1YSExPN6Ksrvb1nzx6Pj9Fg1tP22u6439GW0jZJjR49WoYPH56sXUeaAQDW98Ffl5SNFV97569L2t4Sq/SpyCTJXmNaSsAJxD4Fcr88uHDhghncDPhJa/6mI8yuo8aaVnHu3DkpXry4hIR4OL8V4N92NFA/evSoz9IxghXHimPF+8r/+D3kWPG+4ncws3RkV4NdTWVNi18D3hIlSkiuXLnk1KlTbu16u0yZMh4fo+2pbe/4X9vKli3rto3m+XqSL18+c3EVFubjyQlepsEuAS/HivcVv4PBgs8sjhXvK34HMyOtkd2AqNKQN29eqV27tqxevdptdFVvN2jQwONjtN11e7Vy5Urn9pUqVTJBr+s2OoKg1RpS2icAAACsy+8pDZpK0K1bN6lTp46pvTtp0iRThaF79+7m/ujoaClXrpzJs1V9+vSRJk2ayFtvvSWtW7eWefPmyebNm2XmzJnmfk1B6Nu3r4wcOdLU3dUAWGv26nC3li8DAABAzuL3gFfLjJ05c0aGDh1qJpVp2sHy5cudk86OHDliKjc4NGzYUD7++GMZMmSIvPzyyyao1QoN1atXd27z0ksvmaD5ueeeMwtPNGrUyOwzf/78YnWamqE1jZOmaIBjxfuK38FAxGcWx4r3Fb+DOaIOLwAAAGDpldYAAACA7ETACwAAAEsj4AUAAIClEfACAADA0gh4LWTatGkSERFhqlHUq1dPNm3a5O8uBSQtcVe3bl25+eabpVSpUqZc3d69e/3draAwZswYZ+k/JHf8+HF58sknzSqNBQoUkBo1apiyiXCnS8pruUgtG6nH6dZbb5XXX3/drJoEke+//14eeeQRU05Tf9+0EpErPU5a2UgXV9Lj16xZM9m3b1+OPHSpHauEhAQZNGiQ+T0sWLCg2UZLnZ44cUJyou/TeF+5ev755802WirWKgh4LWL+/PmmprGWJNuyZYvcdddd0qJFCzl9+rS/uxZwvvvuO+nVq5ds2LDBLFqiH4rNmzc3peyQsh9//FHeeecdqVmzJofJgz/++EPuvfdeyZMnj/z3v/+V3bt3m3rhRYsW5XglMXbsWJk+fbpMnTpVfvnlF3N73Lhx8vbbb3OsRMxnkX6G6yCGJ3qspkyZIjNmzDCLKmkwp5/3V65cyXHHL7VjdfnyZfP3UL9c6f+fffaZGdxo06aN5ESX0nhfOXz++efm72N6lusNKlqWDMEvKirK3qtXL+ftxMREe3h4uH306NF+7VcwOH36tA4r2b/77jt/dyVgXbhwwV61alX7ypUr7U2aNLH36dPH310KOIMGDbI3atTI390ICq1bt7Y//fTTbm2PPvqovUuXLn7rU6DSz6bPP//cedtms9nLlCljHz9+vLMtLi7Oni9fPvsnn3xiz8mSHitPNm3aZLY7fPiwPSeTFI7VsWPH7OXKlbPv2rXLXrFiRfvEiRPtVsEIrwVcu3ZNfvrpJ3Nay0EX69Db69ev92vfgsH58+fN/8WKFfN3VwKWjojryoau7zG4+/LLL82Kke3btzepMnfffbfMmjWLw+SBLiCky7//+uuv5vb27dvlhx9+kJYtW3K80nDw4EGzSJPr72KRIkVMGhuf9+n7vNdT9WFhYbzXkrDZbNK1a1d58cUX5c477xSr8ftKa8i6s2fPmpw4x+p0Dnp7z549HOI0fsE1H1VPRbuu1oe/6fLdejpQUxqQsgMHDpjT9JpapKtA6vF64YUXJG/evGb5dPwtJiZG4uPjpVq1apIrVy7z+fXGG29Ily5dOExp0GDX8fme9PPecR8805QPzent3LmzFC5cmMOUhKYW5c6d23xuWREBLySnj1zu2rXLjC4huaNHj0qfPn1MrnNOWJo7q1+edIR31KhR5raO8Op7S/MsCXjdLViwQD766COzTLyOJG3bts188dScQY4VsoPO1ejQoYOZ8KdfTOFOzxJPnjzZDG7oCLgVkdJgASVKlDCjJKdOnXJr19tlypTxW78C3b///W9ZunSprFmzRm655RZ/dydgPwR14uM999xjvvnrRSf96YQZva4jc7hBZ8xHRka6HY477rhDjhw5wiFKQk+Z6ihvp06dzAx6PY3ar18/U0EFqXN8pvN5n/Fg9/Dhw+bLO6O7ya1du9Z81leoUMH5Wa/Ha8CAAab6kxUQ8FqAnjKtXbu2yYlzHW3S2w0aNPBr3wKRfsPXYFdnon7zzTemNBI8a9q0qezcudOMwDkuOoqpp571un7Rwg2aFpO0vJ3mqFasWJFD5GH2vM4zcKXvJf3cQur080qDXtfPe00P0WoNfN6nHOxq2bZVq1aZkoFITr907tixw+2zXs+46JfTFStWiBWQ0mARmjeopwI1GImKijK187QESffu3f3dtYBMY9BTqV988YWpxevIe9OJH1rTEn/T45M0t1lLIOkfDXKe3ekIpU7G0pQG/QOrdbBnzpxpLnCntUA1Z1dHkzSlYevWrTJhwgR5+umnOVQicvHiRdm/f7/bRDUNQHRirR4zTf8YOXKkVK1a1QTAWnZLgxOtKZ7TpHas9KzL448/bk7T69k8PSPl+LzX+3WwKCe5mMb7KumXAS2xqF+ubr/9drEEf5eJgPe8/fbb9goVKtjz5s1rypRt2LCBw+uBvu09XWbPns3xSgfKkqVsyZIl9urVq5sSUdWqVbPPnDmT95QH8fHxprSdfl7lz5/fXrlyZfsrr7xiv3r1KsfLbrevWbPG42dUt27dnKXJXn31VXvp0qXNe61p06b2vXv35shjl9qxOnjwYIqf9/q4nGZNGu+rpKxWlixE//F30A0AAABkF3J4AQAAYGkEvAAAALA0Al4AAABYGgEvAAAALI2AFwAAAJZGwAsAAABLI+AFAACApRHwAgAAwNIIeAEAAGBpBLwAEOBiY2Old+/eUrlyZcmXL5+UL19eHnnkEVm9erVP+xESEiKLFy/26XMCgDfk9speAADZ4tChQ3LvvfdKWFiYjB8/XmrUqCEJCQmyYsUK6dWrl+zZs4cjDwBpCLHb7fa0NgIA+EerVq1kx44dsnfvXilYsKDbfXFxcSYQPnLkiBkB1hHf0NBQeeihh+Ttt9+W0qVLm+2eeuops63r6Gzfvn1l27Zt8u2335rb999/v9SsWVPy588v7777ruTNm1eef/55ee2118z9ERERcvjwYefjK1asaIJxAAgGpDQAQIA6d+6cLF++3IzkJg12lQa7NptN2rZta7b97rvvZOXKlXLgwAHp2LFjhp9vzpw55nk2btwo48aNkxEjRpj9qR9//NH8P3v2bDl58qTzNgAEA1IaACBA7d+/X/QkXLVq1VLcRkd1d+7cKQcPHjS5vWru3Lly5513mqC0bt266X4+HeEdNmyYuV61alWZOnWq2f8//vEPKVmypDPILlOmTJZfGwD4EiO8ABCg0pNx9ssvv5hA1xHsqsjISBOY6n0ZoQGvq7Jly8rp06cztA8ACEQEvAAQoHSUVSsjZHVimub1Jg2edeJbUnny5HG7rc+tKRMAEOwIeAEgQBUrVkxatGgh06ZNk0uXLiW7Xyei3XHHHXL06FFzcdi9e7e5T0d6laYjaN6tK52wllEaECcmJmbqtQCAPxHwAkAA02BXg8yoqChZtGiR7Nu3z6QqTJkyRRo0aCDNmjUzpcq6dOkiW7ZskU2bNkl0dLQ0adJE6tSpY/bx4IMPyubNm01urz5e83R37dqV4b5opQbN6dW6wH/88Uc2vFoAyB4EvAAQwHSxCQ1kH3jgARkwYIBUr17dTCLTwHP69Okm7eCLL76QokWLSuPGjU0ArI+ZP3++cx86Svzqq6/KSy+9ZCaxXbhwwQTFGfXWW2+Zqg2aL3z33Xd7+ZUCQPahDi8AAAAsjRFeAAAAWBoBLwAAACyNgBcAAACWRsALAAAASyPgBQAAgKUR8AIAAMDSCHgBAABgaQS8AAAAsDQCXgAAAFgaAS8AAAAsjYAXAAAAYmX/H8RkMf5WZqh8AAAAAElFTkSuQmCC",
      "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": 14,
   "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": 15,
   "id": "e28013a8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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EF0PaomEgqznYg9zCYjQbt0zt73uzFzxdOcedbDte44wEIiIrt/tkJu6Zuk4Fu7LU649Pd8LQzvWqLNgV8tj3xtZVP0t+5vGzuej36XpsPHq2yn4mWZdaXq5qI9IDjvBWgCO8RGQt1h1JxxOztqgyYk3r+GLm0HYI8nWv1jacvVCAp7/dhvhjGXB3ccT0QW1VFQgiIi1xhJeISAdkNPWxrzerYLdzQ398/1THag92hb+3G2Y92l7lDOcXleLxr7dgxb7y5R+JiKwZUxqIiKzQ1hPn8OjMzSrAlEDzq0fawcfdRbP2SAWIaQ/HonfzYFUd4ulvt+LPw2matYeI6How4CUisjJ7T2fikRnxamRXFo/437/awM1Z+6VdZQU2qdbQp0UdFJUYMGz2VpVfTPpcWnjAZxvUJvtEto4BLxGRFUnOzMdjM7cgO78Y7SNrYfrg2ErX160KsvraBwNiVIpFTmGJCsyPp+do3SyyMFlOeNOxDLVxaWHSAwa8RERWIqegWOXsJmflIyrQG58PaWuV5aBktFnSG5qH+OJsTqEKeqVGMBGRtWLAS0RkBUpKDXhh3g7sPZ0Ffy9XlbPr56Fdzu4/kXziGUPboW5NY8my4XO3q9+BiMgaMeAlIrICH688jOX7UlSe7PTBbS22elpVCvRxVyXKpFTZH4fS1KpsRETWiAEvEZHGJFj8eNVhtT+hfwvERtSErWgW4ov374tR+9PWJuDXnae1bhIR0WUY8BIRaehMZp5KZZBF3ge2D1erm9mau2JCMKxbA7U/6sddnMRGRFaHAS8RkUaKSkrx3JztyMgpVBPAxt/VzGafi1d6NUaHerVU5Ybn525HYXGp1k2iG+Th4qQ2Ij1gwEtEpJFPVx9RC0z4uDmrWrvWVH7sejk5OmDyg61Qw9MFu05mYtLvzOe1ZVIdZP9bvdVmjZVCiK4XA14iIg3sSDqPT1YdUftv949GhL+XzT8Pdfw8MPHelmr/sz+OqtxkIiJrwICXiKia5RWWYOS8HaqM150t66Bvq1DdPAe9mgfj4Y7hav/VH3YhK5/1eYlIewx4iYiq2YTf9uNoeg6CfN3wdr9o3fX/v+9ohkh/T7WAxtuL9mndHKoEWU546Ix4tXFpYdIDBrxERNVo09GzmLXhhNqXcl41PF111/8erk54774YODgA3285iTUHU7VuEl0nWU549cE0tXFpYdIDBrxERNVERspGL9it9ge2D0PXRrV12/ft69XCI50i1b78zkxtICItMeAlIqomU1YdUakMgT5uGHV7U933+6u9miDC3xNnMvPx3tIDWjeHiOwYA14iomqw/0yWWolMvNk3Gn4eLrrvd0ltePceY9WGbzclqsoURERaYMBLRFTFSksNGPPTbhSXGtC7eTB6RwfbTZ/HNfDHPW1C1Upy/5Y+KOGCFERU/RjwEhFVsR+2nsT2xPPwdnPGG32b211/j7mjqRrR3ns6yzxhj4ioOjHgJSKqQpm5RXj3Yv7qCz2jEOTrbnf9HeDthtd6N1H7sgJbcma+1k0iIjvDgJeIqApNWn4QGTmFiAr0xpCLVQvs0YPtwtA6vAZyCkswkRPYrJ4sJ3z83T5q49LCpAcMeImIqsje05n4ZqPxEr6kMrg42e9brqOjA96425jO8dP2U9h64pzWTSIiO2K/775ERFXIYDDgrUX7UGqAWj64U4MAu+/vlnVr4P7Yuqof3vx1r5rMR0RUHRjwEhFVgZX7U7HxaAbcnB3VpC0yeqV3Y3i5OmHnyUws2H6K3WLFi6Q88+1WtXFpYdIDBrxERBYmpbcm/LZf7T92Uz2E1PBgH18U6OOO4T2i1L7k8uYUFLNvrJAsJ7xkd7LauLQw6QEDXiIiC5u7OQkJaTmo5eWKYTc3YP9eYmjnSITX8kRadgG+/OsY+4eIqhwDXiIiC8rOL8LkFYfU/ogeUfB11/+KatfLzdkJL/dqrPan/3EUZy8UaN0kItI5BrxERBb02dqjSL9QiHoBXnioQzj79grubFEH0aG+uFBQjCmrj7CfiKhKMeAlIrKQM5l5+OKvo2pfFlqw5zJk11KmbFRv42Q+Kd2WlJGrdZOISMf4bkxEZCEf/H4I+UWlaBdZE72aB7Ff/8FNUQHoEhWAohIDPlhuTAMhIqoKDHiJiCzgSOoF/LjtpNqXMmQODg7s12tgWnJ44Y5TaqEOIqKqwICXiMgCZKKarKPQs2kQWofXZJ9eo+hQP9wVEwKDAXhv6UH2m5XwcHHCvjd7qU32iWwdA14ioht0IDkLi3adUfsjb23E/rxOL9/WCM6ODlh7KA0bEs6y/6yAXKHwdHVWG69WkB4w4CUiukEfXsw/7dOiDpqF+LI/r1OEvxcGtjdWtDCVdCMisiQGvEREN2DPqUws25sCSdl9oadxBTG6fs90bwBXJ0dsOpbBUV4rUFBcgpe+36k22SeydQx4iYhugKm6QN+YEEQF+bAvK6mOnwcebB+m9j9ccQgGSeolzZSUGtQkTNlkn8jWMeAlIqqkbYnnsOpAKpwcHTCiJ3N3b9TTNxtHeeNllPcoc3mJyHIY8BIR3WDu7r1tQtXKanTjo7wDL47yTl5xmKO8RGQxDHiJiCph64kM/Hk4HS5ODhh+C3N3LeXpmxv+PcrLig1EZCEMeImIKmHKqiPq671t6iKslif70EKC/dw5yktEFseAl4ioEpUZVh9Mg6MDMKxbA/ZfVYzyOjsi/ngG1nOUl4gsgAEvEdF1+nS1cXT37pgQRDJ3t0pGeR+6WJf3k1WHLf8DiMjuaB7wfvrpp4iMjIS7uzs6dOiA+Pj4q54/f/58NGnSRJ3fokULLFmypNz9Fy5cwHPPPYe6devCw8MDzZo1w7Rp06r4tyAie3E4JRtL9yar/We6N9S6Obr1ZNf6Kj9649EMVQ2DqpcsJ7x1bE+1cWlh0gNNA9558+Zh5MiRGD9+PLZt24aYmBj06tULqampFZ6/fv16DBw4EI899hi2b9+Ofv36qW3Pnj3mc+Txli5dim+++Qb79+/HCy+8oALgX375pRp/MyLSq/+tSYCUiO3VPAiNWHe3yoTU8EC/VqHGPl+dUHU/iCokywn7e7upjUsLkx44GDSs7i0juu3atcOUKVPU7dLSUoSFhWH48OEYNWrUZecPGDAAOTk5WLRokflYx44d0apVK/MobnR0tDrv9ddfN58TGxuL22+/HW+//fY1tSsrKwt+fn7IzMyEry+XCSUio8Szueg+aY0qxP/rczehRV0/dk0VSki7gJ4frFUfMJa90BWNg7mwBxFVLl7TbIS3sLAQW7duRc+ePf9ujKOjur1hw4YKv0eOlz1fyIhw2fM7deqkRnNPnTqlajiuXr0ahw4dwm233XbFthQUFKhOK7sREV1q6toEFex2a1SbwW41aFDbG7dHBxv7fo0xb5qqhywn/PrCPWrj0sKkB5oFvOnp6SgpKUFQUFC543I7OdmYH3cpOf5P53/yyScqb1dyeF1dXdG7d2+VJ9y1a9crtmXChAnqE4Jpk1FmIqKyzmTm4YetSWr/uVuYu1tdnrnZ2Ne/7jqDpIxcviiriXywm73xhNq4tDDpgeaT1ixNAt6NGzeqUV4ZQZ40aRKeffZZrFix4orfM3r0aDUcbtqSkox/1IiITL766xiKSgxoX68W2kXWYsdUk+hQP3SJClBB12d/MJeXiCrHGRoJCAiAk5MTUlJSyh2X28HBxktYl5LjVzs/Ly8PY8aMwU8//YQ+ffqoYy1btsSOHTvw3//+97J0CBM3Nze1ERFVJCu/CN/FGz8IP826u5qM8sqqdt9vOYnne0Qh0Me9+htBRDZNsxFeSTeQyWQrV640H5NJa3I7Li6uwu+R42XPF8uXLzefX1RUpDbJBS5LAmt5bCKiyvhuUyIuFBQjKtBb5e9S9epYvxZah9dAYXEpvvzrGLufiGwrpUFKiH3++ef4+uuvVQmxp59+WlVhGDp0qLp/8ODBKt3AZMSIEarkmKQpHDhwAP/5z3+wZcsWVXZMyAy9bt264ZVXXsGaNWtw7NgxzJw5E7NmzUL//v01+z2JyHZJkDVj3XG1/0TX+nCU5dWoWklZLFMu75yNicjOL+IzQES2kdIgpHxYWloaxo0bpyaeSXkxCWhNE9MSExPLjdZKBYY5c+Zg7NixKnUhKioKCxcuVKXITObOnauC5H/961/IyMhAREQE3nnnHQwbNkyT35GIbNuvO08jOSsfgT5u6NsqROvm2K0eTQJRv7YXjqblYN7mJDzepb7WTSIiG6JpHV5rxTq8RCTk7fH2j/7EgeRsvNq7sXmUkbQxZ1Mixvy0G6E1PLD2lZvh7KS7eddWI7ewGM3GLVP7+97sBU9XTcfHiGy3Di8RkbVbeyhNBbterk74V4cIrZtj9+5pEwp/L1ecOp+H3/ZUXL6SLMPd2Ql/vtpdbbJPZOsY8BIRXcHnfx5VXwe0C4efhwv7SWPuLk54uKPxg8cXfx5VI/BUNSRXPayWp9qYt056wICXiKgCe05lYt2Rs3BydMCjN0Wyj6zEoLgIuDo7YufJTGw+fk7r5hCRjWDAS0RUgel/GEd3+7Sog7o1PdlHViLA2w33tqlbbgSeqqY6yf8t2a822SeydQx4iYgucfJcLhbvPqP2n+zKagDW5rGb6qmvK/an4Fh6jtbN0aXi0lL1oU822SeydQx4iYgu8dVfx9VStp0b+qulbcm6NAz0VmXKJIX3y784yktE/4wBLxHRJcsIz9ucqPafYK1Xq2Wqw/vD1pM4l1OodXOIyMox4CUiKuP7zUnIKSzhMsI2sNxwdKgv8otK8c3GE1o3h4isHANeIqKLJI1h5nrjMsJDO9dTS9qSdZLnxjQC//WGE8gvKtG6SURkxRjwEhFdJJOgTp7LQw1PF/RvHcp+sXJ3tKiDOn7uSL9QgF92nNa6OURkxRjwEhFd9NVfx9TXB9uFw8OVq0tZOxcnRzzSyVgjecb641yIgoiuiAEvERGAvaczselYhlpoYnAclxG2FerDiYsT9p/JQvyxDK2boxuynPDvL3ZVG5cWJj1gwEtEBGDmOmPubu/oYITU8GCf2Ag/Txf0u5h+Ysq/phsnywk3CvJRG5cWJj1gwEtEdk9yQH/eacwBfbQzlxG2Naa0hmV7k3HqfJ7WzSEiK8SAl4js3pxNiWr51Ji6fmgTXtPu+8PWNA72QacG/ig1ALM3sESZJcj/hw+XH1IblxYmPWDAS0R2Tf6Yz75Yx5WlyGx/lHfu5kTkFbJE2Y2S5YQ/WnlYbVxamPSAAS8R2bUlu88gLbsAgT5uqswV2aYeTYNQt6YHzucW4ecdp7RuDhFZGQa8RGS3DAYDvlpnLEU2qGMEXJ35lmirpLrGkLhI8+Q1eW6JiEz47k5Edmtb4jnsOpmpAt2HOoRr3Ry6QQ+0DVMlyg4kZ6sSc0REJgx4ichuzbhYiqxvTAj8vd20bg5ZoETZPW0ulii7+NwSEQkGvERkl1Kz8rF0T7Laf4SlyHRjyMXJa7/vS8bJc7laN4eIrAQDXiKyS9/FJ6G41IDYiJpoHuKndXPIQmShhM4NL5You1h9g4iIAS8R2Z2iklLMiTcGQ1xGWH8e6VRPfZ0bn8QSZZXk5uyEn5/trDbZJ7J1DHiJyO4s35eClKwCBHi7qqWESV9uaRKIsFoeyMwrwkKWKKt01YuYsBpqk30iW8eAl4jszqwNxglND7YL5+iV3kuUrWOJMiJiwEtEduZQSjY2Hs2ADFqxFJl+3X+xRNnBlGxsSDirdXNscgXCz9YmqI1LC5MecISXiOzK7A3G3N1bmwUhpIaH1s2hKuLn8XeJslkXn3O6drKc8ITfDqiNSwuTHjDgJSK7kZ1fhAXbTqr9wRcveZP+S5Qt35+CM5l5WjeHiDTEgJeI7MZP208hp7AEDWp7oVMDf62bQ9VQoqxDvVooKTVgzqZE9jeRHWPAS0R2wWAwmC9tD+oYAQcHzjy3B4PiIsx1l5mLSmS/GPASkV3YcPQsjqRegKerE+6Jrat1c6ia9GoejEAfN6RfKMDSvcaV9YjI/jDgJSK7mqzWv3UofN1dtG4OVRMXJ0cMbB+u9mdfLEdHRPaHAS8R6Z5MWPp9X4ra52Q1+yMBr9Tm3Xz8HPafydK6OUSkAQa8RKR7321KVBOX2terhcbBPlo3h6pZsJ87ejUPUvuzN7JE2bWQ5YS/e6Kj2ri0MOkBA14i0jWZqDQnPkntD744gYnsz6COxhJlC7efQlZ+kdbNsXoyIh7XwF9tXFqY9IABLxHpmkxUkglLMnFJJjCRfepYvxaiAr2RW1iCBVuNtZiJyH4w4CUiXTNNVJI8TpnARPZJytCZSpRJWoOUqaMrKyopxawNx9Um+0S2ju/+RKRbMkFJJio5OzrgoQ7Gmfpkv6RCh5erExLScrAh4azWzbFqEuSO+3mv2hjwkh4w4CUi3TItNCGpDEG+7lo3hzTm4+6C/m1Cy702iMg+MOAlIl3KzCtSE5SE6VI2kaks3fL9KapcHRHZBwa8RKRLP249ibyiEjQK8kaHerW0bg5ZiUZBPur1IGXqpFwdEdkHBrxEpDulpQZ8c7He6qC4SDVhicjENOIv5eqkbB0R6R8DXiLSnXUJ6TiangNvN2c1UYmoLMnpljJ1Uq5u2d5kdg6RHWDAS0S6Y5qQdG+bUBX0EpUl5emkTJ2YzclrRHaBAS8R6cqp83lYuT9F7XOyGl2JBLyyglj88QwcSM5iR13C1ckRXz3SVm2yT2TrNH8Vf/rpp4iMjIS7uzs6dOiA+Pj4q54/f/58NGnSRJ3fokULLFmy5LJz9u/fj7vvvht+fn7w8vJCu3btkJjIyQlE9mDOphMoNQCdGvijYaCP1s0hKxXs545ezYPUPkd5L+fs5IhbmgSpTfaJbJ2mr+J58+Zh5MiRGD9+PLZt24aYmBj06tULqampFZ6/fv16DBw4EI899hi2b9+Ofv36qW3Pnj3mcxISEnDTTTepoHjNmjXYtWsXXn/9dRUgE5G+FRSXYG58ktofzFJk9A8GdTSWKPtp+ylk5Rexv4h0zMGg4fqKMqIro69TpkxRt0tLSxEWFobhw4dj1KhRl50/YMAA5OTkYNGiReZjHTt2RKtWrTBt2jR1+8EHH4SLiwtmz55d6XZlZWWp0eHMzEz4+vpW+nGIqHpJ3d0X5u1AHT93/Plqd45M0VXJn7/bPvwDh1Mv4D93NcMjneuxxy6S1dVMdaz7tQ7lstxkla4nXtNshLewsBBbt25Fz549/26Mo6O6vWHDhgq/R46XPV/IiLDpfAmYFy9ejEaNGqnjgYGBKqheuHDhVdtSUFCgOq3sRkS2Z9aG4+rrQ+3DGezSP5JydaY879kbT6gAmP4OeF/5YZfauLQw6YFmAW96ejpKSkoQFGTMoTKR28nJFZeJkeNXO19SIS5cuIB3330XvXv3xu+//47+/fvjnnvuwdq1a6/YlgkTJqhPCKZNRpmJyLbsOZWJbYnn4eLkgAcvzsAn+idSts7L1QkJaTnYkHCWHUakU7rKRJcRXtG3b1+8+OKLKtVBUiPuvPNOc8pDRUaPHq2Gw01bUpIxB5CIbIdp4tHt0XVQ28dN6+aQjfBxd0H/NqHmUV4i0ifNAt6AgAA4OTkhJcVYPshEbgcHB1f4PXL8aufLYzo7O6NZs2blzmnatOlVqzS4ubmp3I+yGxHZjszcIvy805hvyMlqdL0Gxxknr/2+LwVnMvPYgUQ6pFnA6+rqitjYWKxcubLcCK3cjouLq/B75HjZ88Xy5cvN58tjyiS4gwcPljvn0KFDiIgw5mkRkf7M35qE/KJSNK3ji9iImlo3h2xMoyAfdKhXCyWlBny3iSUsifRI0yWIpCTZkCFD0LZtW7Rv3x6TJ09WVRiGDh2q7h88eDBCQ0NVjq0YMWIEunXrhkmTJqFPnz6YO3cutmzZgunTp5sf85VXXlHVHLp27Yru3btj6dKl+PXXX1WJMiLSn9JSg/lStIzuykQkouslk9c2HcvAnPgkPHdLFFyddZXxR2T3NA14JTBNS0vDuHHj1MQzybmVANU0MU3SEKRyg0mnTp0wZ84cjB07FmPGjEFUVJSqwBAdHW0+RyapSb6uBMnPP/88GjdujB9//FHV5iUi/fnjcBpOnM2Fj7sz+rYK0bo5ZKN6NQ9GoI8bUrMLsHRvMu6O4WuJCPZeh/fo0aOoX78+9Ip1eIlsx2MzN2PlgVQ82rkext1VPn+f6HpMXnEIk1ccRrvImpg/rJNdd15xSSmW7TXOmZEV6bjaGtllHd6GDRuqdIFvvvkG+fn5lW0nEdENScrIxaqDxpUZTfVUiSpL1W92dMDm4+ew77R912OXALdPyzpqY7BLelCpgFeWAW7ZsqXKwZUKCU899RTi4+Mt3zoioqv4ZpMsFgB0iQpAvQAv9hXdkEBfd/SONlb9mb3RuIgJEdlxwCu5th999BFOnz6Nr776CmfOnFE5spJL+8EHH6i8XCKiqpRfVIJ5m401s4dcLCtFZKkSZT9tP6XK3dlzSsPiXWfUJvtEtu6GpqFKzVtZxWz+/PmYOHEijhw5gpdfflmtVCYVFiQQJiKqCr/sPI3zuUUIreGB7k0C2clkEZK/2yTYR5W5k3J39qqwpBTPztmmNtknsuuAV0qCPfPMM6hTp44a2ZVgNyEhQdXGldFfWfGMiMjSZK7trA3Hzbm7To4sRUaWIWXtTKO8Uu5Oyt4RkZ0GvBLctmjRQpUJk8B21qxZOHHiBN5++23Uq1cPXbp0wcyZM1WuLxGRpW1POo89p7Lg5uyIAW3D2MFkUf1ah6gyd1LuTsreEZGdBrxTp07FQw89pIJcqYN75513lquXKwIDA/Hll19aqp1ERGaz1htHd++KCUFNL1f2DFmUp6sz7o81fpCatcG4qAkR2eHCE5KyEB4eflmQK5cZk5KS1H2yzK+sokZEZElp2QVYsjtZ7XOyGlUVSZX5at0xrD6YqsrfhdXyZGcT2dsIb4MGDZCenn7Z8YyMDJXSQERUVeZtTlSTaFqF1UCLun7saKoSUuZOyt1J2btvLi5dTUR2FvBeaXG2CxcuwN3d/UbbRERUISmP9O2mRLU/pBMXmqCqZbqCMG9LkiqDR0R2ktIgC02YZrGOGzcOnp5/X+IpKSnBpk2bVI1eIqKqsGJ/Cs5k5sPfyxV3tKjDTqYqJeXupOzdqfN5qgzeA3Y0QdLFyRHv39fSvE9kVwHv9u3bzSO8u3fvVnm6JrIfExOjSpMREVWFr9cbLy0/2D4Mbs5O7GSqUlLu7uGOEZi49IAqg3d/bF014GMPJMi9344CfNK/6wp4V69erb4OHTpUrbTm6+tbVe0iIirncEo2Nhw9Cym5+1AHpjNQ9RjQLgwfrjikyuBJObw24TXZ9UQ2qFLXKWbMmMFgl4iqlak81K3NgtRlZqLqUMvLFXe1DClXDs9e8uVXHUhRG5cWJrsa4ZUlhGUxCRnVlf2rWbBggSXaRkSkZOcXYcG2k2qfpciouskEyR+3nVTl8MbeWYAAbzfdPwlSCeXRmVvU/r43e8GZebxkLwGvn5+fOXdJ9omIqsuCbaeQU1iChoHeiGvgz46natWybg3EhNXAzqTzmLc5Cc92b8hngEivAa+kMVS0T0RUlWSS7NcbjJeSB8dF2M2kIbIugztG4KWk86om71Nd63PEk8gecnjz8vKQm5trvi1LDE+ePBm///67JdtGRIR1R87iaFoOvFyd0L91KHuENNGnZR2Vzytl8VbsT+WzQGQPAW/fvn0xa9YstX/+/Hm0b98ekyZNUsenTp1q6TYSkR2TclDi3ti68HF30bo5ZKfcXZxUxYayr0ki0nnAu23bNnTp0kXt//DDDwgODlajvBIEf/zxx5ZuIxHZKSn4L4tNiEEdWYqMtPWvDuGqLN76hLM4kprNp4NI7wGvpDP4+PiofUljkKoNjo6O6Nixowp8iYgsQfIlSw1Apwb+iAoyvucQaaVuTU/0aBpUbhEUItJxwNuwYUMsXLgQSUlJWLZsGW677TZ1PDU1lfV5icgi8gpL8F18otofHBfJXiWrYCqLJ2XKMvOKoOeV1t7s21xtXFqY7DbgHTdunFpCODIyEh06dEBcXJx5tLd169aWbiMR2aGFO07hfG4R6tb0UItNEFmDzg390SjIG7mFJZi/JQl6JUGufNCUjQEv2W3Ae9999yExMRFbtmzB0qVLzcd79OiBDz/80JLtIyI7LUU2Y90x84iakyROElkBKYv3SKd6an/m+uMokZwbItJnwCtkopqM5krurolUa2jSpIml2kZEdkomBR1KuQBPVyc8cHFmPJG1kPJ4NTxdcPLc35Mq9UYC+Q0JZ9XGoJ7sNuDNycnB66+/jk6dOql83vr165fbiIhuxFd/GUd374utCz8PliIj6+Lh6oSB7cPLvVb1pqC4BAM/36g22Seym5XWynr88cexdu1aDBo0CHXq1OHKR0RkMcfTc7DqoLGw/5BOnKxG1knK5E3/4yg2HcvA3tOZaB7ip3WTiMjSAe9vv/2GxYsXo3PnzpX5diKiK5K8SIMB6N64NhrU9mZPkVUKqeGB26ODsWjXGcxcdxzv3x+jdZOIyNIpDTVr1kStWrUq861ERFeUnV+EH7aeVPtDOxsnBhFZK9Nr9Oedp3H2QoHWzSEiSwe8b731lipNJgtQEBFZyvwtJ3GhoBgNA73RJSqAHUtWrU14DcTU9UNhcSnmbDLWjCYiHaU0TJo0CQkJCQgKClK1eF1cXC5bepiI6HrITHBJZxBDO0dybgDZRImyR2+qhxFzd2DWxhN4qlsDuDpXuvgREVlbwNuvXz/Lt4SI7NqqA6lIzMhVVRnuaV1X6+YQXZPbo+vgHZ/9SM0uwJLdZ9CvdSh7jkgvAe/48eMt3xIismumhSYebB+myj4R2QIZ0ZWKDZOWH1Kv4b6tQnRxdcLZ0RGjb29i3ieydZV+FZ8/fx5ffPEFRo8ejYyMDHMqw6lTpyzZPiKyAweSs9RiE7KimixlSmRLHuoQrgLfnSczsS3xPPRAfh9J0WCaBtl1wLtr1y40atQIEydOxH//+18V/IoFCxaoAJiI6HrM+MuYu9u7eTBCa3iw88im+Hu7oV+rELX/1cUrFUSkg4B35MiReOSRR3D48GG4u7ubj99xxx34448/LNk+ItK5jJxCLNxxyjxZjciWS5Qt3ZOM0+fzoIdJpDuTzquNSwuT3Qa8mzdvxlNPPXXZ8dDQUCQnJ1uiXURkJ76LT0RBcSla1vVDbERNrZtDVClN6/girr6/Cg5nbThh870oywn3/XSd2ri0MNltwOvm5oasrKzLjh86dAi1a9e2RLuIyA7IH9KvWYqMdMJ0hUI+xOUUFGvdHCK60YD37rvvxptvvomioiJ1W2akJiYm4rXXXsO9995bmYckIjv0847TqpxTsK87+rQw5kAS2aoeTYNQL8ALmXlF+H5LktbNIaIbDXhl4YkLFy6o0dy8vDx069YNDRs2hI+PD955553KPCQR2RmDwYDP/zhqHhljwX6ydVJl5LGbjLm8X/51DMUlpVo3iYhupA6vn58fli9fjnXr1mHnzp0q+G3Tpg169uxZmYcjIju05lAaDqdegLebMwZ2CNe6OUQWcV9sXXyw/BBOnsvD0r3JuLMlr1wQ2WTAW1paipkzZ6oSZMePH1fpDPXq1UNwcLAasdFDwW0iqnqm0d2B7cPg615+eXIiW+Xu4oTBcRGYvOKweo33aVGHfxeJbC2lQQJayd99/PHH1QITLVq0QPPmzXHixAlVpqx///5V11Ii0o09pzLVQhPOjg7mck5EeiErr7ldXIhi0zHjwkxEZEMjvDKyK3V2V65cie7du5e7b9WqVejXrx9mzZqFwYMHW7qdRKQj0y+O7t7Zsg5CuNAE6XAhCklt+HZTohrl7VjfH7ZGlhMe0SPKvE9k667rVfzdd99hzJgxlwW74pZbbsGoUaPw7bffWrJ9RKQzJ8/lYvHuM2r/8S71tW4OUZWQyWuS4bfyQCqOpGbbXC/LJNIXb22kNk4oJbsLeGVJ4d69e1/x/ttvv11NYiMiupIZ646r4vydG/ojOtSPHUW6VL+2N25tGqT2v/iTyw0T2VTAm5GRgaAg43/gish9586du+5GfPrpp4iMjFTLFHfo0AHx8fFXPX/+/Plo0qSJOl/yiJcsWXLFc4cNG6YmDEyePPm620VEliX1SefGJ6r9Jzi6Szr3ZFfjFYwF204hNTsftqS01IBDKdlqk30iuwp4S0pK4Ox85bRfJycnFBdf3+oy8+bNw8iRIzF+/Hhs27YNMTEx6NWrF1JTUys8f/369Rg4cCAee+wxbN++XeUNy7Znz57Lzv3pp5+wceNGhISwLAyRNZizKRE5hSVoHOSDbo24KiPpW9vIWmgTXgOFJaWYtd62lhvOLy7BbR/+oTbZJ7KrSWtSpUGqMcjSwhUpKCi47gZ88MEHeOKJJzB06FB1e9q0aVi8eDG++uorlRN8qY8++kilVbzyyivq9ltvvaVqAk+ZMkV9r4lUkRg+fDiWLVuGPn36XLUN0u6yba9o2WQiujGFxaWYsc54afeJrvVZqonsZpR32DfbMHvjCTzTvQE8XStV/p6IqnOEd8iQIQgMDFQLT1S0yX3XU6GhsLAQW7duLbdghaOjo7q9YcOGCr9Hjl+6wIWMCJc9X2oFDxo0SAXFUjbtn0yYMKHc7xEWFnbNvwMRXZuFO+SybgGCfN1wdwyvupB9uLVZMCL8PVU6z7zNXG6YSCvX9VFzxowZFv3h6enpKk3i0rxguX3gwIEKvyc5ObnC8+W4ycSJE1XqxfPPP39N7Rg9erRKqyg7wsugl8hyZJLatLUJal/q7nLWN9nTcsOSrz524R5VouxfHSL4+ifSgO6K68mIsaQ9SM3ga131TVI0fH19y21EZDnL9ibjaFoOfN2d8XDHCHYt2RWpyVvbxw2nM/PVlQ4isrOANyAgQE10S0lJKXdcbstSxRWR41c7/88//1QT3sLDw9Uor2yyEtxLL72kKkEQUfWS3P9PVx9R+490rgdvN+Ywkv0tN/xEF+OKgtPWJKgrHkRkRwGvq6srYmNj1cptZfNv5XZcXFyF3yPHy54vZNKa6XzJ3ZV6wTt27DBvUqVB8nllAhsRVa+1h9Kw93QWPF2dMLQTP3SSfXqoQwT8PFxwND0HS/f8nYJHRNVD86EWyZ2VyXBt27ZF+/btVb3cnJwcc9UGmQQXGhqqJpaJESNGoFu3bpg0aZKqvjB37lxs2bIF06dPV/f7+/urrSwXFxc1Aty4cWMNfkMi+/a/1cbc3Yfah6Oml6vWzSHShFzZeKRTJD5aeVhd8bijRbBVVyqR5YRNdYS5tDDpgeYB74ABA5CWloZx48apiWetWrXC0qVLzRPTEhMTVeUGk06dOmHOnDkYO3asWuY4KioKCxcuRHR0tIa/BRFVJP5YBuKPZ8DVyZHLCJPdk4D38z+PYt+ZLKw5lIbujQOttk9kYumYO5pq3Qwii3EwSIIdlSNVGqQ8WWZmJiewEd2AR2bEY83BNAxsH44J97RgX5Lde2fxPnz+5zG0i6yJ+cM62X1/EFVXvKa7Kg1EZB32nMpUwa6jAzCsm/HSKJG9e7xLfXXFY/Pxc+oKiLWS5YSTMnLVxqWFSQ8Y8BJRlZi6xpi7e1dMCCL8vdjLRFI33tcd97Wtq/rCVL3EGslywl3eW602Li1MesCAl4gsLiHtApbsOaP2n7m5IXuYqIxhXRuoBSmkgolcCSGiqseAl4gsTmqNyuyAW5sFoXGwD3uYqIxwf0/z8tr/W2O9o7xEesKAl4gsSnL+ftpuXE3qmZsbsHeJKvD0xf8bv+1JxqGUbPYRURVjwEtEFiV5icWlBnSJCkDr8JrsXaIKNArywe3RwepKyMcrD7OPiKoYA14isujo7g9bT6r9F3pGsWeJruL5Hsb/I4t3n+EoL1EVY8BLRBYzZdXfo7uxEbXYs0RX0bSOr3mUV1ZgI6Kqw4CXiCwi8WwufthmGt1txF4lugYjLl4JWbL7DA4mW08ur1SRGNQxQm2yT2TrGPASkUVMWX0YJaUGdG1UG7ERzN0luhZNgn1xRwvry+V1c3bCW/2i1Sb7RLaOAS8R3bATZ3Pw4zZjZQbm7hJdnxE9GplzeQ8kZ7H7iKoAA14iskjurozudmtUG21YmYHoukit6j4t6qh9axnlNRgMOHuhQG2yT2TrGPAS0Q05np6DBRfr7nJ0l6jyFRscHCSXNxn7Tms/yptXVILYt1eoTfaJbB0DXiK6IR8sP6RGd29uXJt1d4ksMMo76feD7EciC2PAS0SVJiNRv+w8rfZfvq0xe5LoBoy8tZGqiLDyQCq2nshgXxJZEANeIqo000hUn5Z1EB3qx54kugH1a3vjvjZ11f57Sw8yd5bIghjwElGlbDmeoUaiZETqpVtZd5fIUnV5XZ0dselYBv44nM5OJbIQBrxEdN1k1vZ7y4yju/fH1lUjU0R040JqeKjFHsT7yw6gtJQVEogsgQEvEV23tYfSEH8sQ41EmVaKIiLLeObmBvBydcKeU1n4bU8yu5XIAhjwEtF1kRGn9y+O7g7uGIE6fh7sQSIL8vd2w+Nd6qv9ScsPoriktNr7V1KV7m1TV21cWpj0gAEvEV2XJXvOYO/pLHi7OeOZ7g3Ze0RV4PEu9VDT0wVH03Lww9aT1d7HspzwpAdi1MalhUkPGPAS0TUrKC7BxKUHzH+Qa3m5sveIqoCPuwuevfiBUmpd5xQUs5+JbgADXiK6ZrPWn0BSRh4CfdzwZFfjJVciqhqD4iIQXssTqdkFmP7H0WqfmJpbWKw2Li1MesCAl4iuybmcQnyy6rB5kQlPV2f2HFEVklSC13o3UfsS8KZk5Vdbf8tyws3GLVMblxYmPWDAS0TX5ONVh5GVX4wmwT64N9ZYHJ+IqtYdLYLRJryGCjq55DBR5THgJaJ/dCw9B7M3nFD7/+7TlLO2iaqJg4MD/t2nmdqfv/WkWs6biK4fA14i+kcTfzuA4lIDbm5cG12iarPHiKpRbERNtXy3wQD835L9zKklqgQGvER0VbLAxNK9yXB0AMbc0ZS9RaSB13o1gauTI/46ko41h9L4HBBdJwa8RHRFJaUGvLVon9of0C4cjYJ82FtEGgj398SQTsYlh99ZvB9FGixGQWTLGPAS0RV9vyUJu09lwsfNGSNvbcSeItLQc92jVO3rI6kX8PX643wuiK4DA14iqlBmbpF5CeERPaNQ28eNPUWkIT9PF7zaq7Han7ziMFKzq65MmaODg6oQIZvsE9k6BrxEVKEPlh9ERk4hogK9MaRTJHuJyAo80DYMMXX9cKGgGBN/M34grQruLk74379i1Sb7RLaOAS8RXWb/mSzM3mgsQ/afu5vDxYlvFUTWwNHRQf2fFD9uO4mtJ85p3SQim8C/YkRUjiwjOv7nvSg1GIved24YwB4isiKtw2vi/ouLv4z/ZY+aXEpEV8eAl4jK+WXnacQfz4C7i6O54D0RWZdXezeBj7sz9pzKwrzNSRZ//NzCYkSOWqw22SeydQx4icgsO79IFbYXz9zcEKE1PNg7RFZIJpG+2NNYOeX9ZQdUvj0RXRkDXiIy+++yg0jJKkCEvyee7FqfPUNkxQbHRaBJsA/O5Rap2rxEdGUMeIlI2ZZ4DrMuTlT7v/4tODObyMo5Ozliwj0tIFXDZALbuiPpWjeJyGox4CUitWrTmAW7YTAA97QJ5UQ1IhuawDaoo3EFtjE/7UZ+UYnWTSKySgx4iQif/3kUB5KzUdPTBWM5UY3IprzSqzGCfd1x4mwuPll1WOvmEFklBrxEdu7E2Rx8tML4R1KCXVm6lIhsh4+7i7k272dr5cNrltZNIrI6DHiJ7Lzm7tiFe1BQXIrODf1VOgMR2Z7e0cG4rVkQiksNGL1gN0pvsDavLCfcvXFttXFpYdIDBrxEdmz+lpP483A63Jwd8U4/mfzioHWTiKiS3ujbHN5uztieeB4z1h+/oX6U5YRnDG2vNi4tTHrAgJfITp06n4c3F+1T+yNvbYTIAC+tm0REN6COnwdG3d5E7b+39AAS0i6wP4kuYsBLZKepDK/9sAsXCooRG1ETj3dhzV0iPfhXh3B0iQpQaUovz9/JZYeJrCng/fTTTxEZGQl3d3d06NAB8fHxVz1//vz5aNKkiTq/RYsWWLJkifm+oqIivPbaa+q4l5cXQkJCMHjwYJw+fboafhMi2/DNpkT8dSRdLR/83/tj4OTIVAYiPZC0pIn3toTPxdQGqcBSGbKccNPXl6qNSwuTHmge8M6bNw8jR47E+PHjsW3bNsTExKBXr15ITU2t8Pz169dj4MCBeOyxx7B9+3b069dPbXv27FH35+bmqsd5/fXX1dcFCxbg4MGDuPvuu6v5NyOyTolnczHh4vLBr/VugnpMZSDSlZAaHnj9rmZq/4PfD+FQSnalHievqERtRHrgYJBrmxqSEd127dphypQp6nZpaSnCwsIwfPhwjBo16rLzBwwYgJycHCxatMh8rGPHjmjVqhWmTZtW4c/YvHkz2rdvjxMnTiA8PPwf25SVlQU/Pz9kZmbC19f3hn4/ImsiM7cf/Hwj4o9loGP9WpjzeEc4cnSXSHfkT/vjX2/BygOpaBHqhwXPdIKL07WPccmobrNxy9T+vjd7wdPVuQpbS1Q51xOvaTrCW1hYiK1bt6Jnz55/N8jRUd3esGFDhd8jx8ueL2RE+ErnC+kIucxTo0aNCu8vKChQnVZ2I9KjL/46qoJdL1cnvH9fDINdIp2Sv3my7LCfhwt2n8rEJ6uOaN0kIk1pGvCmp6ejpKQEQUFB5Y7L7eTk5Aq/R45fz/n5+fkqp1fSIK4U/U+YMEF9QjBtMsJMpDe7Tp7H+8sOqv2xdzZDWC1PrZtERFUo0Ncdb/eLVvtTVh3GxqNn2d9ktzTP4a1KMoHtgQceUJd2pk6desXzRo8erUaBTVtSUlK1tpOoqkk1huHfbUdRiQF3tAjGg+34oY7IHtwVE4L7Y+tC1qF4Ye4OnMsp1LpJRPYX8AYEBMDJyQkpKSnljsvt4ODgCr9Hjl/L+aZgV/J2ly9fftXcDjc3N3V/2Y1IT15fuAcnzuYitIYHJvRvyQUmiOyILDtcP8ALyVn5ePXHXWoQiMjeaBrwurq6IjY2FitXrjQfk0lrcjsuLq7C75HjZc8XEtCWPd8U7B4+fBgrVqyAv79/Ff4WRNZtwbaT+Gn7KVV67KMHW8HP00XrJhFRNfJyc8bHA1vD1ckRy/elYPbGE//4PbKccId6tdTGpYVJDzSfdiklyYYMGYK2bduqSgqTJ09WVRiGDh2q7pcauqGhoSrPVowYMQLdunXDpEmT0KdPH8ydOxdbtmzB9OnTzcHufffdp0qSSSUHyRE25ffWqlVLBdlE9uJYeg7GLjSW7HuhRxTaRtbSuklEpIHoUD+1Cpusrvj24v1oG1ELzUKufDVTlhOe91TFA09EtkjzgFfKjKWlpWHcuHEqMJXyYkuXLjVPTEtMTFSVG0w6deqEOXPmYOzYsRgzZgyioqKwcOFCREcbE/NPnTqFX375Re3LY5W1evVq3HzzzdX6+xFpJa+wBM98uw25hSVqlOaZ7g35ZBDZsaGdI9WCM6sOpOLZOdvw83Od4evOKz5kHzSvw2uNWIeXbJ38t35x3g4s3HEaAd6uWDS8C4L93LVuFhFp7OyFAtz1yV84nZmPW5sF4bOHY1mekGyWzdThJaKq8fX64yrYlbzdKQ+1YbBLRIq/txumPhxrzuf935ojV1x4os1by9XGpYVJDxjwEumMLCwhOXpizB1N0bE+J20S0d9iwmrgrX7N1f6k5Yew5mBqhd2TkVOoNiI9YMBLpCMpWfkqb7e41IC7Y0LwaOdIrZtERFZoQLtwDGwfDklqHDF3B5IycrVuElGVYsBLpBP5RSUY9s1WpF8oQJNgH7x7bwvW2yWiK/rP3c3UaG9mXhGemLUFOQXF7C3SLQa8RDpQWmrAy/N3Ynviefi6O2Paw7HwdNW8CAsRWTE3ZydMe7iNmth6IDkbz3+3HSWyJBuRDjHgJdKBD5YfwqJdZ+Ds6IBpg2IRGeCldZOIyAbU8fPA54Pbws3ZESsPpOKtRfu0bhJRlWDAS2Tj5m9JwpTVxpnWE+5pgU4NArRuEhHZkNbhNfHhAGPd+pnrj2PmumNaN4nI4hjwEtmw9QnpGL1gt9p/rntD3N82TOsmEZENuqNFHbzWu4nal9XY/jiUhpZ1/dTGpYVJD5jkR2SjDiRnYdjsraoiw50t62DkrY20bhIR2bBh3erjeHoO5m1Jwsjvd2LOEx3RKqyG1s0isgiO8BLZIPmjNOjLeGTlFyM2oib+e38MV0siohvi4OCAt/tH46aGAWpJ8kdmxONQSjZ7lXSBAS+RjUnOzMe/vtiEtGxj+bGvhrSDu4uT1s0iIh1wcXJUE19lZPd8bhEe/mITEs+yRi/ZPga8RDZEVj16+MtNOHU+D5H+npj9WAf4ebpo3Swi0hFvN2dMfbiNqvqSml2Ah77YqBa1IbJlDHiJbERWfhGGfBWPI6kXUMfPHd883gG1fdy0bhYR6ZCfh4uaHyBOnsvDoC83cZlhsmkMeIlsQGZuEQZ9sQm7T2WilperGtmtW9NT62YRkR0I9HHFoZQLeOjzjWolRyJbxICXyAbSGOSS4s6Tmajp6YLZj7VHw0BvrZtFRHbiy0faI9DHTa3G9uD0jUhlegPZIAa8RFZMRlNkVGXv6Sy1/OfcJ+PQPMRP62YRkR1pUNsL856KU6lUklI1YPpGnMnM07pZRNeFAS+RlZJRFBlNkVEVGV2RYLdxsI/WzSIiO1QvwAvfPxWH0BoeOJaegwc+24CkDFZvINvBgJfICh1JzUb//603T1CT0RWmMRCRlsJqeeL7YXGI8PdEUkYe7p26HntPZ/JJIZvAgJfIymw+noF7p24wlx6TURUZXSEiqi4OcEBUoLfaZN9ERnjnPRmHRkHeqmTZgM824s/DaXxiyOo5GAwGY90RMsvKyoKfnx8yMzPh6+vLnqFq89vuMxgxbwcKi0vROrwGvhjcFv7eLD1GRNYlM68IT83ego1HM1S93on3tsS9sXW1bhbZmazriNc4wktkBeRz5xd/HsUzc7apYPfWZkGY83hHBrtEZLV1er9+tD3ujglR9Xpfmr8TH688rN7LiKwRA14ijeUXleCl73fi7cX7IX8rBnWMwLSHY+HhyuWCich6uTk7YfKAVhjWrYG6/cHyQ3jm2224UFCsddOILuN8+SEiqi4nz+XiqdlbVdkxJ0cH/PuOphjaORIODn/nzBERVbe8whLcPeUvtf/Lczdd8QO4o6MDRt3eRM03GPfzXvy2J1lNtp0+uC3nHpBV4QgvkUbWH0nHXZ/8pYJdWT3tm8c64NGb6jHYJSLNGWDA4dQLapP9f/Jg+3DMfaqjKqEo3yPB8qoDKdXSVqJrwYCXqJoVlZRi0u8H8fCXm3AutwgtQv3w6/CbENfAn88FEdmsNuE1sWj4TWgbURPZ+cV4dOYWvLN4HwqKS7RuGhEDXqLqlHg2VxVs/2TVEZQagAfa1sX8YcZi7kREti7Q1x1znuiIIXER6vbnfx7DPRdrihNpiSO8RNVAZi7/tP0k7vj4T2xPPA8fd2d8PLA13rsvBu4unJxGRPrh6uyIN/pG4/PBbVHT00Wlbd35yZ/4Lj6RVRxIMwx4iapYcmY+npy9FS/O26lmL8vlvt9GdFHlfIiI9ErKKy59oSs6N/RHflEpRi/YjSEzNnNJYtIEA16iKlJaasCcTYm49YO1WL4vRRVnf7FnI8x9siPq1vRkvxOR7gX5umP2ox0w+vYmauT3j0Np6DX5D3z11zGUSF4XUTVhWTKiKnAkNRv//mkPNh3LULdjwmpg4r0t0CSYK/cRkfWT5YRNcwvKLi1cGVK67KluDdCzWRBG/7gb8ccz8Oaiffh552n8X/9oNA/xs1Cria6MSwtXgEsLU2Wdzy3E5BWHMXvjCTV64eHihJd7NcYjnSJVnV0iInu/8vXd5kS8u+QAsguKISXHH2wXhpdua4wALqNOVRivMeC9wQ4kMpUa+3bjCXy44rBaY96UvzbuzmYIq8X0BSKiS+c2vL14HxbtOqNu+7g5Y3iPhhjSKVKt4EZ0LRjw3iAGvHStZBT3152n8dHKwziWnqOONQn2wet3NkPnhgHsSCKiq9gs6Q2/7sPuU5nqdt2aHnj+lij0bxMKFydOM6KrY8B7gxjw0rVcllu8+wwmrziEhDRjoCurpY28tZG6POfMN2oismH5RSWqZrj4/qm4Ki2fKO+nP247ifeXHURqdoE6FuHvqQLfvq1C+H5KFonXOGmN6DrIikE/bz+Nz/88qpbPFDU8XfBk1/oYEhcJLzf+lyIi21dqMGDXyUzzflWSSW33tw3DnS1D8O2mE5i6JgEnzubipfk7MWX1ETx2Uz3c26YuPFyZ6kCVx7/ORNfgXE4hvtl4Al9vOIH0C8YRCFk84oku9TG0cyR83F3Yj0REN0AC2se71MdDHcIxa8MJfLY2QaWKjV24Ry3HPqhjBAbFRaK2jxv7ma4bA16iq6yOtuXEObU60JLdZ1ThdFHHz10FuQ+2D4cvA10iIovydHXGsG4NVID7/ZYkfLXuGJIy8vDxqiOYtvYoekUHY2D7MMTV94eDlHkgugYMeIkukZZdgJ93nMLczUnl1n+PDvVVI7p3tKjDyRRERFVMUsSGdq6HwXGRWLY3WaWSydLsMlFYtkh/TwxoF47+rUMR7OfO54OuigEvEaBKiS3bk4xfdp7G+oR0mBYAkjq6d8XUwcD24WgVVoOjCURE1UxqmMtAg2y7T2aqOr6/7DiN42dzMXHpAby37ADaR9bC3a1CcEd0HdT0cuVzRJdhHd4KsEqDfTh5LherD6Ri5YFUrD9yFoUlxpQF08po98fWVTOEmZ9LRPYmt7AYzcYtU/v73uyl0gysSU5BMRbvOqNSHiT1zESWcI9r4I+eTYPQo2kgl3HXuSxWaSCqeHGInUnnsepAqtoOJGeXu1/q594VE4K7WoYg3J+LRRCRfZNSi9ac7vBAuzC1yeCFBL9yhW7v6Sz8eThdbeN/2ave17s3CUTnBgGIjajJSg92jCO8FeAIr37qSEqAG38sA5uOZWDriXPIKyox3y8r/baNqIVbmgaiR5NARAX5aNpeIiK6MUfTLmDF/hSs2JeKLScyzOlpwtXJEa3Da6BTgwB0auiPlnX9uKqbjePCE9XYgWQdpHD5sbM5Kr9LakfuPnUeO09morD47zQFU83crlG11aWubo1qo4an9Y5gEBHRjZWTXH0wFX8dSVdpa8lZ+eXud3FyQLM6viqFLaZuDbQKr4F6/l6qLjDZBga81diBpM2b2KGUbLXwg1RR2H8mS13GulBQfNm5Ad5u6FC/FjrUk80fUYHefDMjIrLDMpMyyU0mJa9POIuNCWdxNqfwsvN83JzRONgHjYJ90DjIR+3LV06Es04MeKuxA6lq3pikNFjSuVwkZuSq+otJGcb9hLQLSL9w+ZuUcHdxRPMQP7QINW7yab1+gBcrKxARVSIlbMhX8Wr/60fbV+nSwlr9nTl5Lg87ks6r1LedJ89j96lMc731S/l7uaq5HRG1PBHu76VKosnyx+G1vBDg7cq/MxqxuUlrn376Kd5//30kJycjJiYGn3zyCdq3b3/F8+fPn4/XX38dx48fR1RUFCZOnIg77rij3At5/Pjx+Pzzz3H+/Hl07twZU6dOVeeSduR5ycorRmp2vgpoZc30cvtZxtvyJlRwSSrCpcJqeSAq0EeN2ErurQS4DWp7cc11IiILkOWEZe6DaV9vZMGKsFqeapPJyqaJzTKocjA5W11FlK8HU7LVoIuMBssmdYArGmwJ8nVXW7Bsfu4I9HG7+NUdtbxcUNPTFX4eLvwbpSHNA9558+Zh5MiRmDZtGjp06IDJkyejV69eOHjwIAIDAy87f/369Rg4cCAmTJiAO++8E3PmzEG/fv2wbds2REdHq3Pee+89fPzxx/j6669Rr149FRzLY+7btw/u7ixOXZn82PziEuQWliBPtiLjvpStkdumfallK9v5XONX2bLyyuznF6Ok7AyCq5AUqjp+HghXb0geCKtpfGNqUNsbDQK9rK5EDhER2TYXJ0c0CfZVW1mSLnc8PUddZTxxVrYc9VVun87MU6PCxuO5//gzJOiV6hcyn6SWp3x1VcvUe7s5q8oT3mrfCd5uLvBSX53Nm5uLE9ycHdXGFeZssEqDBLnt2rXDlClT1O3S0lKEhYVh+PDhGDVq1GXnDxgwADk5OVi0aJH5WMeOHdGqVSsVNMuvExISgpdeegkvv/yyul+GuoOCgjBz5kw8+OCDVpfS8NfhdGTnF6HEYFAzSiXAlMBQPlUbN6jb8rvJ1xKDcbTUeI7x07f5/IvHjI9lvF1UIlvpxc2gJnJJzVnzsWKDui3Hy54nl7RUkFumsoEl+Lo7I9DXHbW93RDo66Y+Ccva6PJJWPZDa3ogpIYHVzMjItKItdfhtRYFxSVIzsxHSlaBmhSXkpmvvsqWmmW8gnnu4iCQJbleDHzdnJ3UCLNp3+3ivqSgSAAvE/OcHB1VfWK1qduybzzm5GQ8Lue4XHLbyQFqzosE1zII5Xjxq/H238dkdWfHMsfcXZ3QvfHlA5Z2ndJQWFiIrVu3YvTo0eZjjo6O6NmzJzZs2FDh98hxGREuS0ZvFy5cqPaPHTumUiPkMUykMySwlu+tKOAtKChQW9kOrE7jf9mDhLQc2AL5j+Tp6qTe/DzUV/nP5gQvVyf1SVU+vfp6uKivFW3yqVZvuWBERGSfJMiM8PdS29UUl5SqoPdcbiEycoxfZQK2BMMXCoqQU1CC7PxitaDGhTJbTpmvZS+QqoGr4lJk4/LJ2lqr4+eODaN7wNpoGvCmp6ejpKREjb6WJbcPHDhQ4fdIMFvR+XLcdL/p2JXOuZSkR7zxxhvQSsu6NeDv5aY+JcknL/UpST5hmT41qWPG++STlZNsah9q/9JzTJ+0nByN32/8lOcIF2cHVYfQfNvJQX1KLHfbyVEdc3aST4iO8HQxBrZqc3FSj09ERETXTv6m+nu7qa0y5KpusaQXFpWoOS5qK7NvPl72/uIS81XeklLj95eUlv7jbflaXGK8Siw5AGWvNks7TFeWTVekL73fWhcs4TUKQI0wlx01lhFeSauoLh8OaFVtP4uIiIhsiwx2yaCUDE5xiSQbDHgDAgLg5OSElJSUcsfldnBwcIXfI8evdr7pqxyrU6dOuXMkz7cibm5uaiMiIiIjuapHpBeOWv5wV1dXxMbGYuXKleZjMmlNbsfFxVX4PXK87Pli+fLl5vOlKoMEvWXPkRHbTZs2XfExiYiI6G8yT2P/W73VxglrpAeapzRIKsGQIUPQtm1bVXtXypJJFYahQ4eq+wcPHozQ0FCVZytGjBiBbt26YdKkSejTpw/mzp2LLVu2YPr06eZh/xdeeAFvv/22qrtrKksmlRukfBkRERER2RfNA14pM5aWloZx48apSWWSdrB06VLzpLPExERVucGkU6dOqvbu2LFjMWbMGBXUSoUGUw1e8eqrr6qg+cknn1QLT9x0003qMVmDl4iIiMj+aF6H1xpxaWEiIrJnMuv/6W+2qv2pD8eynCRZJZupw0tERETWR8pMrT6YZt4nsnWaTlojIiIiIqpqDHiJiIiISNcY8BIRERGRrjHgJSIiIiJdY8BLRERERLrGKg0VMFVqk3IXRERE9ia3sBilBbnmv4XFrgwXyPqY4rRrqbDLOrwVOHnyJMLCwiz/zBARERGRRSUlJaFu3bpXPYcBbwVKS0tx+vRp+Pj4qKWKbemTjgTq8sT/UwFmYv9aG75+2b+2jK9f9q8ty7LR+EFGdrOzsxESElJuVd6K8BpFBaTT/umTgjWTF6stvWBtDfuX/WvL+Ppl/9oyvn7Zv5eSldauBSetEREREZGuMeAlIiIiIl1jwKsjbm5uGD9+vPpK7F9bw9cv+9eW8fXL/rVlbnYQP3DSGhERERHpGkd4iYiIiEjXGPASERERka4x4CUiIiIiXWPAS0RERES6xoDXxkydOhUtW7Y0F9+Oi4vDb7/9Zr7/5ptvVqvDld2GDRumaZtt2bvvvqv68IUXXjAfy8/Px7PPPgt/f394e3vj3nvvRUpKiqbt1FP/8jVcef/5z38u+//fpEkT8/187VZt//K1e+NOnTqFhx9+WL2/enh4oEWLFtiyZUu5lbXGjRuHOnXqqPt79uyJw4cPW+An24dT/9C/jzzyyGWv8d69e0MPuNKajZEV4CRIiIqKUv/xv/76a/Tt2xfbt29H8+bN1TlPPPEE3nzzTfP3eHp6athi27V582Z89tln6gNGWS+++CIWL16M+fPnqxVennvuOdxzzz1Yt26dZm3VU/8KvoYrT94HVqxYYb7t7Pz32zxfu1Xbv4Kv3co7d+4cOnfujO7du6uBnNq1a6tgtmbNmuZz3nvvPXz88cfqb1+9evXw+uuvo1evXti3bx/c3d1v4Kfr37lr6F8hAe6MGTPMt/VSqowBr4256667yt1+55131Kjvxo0bzQGvBLjBwcEatVAfLly4gH/961/4/PPP8fbbb5uPZ2Zm4ssvv8ScOXNwyy23qGPyxtC0aVP1HHTs2FHDVtt+/5rwNVx5EoBV9P+fr92q7V8TvnYrb+LEiQgLCysXbElQayKDPJMnT8bYsWPVQI+YNWsWgoKCsHDhQjz44IM38NP1b+I/9G/ZAFePMQRTGmxYSUkJ5s6di5ycHJXaYPLtt98iICAA0dHRGD16NHJzczVtpy2SlIU+ffqoy2Vlbd26FUVFReWOyyXN8PBwbNiwQYOW6qt/TfgarjwZsQkJCUH9+vXVh4rExER1nK/dqu1fE752K++XX35B27Ztcf/99yMwMBCtW7dWH4pNjh07huTk5HLvG3KVrUOHDnz/tUD/mqxZs0bd37hxYzz99NM4e/Ys9IAjvDZo9+7dKsCVfDzJIf3pp5/QrFkzdd9DDz2EiIgI9Ya8a9cuvPbaazh48CAWLFigdbNthnyI2LZtm7rkfil5s3V1dUWNGjXKHZcRBrmPbqx/BV/DlSd/+GfOnKn+UJ05cwZvvPEGunTpgj179vC1W8X96+Pjw9fuDTp69Ki6Yjly5EiMGTNGvUc8//zz6j13yJAh5vdYeb8ti++/lulfUzqDpOjJyG9CQoI67/bbb1cfKJycnGDTDGRzCgoKDIcPHzZs2bLFMGrUKENAQIBh7969FZ67cuVKgzzNR44cqfZ22qLExERDYGCgYefOneZj3bp1M4wYMULtf/vttwZXV9fLvq9du3aGV199tVrbqsf+rQhfw5V37tw5g6+vr+GLL77ga7eK+7cifO1eHxcXF0NcXFy5Y8OHDzd07NhR7a9bt079PTt9+nS5c+6//37DAw88cJ0/zf64/EP/ViQhIUH1+YoVKwy2jikNNkg+jTVs2BCxsbGYMGECYmJi8NFHH11xREIcOXKkmltpm+Syb2pqKtq0aaNy9WRbu3atmiQh+zKSUFhYiPPnz5f7PqnSoMecp+ruX0nTuRRfw5UnVyIaNWqk/v/L65Ov3arr34rwtXt9pPKC6WqlicyPMKWNmN5jL62Kw/dfy/RvRSR1R1Ik9RBDMODVgdLSUhQUFFR4344dO8wvdPpnPXr0UCkj0m+mTXKeJFfPtO/i4oKVK1eav0dSRuQNo2weNVWufyu6ZMbX8I1NDpTLkvL/Xz4g87Vbdf1bEb52r49UEJD307IOHTqk0vSEXGaXoLfs+29WVhY2bdrE918L9G9FTp48qXJ4dRFDaD3ETNdHUhjWrl1rOHbsmGHXrl3qtoODg+H3339XaQtvvvmmSnWQ+3/++WdD/fr1DV27dmU334BLL7kPGzbMEB4ebli1apXqa7lEdOllIqpc//I1fGNeeuklw5o1a9T/f7n827NnT5XylJqaytduFfcvX7s3Lj4+3uDs7Gx45513VNqepJB5enoavvnmG/M57777rqFGjRrq75v8Dezbt6+hXr16hry8PAu0wL77Nzs72/Dyyy8bNmzYoF7jksbQpk0bQ1RUlCE/P99g6xjw2phHH33UEBERofJIa9eubejRo4cKdk35kRLc1qpVy+Dm5mZo2LCh4ZVXXjFkZmZq3WxdBbzyxvrMM88Yatasqd4s+vfvbzhz5oymbdRL//I1fGMGDBhgqFOnjnp/CA0NVbfL5u/ztVt1/cvXrmX8+uuvhujoaPU3rEmTJobp06eXu7+0tNTw+uuvG4KCgtQ58jfw4MGDFvrp9t2/ubm5httuu03FFpLvK7HGE088YUhOTjbogYP8o/UoMxERERFRVWEOLxERERHpGgNeIiIiItI1BrxEREREpGsMeImIiIhI1xjwEhEREZGuMeAlIiIiIl1jwEtEREREusaAl4iIiIh0jQEvEREREekaA14iIiIi0jUGvERERESkawx4iYh0Ki0tDcHBwfi///s/87H169fD1dUVK1eu1LRtRETVycFgMBiq9ScSEVG1WbJkCfr166cC3caNG6NVq1bo27cvPvjgAz4LRGQ3GPASEencs88+ixUrVqBt27bYvXs3Nm/eDDc3N62bRURUbRjwEhHpXF5eHqKjo5GUlIStW7eiRYsWWjeJiKhaMYeXiEjnEhIScPr0aZSWluL48eNaN4eIqNpxhJeISMcKCwvRvn17lbsrObyTJ09WaQ2BgYFaN42IqNow4CUi0rFXXnkFP/zwA3bu3Alvb29069YNfn5+WLRokdZNIyKqNkxpICLSqTVr1qgR3dmzZ8PX1xeOjo5q/88//8TUqVO1bh4RUbXhCC8RERER6RpHeImIiIhI1xjwEhEREZGuMeAlIiIiIl1jwEtEREREusaAl4iIiIh0jQEvEREREekaA14iIiIi0jUGvERERESkawx4iYiIiEjXGPASERERka4x4CUiIiIi6Nn/A3MTjrwc8r1ZAAAAAElFTkSuQmCC",
      "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": 16,
   "id": "9617ab65",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Simulated mean: 50.002185302479354\n",
      "Theoretical mean: 50\n",
      "Simulated std: 3.9891411700286694\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": 17,
   "id": "f3182d6f",
   "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(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": 18,
   "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": 19,
   "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": 26,
   "id": "cd561dd9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "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=100, 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": 21,
   "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": 22,
   "id": "d2c74f8f",
   "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_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": 23,
   "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": 24,
   "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": 25,
   "id": "55007845",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Population mean (approx.): 2.0012337957358866\n",
      "Population variance (approx.): 3.983317421944735\n",
      "\n",
      "For n = 5\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: 2.006761294144693\n",
      "Variance of sample means: 0.12896356422754562\n",
      "Theoretical variance approx.: 0.13333333333333333\n",
      "\n",
      "For n = 100\n",
      "Mean of sample means: 2.0015222052034187\n",
      "Variance of sample means: 0.040359743223367446\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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