HW#1_StatisticsReview, CLT, Confidence Interval, Parameter Estimation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br><br>\n",
    "\n",
    "<font color=#0C2C76 ><font>\n",
    "<p style = \"font-family:courier;\">\n",
    "    <font size=\"7\">\n",
    "        Interactive Learning \n",
    "    </font>    \n",
    "</p>\n",
    "\n",
    " <br>\n",
    "    \n",
    "<font color=#CF3A69><font>\n",
    "<p style = \"font-family:optima;\">\n",
    "    <font size=\"6\">\n",
    "        Homework #1 - Basic Statistics \n",
    "    </font>    \n",
    "<font color=#000000> <font>\n",
    "</p>\n",
    "\n",
    "> $\\textit{Sahand Khoshdel - 810196607}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import stats as st\n",
    "from dists import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mean_confidence_interval(sample_means,confidence_level):\n",
    "    sample_mean = np.mean(sample_means)\n",
    "    \n",
    "    standard_error = np.sqrt(np.var(sample_means))\n",
    "    z_score = st.norm.ppf(confidence_level/2 + 0.5)\n",
    "    h = standard_error * z_score\n",
    "    \n",
    "    return sample_mean-h,sample_mean, sample_mean+h"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color=#CF3A69><font>\n",
    "    \n",
    "# Problem #1 - Parameter Estimation\n",
    "\n",
    "<font color=#2480B6 ><font>\n",
    "## **A) By calling `my_kappa(n_sample, student_id)`, draw a sample of size 100 from the my_kappa distribution.**\n",
    "<font color=#000000 ><font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "student_id = 810196607\n",
    "n_sample = 100\n",
    "sample_size = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "kappa_samples = my_kappa(n_sample,student_id)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color=#2480B6 ><font>\n",
    "## **B) Calculate and print the mean of the sample you've just drawn.**\n",
    "<font color=#000000 ><font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The sample mean is: 0.16313185956308301\n"
     ]
    }
   ],
   "source": [
    "kappa_mean = np.mean(kappa_samples)\n",
    "print(\"The sample mean is:\", kappa_mean)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\boxed{\\mathit{\\overline{x}=\\frac{\\sum_{i=1}^n x_i}{n}}}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style = \"font-family:Times;\">\n",
    "    <font size=\"3\">\n",
    "            I aslo drew a <b> sample of size = 10 Million </b> and calculated the mean to <b> assume it as the population mean </b>(as its very close to it due to large sample size and <b> acts as a census </b>). Using this approach the fine approxiamtion for the population mean ($\\mu$) is shown below and we will consider it as a reference to <b> testify the CLT</b> theorem in the next parts.\n",
    "        Its good to mention that as in a real experimental sample survey, we dont have any information about the true population at the begining, there is no reference for testifying our results but statistically they are proven to converge to the true results.<br><br><font color=#287BB6 ><b><br>Even Running this large simulation with 10M samples has its own error and the fact we're assuming at as the true population mean doesnt mean that the true population mean is it! but we can claim its close enough for our assumption<br><br></b><font> <font color=#000000 ><font>Therefore: <font color=#E31339 ><b><br>P.S 1)I have not used this 10M sample mean estimation (as true population mean) for obtaining confidence intervals ot other problems!</b><font> <font color=#000000 ><font>\n",
    "(to respect the goals planned for this assignment that helps understanding the process of optimal estimation during survey sampling), I have just used it as validation test for my code and results \n",
    "    </font>    \n",
    "</p>\n",
    "<br>\n"
   ]
  },
  {
   "attachments": {
    "10M.png": {
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pWPf6JpGf+vadCaNznRIGDa0Ps2QlI1eLIdomcrwhPT1mnM1mjVz2M8O4LCLKh7XRGPNJfGYMfJQjIwcMo+4qOTLdXL3dSM+nI8lWyX6aMsZHZJVMpmt9pL82nRxvpD7Nkmn9kvXLj3+yAACAiGSoJOZbt87BRSbHjL54JEiryqRInfjExRrmyHDlZnkFVaj5qaGzKsGKl/3k0qskS0yKkDAo/4zGn2//zflvOv/+nz+L8aWifVTXXe7euEMDjp7ssrbBdqt+wkQ7hUQ+XTbYJlthVEe6qtevizQP9kRdmox8k/XLj3+yAABjFiKSYa1mUc/gzgQNStz6bei/fhcld+oVxWoWaHOPZUo8JUaG50NeUeHeuMMrKrKuAYeoqMgOyt4kqiyvOGmT3T50fsn65sc/WQCAsQwRybA3s1302ugwDKXfButikkrs5CMJ2nZQUawqJWZ2ajEpDUleiu9H4udqWkMT397f0GxVVMjGkZrIZYbxfpT2lVkir/5mYw1bk8R2LW7IfURHRmqMyOUx42w8qgUc2exZI3Z5hJaBT7J++fFPFgAAEJGMHPXLWVAiOqDk0qmU0ZiM548G8stsT6i9VTwFbaMZKjXRhvGGcd0ypb7B6rJafwOJ0GLJ2VYthtK3tD56nWGMT8atBpdc+njKuC5Kpq7524YYiVduVVI9wpqr/pZ+4Zesb378kwUAAEQkw1mud7H6iq1MutPsFFITIZfAvv40jw/oA73Fttrs74p2Gok25UrpZVLTsg4jMVd9oiegCvUjqWm6NWG8H+2ij88Qud6N0cT45Hpe7XFznD7Q+6+yC86RrsihVGK+qJ+on52MnY23yfeIZPoj8bOJNG++qWladp2R2C5LPtfbvD0Rm75eFJBfsr758U8WAGDMq7pw4YL4CCU7ePDg1KlTxYCJhAtT4nU7rdaNzDPV0SPJrPKkjLdMlxJqxLqz8oEdgsQrkXgf/5xID0bT1dEBPsH+LvaMbk/TJDY7e6xGPkjc02TQ/Cj9P2JsSjHAG4PEgKQu1z5BY8AVKVIu3Uwu+WLAND6ZNRtNjnRVb5clpH5PkZiAhBpiIDFf74VKYoIesxwSab1TSKa/Ovq++BybntU7hfgm65cf/2QBAMY0RCTl5B6RDDeOCAkAACB0aLUBAACA8CEiAQAAgPAhIgmP+N0ZD8Fe6w4AADA6oB9JOY2MfiQAAADDD+pIAAAAIHyISAAAACB8iEgAAAAgfIhIAAAAIHyISAAAACB8iEgAAAAgfIhIyunSSy/99NNPxQAAAAAEhveRlNP58+dPnDhx7tw5MQwAAADBICIBAACA8KHVBgAAAMKHiAQAAADCh4gEAAAAwoeIBAAAAMKHiAQAAADCh4gEAAAAwoeIBAAAAMKHiAQAAADCh4gEAAAAwoeIBAAAAMKHiAQAAADCh4gEAAAAwoeIBAAAAMKHiAQAAADCV3XhwgXxEUp2/vz5EydOnDt3TgwDAABAMIhIyuno0aPjxo27/PLLxTAAAAAEg1abcjp37hzCEQAAgCIgIgEAAIDwISIBAACA8CEiAQAAgPAhIgEAAIDwISIBAACA8CEiAQAAgPAhIgEAAIDwISIBAACA8I20iOTDfY9Ek3Xi7+cvfSi+LtFbG8w0k3UbjopvyybTVV3dvCUnhsAh80y1qWu/+HJs2U/3kd5TYmi4yW1prl7cO0L34JG8d+V6F1dXP5MRQ6Fh2chbeqd6m9Vp6ODw3aVheBqRdSQPPRcfSJO/b91/tfimRLcs5Qne92S9+AaGUv3yQepYMia+gOFkf1ekNZVoa6oRwyNMSHvXcLsPGfL8TGpa1pGKT+kKPZ6CEaQiEcnHr/zcqnKQf88eFmMr45OX2vMu7uiz1gS/eEt8CQDeyJ3u3ESsO9s+U3wBY09N0yYa1BW6D9QvzyYbE9ERW7sGQ68iEcmV937LqnJonsM+xx+dJsZWxhX3d/F6Dvr3evu4Fx7RghIWJO02ROUK+fv6LWIMAHjK/DSeakyuXzRC60cgXDVNa5Kxvngb2qwhmKFvtaEVFSRWUOpRyl9dceW90x8yjOMnPxHDH+5LdH3+0HPFR0Wso0mZuq2w1latUZb2ITCplZy0opVMRlvxBWusbNqn03D2KlnPZPOy0nR2blBb5ZUWbtrSTDLAx9KciKWL2en3ZGK57kQhLfqiGZtxtEwraRa4mkXwW02+mfT1Yjkv/B5RbnFldby2pmytt7aLsri8xW7NRTj7K5zqXddpONtrStuaI2rv8qXmluaKkdsumjCMVGuEfabkBPbWEza9tt8qyUbifeJLSS09dS76PVlruXRCjM2XH395C0fJz5R4SnypoG03ZLlJx74F4CKcfiQvPJK8+73prK7ivifrT7e27/tYjKmIt7a9/cv6qa3FV9Icfb2H/P/z7f8mQ5yikZMmOW4bk1mzCpR8sz3KGroJVsmpn54Sc6sjqQYyvRirXt764pHqqLGTzbozQU431ok4X7LeyCkmmuhIi1kHl2Uft5ZIzm7p+WIEbZjvjGqXsVTbusnZbHcslWprnmukB9MJI9W/W85NJp7S33CMzkqmScwNePYn+YnEbxb5yXYb8SnKjKw8jW5WPMSxyDrnZdXFXx1YevG/fNXxt/Sij8QEvjxWs2bRMnLST2xXMnAq3d9nxGLRgmoYSCFHWlMxulLtol9Tnq2Zik8h+wEvonSC7BVqIXgXe56tSSbY3Z8yElHXunqabHYZm7XArTly9i5fJG6IdiasNXmnjc9Ys6iHfUGyZ7CNKPQEqmeiEUD0CD0/MGRbixEU2Q2qowMyzXSH27niHbFNzHNFafkR7TXk9CK+UOn58eqpUz+fHhbpAmJEGLtC6tlaP/X1pTewT1fcER1nZP4Q7CQQ1Fsbdr9gTPz7e69gQ5+8e9wwaq88pTxQ88grBcUWN9zdTP4/bv7f8QSLluni4cgm5aZzUlPPcrM/bU1Tm+PotaZnY/v600phJXbKyGZmnJy8rMth3mS9nMoOkEnnm/PWtyu5JWc3qy2Z3f0YnWnznJjqq1vGT3N9qbqd4mqaeifL/iViyWM9TZPoJ3bxVi4n3nJb1iVIzuW61Cxan2xMxX8ql3kqmzJiDXNkBrW1rhTv1ayP6gXCr+hi4oBYN1Jy5dAuGHm3JrnGiwnq490xNQ8+xe6/NUn206mU0RH1KFCSrFj3mjkNMSOVDXIMj6y9y08ue4QUu1U49cvF0kuyPxnviyXX2CulOFsLWv1yEmQk1qlVHeRcIdalJhqLGX1Zs3QqIWiL3kxaPTOQzb85AMKJSG6PfuVK8bGczId4W3vGPbnV7Cny8bvkDNOz+/U5shPJcxN/2fVyQUEJexinxEd70vTu0BaOOE2K2O4ztDtsOlY99av3rzWRmw3jiMdx70jW06RIHUl3bqB678hkPVXrBB2LOM/OjQ1R68tIpFG9nHhxXhT11WQFEvy+VvrLjA3nv/kbx9+GL64SE/jyXk39dtD/iu5md1c160aa5/7VsTWVazwpILIBB6ydJHCx27emkc32GbHJETFkoyUb2Mjau/ywKR21SiXKbE94F2wm3Wmrb7OvZqG1caVx5sdLwM0BEFYdSWXIh3jjA1uv2b5Qf7NI8xyrE8m0r3c3G79M/5+KNhXZpFrj5GJl3BxxHsBqa7R7W2xRik22vp3VFZPLBmO72CvNxtXV5G5efF0p9KJIz/uKaKcYR01q6mG19/EpfGTAlqmKUWuqaJNNLPnt4AFJKt5K95E6l32kQjvJEG9NYkTtXb7ql9PmIXP2YN0ySsCql9SOIG69TABGtlEVkViuvi3RPs7oeZf1mb3y+gLuUiuFtuDuTDhvqlhrdCzJ2r+pMr01obRkZeMxnUutgWCdAFgnGI6ekSuL3l3RJgkbrZ6JXOQY2tQdsLtMaf1I/LDactbWQJtsCqtIoNsr3eFShVCZnWTotyY3svYuP7KLBo2xSKxQ2aCEVS+pHUGE5cPg7AZQJqM0ItFccX2tYRz/WKkRET1LgrccledZm5nt/KZKOXPRmk+jY1nAFmi/noZaJWphyXqa1NTDLhuiCWA/7RxXnjdlsS6faluDh+C16LR4WVCiNFiEgXViSKT30xaBImrR2SscSFCiVh4UtjX9av7VYs+/NStc2T5S9i7+XI/fA1MkxmJBiVZWAUuPtRxJtKFK7fxBu5WIjyVvjrJvTXuCtFuJ+Gjj2/wHoBilEcnhX9zd9fnt7bfyriS3LJh6e+bthOw48vErO57KjHtyAe9aG0TZnrUhN1XkJlh5KIYe1Vb3PXLu86mQP9XbRvs8xl1PtJlnouRCKDtRFpKszf4u7dFEGgPJZnvWfcHsPEtu3IutV8/1Pk77xMXdQytN/bfp+wy0h0cUuS3NanUCvRgbdS6dDOxK60eSB+3fmpgbifcV2KdVIJc33g5lVvYUsjX3d0Xdntdl9GLPvzWt+p6yGVF7F5ejrSX0ubakVnGV6VJjFP5QlXbR5R1N1unNUgS7kKfSbN5c72Kt5YX1EZadVU/1Ns8diJFNL7Aezdr9TEG88lM0vnuIBMmRGD1Cht2wWNO1LRLApiIRiXzXyMtPkSO9ZzfvbVrhd7aq72NN1j1idKfjz4lnbWgjznNbpxpdL/Oxd3d9qbuwbqrletaGkjfBvOGZX34Soi16fSTrqJC3Wo6nxOt22p7ZkzNW8ycG5cOiAZL1NLN9vdHG5yMirXXpQfkQAbmp5Q1PDH8Uk40Ihj6rzLHnLa26cdl7gF1oZQ8DeT3mPUX0xn4zCiERXnS7+JLQCyE0rH+rUVifVk19O91eZPPxmpL8W1MWWnX13IHkMf3dml7FHmBr8gtkOZ/bHFF7F8cf6naob1+jrInLscmPdLOHk9nRhG1NkdtIf4w15ppYIYhDnj5c3bOMhBGmme2Dx5KG1pXE1hHHj0d+fNHne5m5JJNyXhmKsfsr8SV96njTsjr2vQ2rtAsUIAJUXbhwQXwcET7c98jCt2tLeNeZr09ean/5qdo5A+LJ5IIdPHhw6tSpYqAMaMv6gMeTF+ytFeSEHv4FOAjaE4KEC4Fb6Ee2/fSRGevB7Ioi1wx2OXRdVunFTlOgb90Y1rtZpfcuVgjW08VQAN/9E8BmLPQjARhSo+mmkLZrGIloWZ9xHWFYQ1isez3CkcIV0IIGQCAiASgn2qBO7qc9XnI18sjGlGK7L4xorMWHVXfleUMMuMk8Q3tTpcdIzSiUw4iMSF54hPcXKdMPzVivVmMdX0a1jPpaC7sC2qTBiZdtpNVwVu+TMIWVsDtbx4Vhhz0jJjtj+hl1e5d4sHzUtjiY3URclVgxRn8UKWa+2BcgiJHWj2R4K3c/EgAAgLECrTYAAAAQPkQkAAAAED5EJAAAABA+RCQAAAAQPkQkAAAAED5EJAAAABA+RCTldOmll3766adiAAAAAALD+0jK6fz58ydOnDh37pwYBgAAgGAQkQAAAED40GoDAAAA4UNEAgAAAOFDRAIAAADhQ0QCAAAA4UNEAgAAAOFDRAIAAADhQ0QCAAAA4UNEAgAAAOFDRAIAAADhQ0QCAAAA4UNEAgAAAOFDRAIAAADhQ0QCAAAA4UNEAgAAAOFDRAIAAADhQ0QCAAAA4UNEAgAAAOFDRAIAAADhQ0QCAAAA4UNEAgAAAOFDRAIAAADhQ0QCAAAA4UNEAgAAAOFDRAIAAADhQ0QCAAAA4UNEAgAAAOFDRAIAAADhQ0QCAAAA4UNEMhT2Pl3lYfVeMYlx5sUFZHjBi2fEsDc+peVpM418Tm7mc67eJ74ohVipRZvz55g6s3lRoLWruLIWAlVEgvtWq5veiW5is2DLnuGRST2IXHek0V9ow3OlKpQreowQCzafFF+UKt9Bp9srFj8cTlljCSKScK2cLQ+5CXcsaDSMvpaf+B4z9DiZ2NInhriO2YUcaaEg2Z64eKsYGOPohXPWSjHghlx67ZsY9q2e3SE+EjNqJ4hPEgoNfOQ96GCYQEQSur5tu1gYfs28BQvJPyt3eN5qnNm8aLbHUbVydtC6Cii3a1q2XaBW3Ca+gIpp3HQCRT023LaCHVXbWq4RX8BYgIhkCC3cdJodZNKeVezrvmPH2b8T5jU0kn9WPusRW+z7iaxmWLVHpHDhwolNdB5i67YdsnrT1qzjX/GoT2zVtTgbZeSUnvWoar06IWpxaWWpCKT6WiZa37N2HJN/la/3GslEnt4rq3kpfZWVBeWJ26yqWmVdrPWV2Vi911wWWa6t1tqqbVZXkBcs/Ubeyq+cTb6254dmQFQGbF1MC0tvknPNFROsMJWsWknxPMhRhGfpOVIubbs4KFOqK0izKm5w+xZfS0bZagQrXGiU2DEklwwo3A4ipXj5gpRcyemtraNmzLYsOyUdr+K19mrxBeX8UisNtQyt3V58YW0pui7X1M6gXzXWktDB2vnZZIzIoZmgUhR+a6cnlScPjMfeSNfL96ATXLaIZG7HvXIRPHGPJTrK1jOrq/e6HpL2HXUsERc2qKQ9naysPSKSxs3y673iC34jaCMSUcMRjs5lzXJ6swhRVGIRMnxZtZdNaqWpEkk58yxTdp/ALSm2ILFSFrZ0se4qqxx0fmt04fQmWrHkQk7gsiDOLARFnomdOaHf20rVsb4S2XCO3HrsEpbOPVbQaWfuCYEL0yuphY2272Xh+KVc2naxc91/+MSOUbZDoMKF5jalfzrmWNeVIstpdN0NPPMsj27bnuZayGTdHcSWUnc226nGfdFiLeSGVopd7uQsJzwbfKwoDaUkxTfeR4d17tLoOcyXB5+9Me9BR+TZXR3bkebKZ/8X08ttYc0uvpGL89tRPYpltENEMhQ8TkyccozZzzgqZSf2ox//5lz6Kc92dhCnD/PYYIsQeVaOXnkEikNFm0DMax5F8jQtcms/T8kC8T7lWXzXSDmViAnMtWATmGcNObvMmPWNyjlWfqOnpm0Fj1I1i87c+nwC35Wl7CVvrpE5i34uLqAw7UlZpSfWSE6gn4hdUy5pu9jZdkVr0XKPEhN4nqYrWGi2RetFJGY0l+u+FLlecqyZmpYNK8/2Zdm2Dk9c5jlAEYkZrVF6cZkbS66+vlyXwtFXU2XbEK77jDx85HLVo8mkr06+PNiTKmD7EjIpuftZe69+IFj7p7kusgTkLHzFRYJ8cVZqsliUea2NbsuquqwxBBHJUDB3aCd9txN7qtu+6Hv0upKHGcWPBP2MZjt38EWYi3aMNQ8VcY5wTsCZRxQlcmtbL+dq2g5vD841sp0IGCVjLmP1E5mNyIZWyGJ6uta2EhD0UnVJX58gz8lRyz8jZ3cWF/umkMJ0JOVYI3U3C5xywdvFzm2UvnRlK7iqYKFZa+e5yRi5ygxPR+TKmlEsxdrB1PVyybO+t2g7krqlOPGNOrtkG6WvvpasoC7XZY917uQmbUvpmXRuRPGNW8HqE+fLg1X4bqvvNrvCsZns28JlApXMCSX2QGV3kkkxbHXUtXbZ6M6dcwxBP5KQ0a4VVpNtbS07rmTPkqLINsvC+5ZPaNlyYdsD9qcYAjKbVPM/8nDy+AH2L+9WwoiOJgeOu7XwBlmjaY6nL1Tq2GtqlROEu8YpteITIabvO2617M6gTeZ5sGb1snI+YEIVWpiMIym3NcqbcunbRThz/DD7V5u4HMdCWQrttu/Iqx3rhaD2D6DM7hfeT5MtrFX2J0rbwRzUPE/gnTRIvuwdC44f54ujj9pxIgNuJSb6qPX176BZ37eDreyqx/jBfvI4O2K1PdZ7ufmI4mId9k/u2MaytOqeWeT/Z2Sps85AjNhzCl+K3YSWR0VYILdpnv43LtTNJDrH6Gzb0W//F3sv3Z148S5ctYoVC1lTUQ6d82ihSO476tiDiGQIOe4OReTesTZAP6YJtdPYvx077EcaPTBkT6iTmxfIw8N261BZ+1bLQITf08h7wdKFtUbgbwxtFxqpq7s0v+bJDqoyEOFHt3q7PJzwlwvw/u97X2MbTr8ilo8V/ezdtY2dFFbNG4Jno9izObIuhPDrxFoGefZ/qxA2s9JubPjOd/iDC69t3tFPS8U/Kh2zEJEMR64766x7+MmOHGlK+C8ODHrbQU+R4naH1gcGfUJy63Hzlop29i7qGBZRPz0pB3haT95/OKslXWpoilgjp8PKna9I0I92l+l2BzmMFFSYBfFPuSzbRZDRtrqZZB1ARU7cxRTaLP40qnntYc/Eidodms6WlnLd5Kr1NLJewVmJJe7CtRZG7gm3SOOalsdo00Pf4o2rd7Dnkni9BeVSC+iz3PzM6Gctv/Ru/g5fkqx3UVpthLI94jvhAf4kvgwNty7+iXy8JT/lTEh2b77+nvLt/7IQFi+mpd244I4J4puOxSyEpd+Qf8AGEckQ4o8mKmS9gnnYy5pYV47aY+raxTwJEg18xzow5EtNrAeGXZghzlr50Bo9VZFMsqCkdgo7TZmH9MnN38vbHCOfQD7z4lpx++Bu1jzWLmu9Dk7Uf/o88xZojRzEnQpZi++ZD+bJOxs/HbPlc3py+oUL5g3PiKSYwgwoSMrFbRc7sStam4kEx7wZpUIn7gIKTTZHmqNk/KRcwERriHFm87MB9q58+lq+J5ZlHnQu9Rly3zZrWMnNCcuo+YipjSjkjpUsi0q9hXgTkrFylrzV0ZcrIwnrRJHnIBIJ9vXZLr23zWM5IFGRWI75VK3Y6t7y5UE+gG22gMvGWZ+2S5N1sydmP7P5UXlezcN7/5elyrAzvNoSFPh8EryIRgkRUUIlyY5R7qwbNbcuZjqv1hDztsNjAl6l7EjfNWNirGf9s1iWmFdP2U7cwGlVmjR91+mdd3uU7xqZKSvzahnzbj9yK+Q8E7v3j7OVqig35UbQfQJGZFKj1Dyz9XJsNTOfYs8JXpiOpBxrpJenX8olbhc7v12RcJaqroKF5rGmPB1tuQq+XMcq63kg1PVyzRIl19q+Um4Z8yheRpnetqauizaT8syYWrwaq1j0/LgWl3siti2eLw8eG0Lu2HkOOu0EpeJbym3Xdd8r1GmsLMnSNndyawewb1NC20n8j5rRB3UkISM7olVRLGsCvZtdadWx/diju7tZ7TlrhXLo0n2aH4rK+9NUs56wpUaPf1EJedsK7TDu3ONxzDPXtGxTJiYrJSYWvV6sfmcEvWuh7znVzgI0q661zQWukQMpMXVBq/Z4n9pMZCnKyiplUhZWXZd2n22a8MBjVmFpDRkeCijMAvmlXOJ2sSO7ora/FVjslSw0etDZAibzsJ3wwDZlFLn+iTRXviZv1gtHEtfT9GrUcGSMnAr8Go9EzRBhNdlwjtLQkiJj1aOGXB21LeXC3ByNDfPU/NBWFe0ADLyV8+XBkTK/iq8Q65nnoKNdhZSSJLnyCDgs+fd/Wa9jtTyKimc02XirIlGJ+AhhO/PiAtqOQw6k8rVJQyH2rmbPXJDzS6mdMAAKdXLzAtYISyKSckbAir1P85fbkihHXqqHrX2r2TMsJDjAi+THENSRDB9neB/sVY8iHAGAcju5eS1/136lnrIpJ9m1FsYWRCTDhnh2f0ielAOAsYN3ehW94Bs3LRnmAQntpip6/Q/fHuVQEYhIhosz7Nl980k5AICyW7V32DeCiBe4EY2bnkWF8diCfiQAAAAQPtSRAAAAQPgQkQAAAED4EJEAAABA+BCRAAAAQPgQkQAAAED4EJEAAABA+BCRAAAAQPgQkQAAAED4EJEAAABA+BCRAAAAQPgQkQAAAED4EJEAAABA+BCRAAAAQPgQkQAAAED4EJEAAABA+BCRAAAAQPgQkQAAAED4EJEAAABA+BCRAAAAQPgQkQAAAED4EJEAAABA+BCRAAAAQPgQkQAAAED4EJEAAABA+BCRAAAAQPgQkQAAAED4qi5cuCA+QsnOnz9/4sSJc+fOiWEAAAAIBhFJOR09enTcuHGXX365GAYAAIBg0GpTTufOnUM4AgAAUAREJAAAABA+RCQAAAAQPkQkAAAAED5EJAAAABA+RCQAAAAQPkQkAAAAED5EJAAAABA+RCQAAAAQvpEWkXy475Fosk78/fylD8XXJXprg5lmsm7DUfFt2WS6qqubt+TEEEBJ6O7UtV8MYO/KK/NMtUkpt5Ltp9shIwYAoAxGZB3JQ8/FB9Lk71v3Xy2+KdEtS3mC9z1ZL74BGJZyvYujicZkfKYYhrzqlw9Sx5Ix8UWZzIwnGxPRxb0IBgHKpSIRycev/NyqcpB/zx4WYyvjk5fafRenVa4kH3nlE/E9wMiReSYS70ukNzXViC8gRDVNm9KJvnjkGVSUAJRHRSKSK+/9llXl0DyHfY4/Ok2MrYwr7u/i9Rz07/X2cS88ogQlh39Rt/DtWlGzEh94buIvu15GUAIjzKnedZ1GYmc7KvKGjfr2nQmjM1rOxiCAMWzoW22OPssqMJR6lF+8JUaVzZX3Tn/IMI6fFDHHW7tPG/VTW82QaNqtJFT65Xsfi8EAWEeTMnVbOdXbbGvSpg3SJrVlWvQYyG3hcxDWWPolrTGm03D2zgSeyXqjeWvuPcXTJB9kG7xaNa0ma787zPUuFmMINT80HTKxXHei4idxsS5KNwJlLfKXnju6gmRKniadRZQGXZBkpeksdrVPg1p6QfKT+Wk8lbe9xrl3KWXuzKfX3uVfelQRe5eglo+aH8qjfPIUO/2++L1L3Wnt+dFLz201aduNkVivFw4AFCWcfiQvPJK8+73prMbivifrT7e27ysgOihO5g/KqebjdzPG7X9zpRjK7+jrPeT/n2//t5KrVcgJbgq9rmQHB9v5pYV8sz3KGrqJLG2Z1k98ibnVkVQDmV6MVS8MffFIddTYyWbdmUi1RrTrkG+yPvofXxc5RmZJ9T/eHDXSJGWjrz/Nio9eveYOJI/xZNOJzqh6Wc0802as4aNEfrTLKpl4SnYZG5ntjiXmOs7+Lv7qwNKL/+Wrjr+lF30kJvCXik+pXjeZFR7Jra2C3af0/KXaSJpkFVKptua5pIDSCSPVv5utKb2ARQe6+RIH0x1asZPSS8/nY1i3Br30WH5IybOxLvnJpDuNWCzq117j3LvI5f9xYz1Lkkh3kALRit1v72KlR3cANqtWesXvXSQciSY6eJrEsuzj1hLzlI9PsRN07+pvYKUXeO8iSH4i8ZtFfrLdhlY+rDwNuTUHj0XWqfkRaqKxmHmAAEApQurZWj/19aU3sE9X3BEdp4cLZfDWht0vGBP//t4r+OAtS+c8ZJxuFZUcR5+N7n6hfmpCjg3ghrubyf/Hzf+74LO4ynTxC4baD2BSU89ysxq+pqktQS4TafVSZE3PxurnvsROee3h92rb5Rkzb7KeUqmblzVNYp/66tIikVSWLjSTbE3FutfzsbLKep15Bq9f3iNHifykUmnlChdLHhMtDjVzGmIizQrrSPcs4oVdH+0wjCNZJT/epeeLFMsynmZfqk62oaTeyZL/82qM9WKJpEDIVTOxToZlNYt6ZKBAN9Aykp/OtLrIxE5ZgDOjZIMNqJndT5KKNcyxdhwHt72LbCNlsP7bSVLs1lWc8N27SOkNih2gPt4ds3Jb9N51KjtAJp1vzqtlz798fIqdIXuXKL2aRcu0YMVbbss6soHkTk5mXE8C8fhP5TJPZVNqmWtrbRm6nRlgtAsnIrk9+pXgFRTBmQ/xtvaMe3Lr128RXxM3PJqOdzd//tRCMnb3C81zBrpuKygD7GGcEh/tSdO7Q/sFw2FSxPZEgHZbTMeq575E1DyDGzWRm+1XXIsjWR/WBaMxEhGfGOdF0Z4fFcuPqrEhasYrQf1lxobz3/yN42/DF1eJCfJQLn5OgUvPpiMqE41FtDVyVmNEIiQss66amshk2zZR82OXo5fyOn1xqqB7V534JPjuXVrp1dBZB9y3dfC9i2UgMTdQq4q9fDyLndH2Lr9iV+TSqZSSLKHvBqxAbLVKLthKaeEjABQlpDqSypAP8cYHtl6znQQf1ptFaOeV1p6J3XTU1Nt7dpfxXSYBpVrj5EbSuDnivGBobefkNld8XaqyJ8suirQm32JLlrZZWKKd4uuxglUApFojYv2pSLxPjGTULhTVkdZybWq/vUvpJkLQqpeyKHbvqm+nrTw0KGFsF/tKlY+HbJZsnc6oWB6j7bSTmnpY25Dc54O2ewJAcUZVRGK5+rZE+zij513WZ/aTl9ppI053mtWaXH3bc+k5DxmfP7W28p1XFLHuLO2QYWsaZ2f2aGdM9swo21sTKpEsu0tW0pRETTvvxGB1ERhMd7DvS1JiP5Khxe6V6Ya2Wc5vwlkXikbayYPLdpdlU1NeexcJR8h1PcH7ylDk+loGpe1dNU2bzLnUGogKlo8HWpVCW6ZstHomEkIxpHiNAjpjAUARRmlEoqH9WI36v1Yqeq+8nlwjCum8Up5nbWa205NsZ1Tp70nr+Y0O0W8jr9zu/pRn3b7aZFBYskH5tdHwvMWS31aqwEcSl36jvBrA+cyLN9/GAtrmZSTafFtVvPk1mnAuexdrlQj8OjXfvcvIbE/IlpEy7V2TmnpYUCJWqrTy0ZxK9/f5N9hxhTTVzWxnQYnbJmB1Y3Uu9VMAUJhRGpEc/sXdXZ/f3n4r60rC+qVm3u62Xk/yq6dIjNJ8vdLRxF/ZnrWpWdST7qAV+7Idnd2lmd339nf5VYCf6m2jHUvjrifazDPRhJEQXf8KSjY41tnQ6ykGdsk0uxPSJyrL0WpTaj+SgPTS49h1l6yS1jnXH+vjqcUECtbZwuw8S8KdwlolaF/XPL01HXsXu+KanVVpm5p3q43v3kV2IbI1ZbhQwt61v0stHB7Fik4hJZaPJdf7OO3hGyQOo119bU9gKXJbmtX+LjQmc+vKo60FAJSgIhGJfNfIy/TCTztt0N6mFX5nK+0pwhdE/x4xutPx56xnbeLdzfSRYzn29O3t9w2Ih32CKNezNlT9ctGOzk7N7LWPtDaYWR/JOirArX4JU+J1OwflkyOcnLG6OnokmR00352VP9ni1C/nT0jydBnzeVF2jy5zG8m2laXVpqK8So9jz+YY9oqTPMid9LGkoXUlkQHcpKYe3rDC8AdZ2YiAaH7yhkf63sUHZTcI+ui1vdXGd+8ye3tU80e+5YMwJexdM9vXG218PiLSWpcelI8XlVg+9Nlpjj3Na7W8yL4pLGySayQbX3hPEb0riRmFkAgvul18SbjtJATvHlvu+kiAManqwoUL4uOI8OG+R9jbVyvzBthPXmp/+anaOYUEK5qDBw9OnTpVDJQBbVkf6M7arhMc6yJATujOUyTkNyJLT74ew3V/KJzf3sWXRWIU63HcYYz2ayHhgv9zRhWyv4uFa8pz7wBQrLHQjwRgVGCtZqnWtjwPo8LQyXTNTaCCBKBcEJEAjBiyFQZPfAwHOf47zFnxLBUAlGpERiSyR0jZ3ikiX63GOr6Mavz5EQ/53gQF4RN9OIK9fneoja29a38Sv8MMUF4jrR/J8FbufiQAAABjBVptAAAAIHyISAAAACB8iEgAAAAgfIhIRoBMb3V1V3Xz6/4vxyoS/SU28y1n1Ee/++5Nu25a+jvy1YEf7Lrppl3f3faZGOUrty1z002HDoihEe3EWlIC4m90rFF+dFv/4IQYCEdoxc523dBXPzz0kM/0F/tTUeUvvYOHZIKf9S+l+8Pag2JMCeiJDj9L5Iv2TPd4f/GQQUQyep3pbe6q7jokhtzt76K/xOb1YyKTrr+I/P+GyZfxwTHj2sd+e8dvf3vHG0/T1R8LyEXlwY0XrV5yrRgOx5gr9uHiqhu/u+SLFXcOw+D7sr+ZTP5/0eRr+CBUFP1RBa8fwRgqiEhGgPqmwcH2wZ67y/2Y4ane5rmJWHdWfy/nVZfQN9ZOvsS+NF534vZXjjsYCM/BQ3c98cXDm+sbyvtjQSNHzYJ6Egn99h/DDciC4jWXbnUSokbBflRaVQ6Cs1Zjxj9OW33n2QdZzWihyl9611x8h2Hccf2XxCAMFfZLDsoPY4UAEcnYlfkp/UGy9T6vJK+ZfLF1g3LVjT9mt7Dk72dLDOPOL78hBx/7GpsARqTP+jecNZZEsBFHABZb7Lgn8rAYVp1Ye9PhFYY4Kt94+qLnW/RbhY2fyCqQz/a89oX4aLmsYdWX73jzg45gTbRDhlXTXvw3YzVWHnoz29P051RDa95CRFJ5tPWkufeM6A5C/zZY/TZyrzdXd5HNn+vd4DLWmsXR/kJnpFNmuuQEZkcTMVc3+2mxV8VY8qelcKp3nfVrrhpWec7veL42/be/LfTW2eoNYO+Awu/V+F9Brc7qjI7bOHHLyP/MZEXTOM8MbSMXk4nZ6d0kzZ6VciHt6Gp1UcDbyjz5YfySVftYaFcaer9LJ/Yudn8H31vxpkd7zXArdq0OoOgZHaUnv3eUm1bm4k/bb4vOT1FI2bYYP/O4Acht+/3zxvifbbiRH881C+rJbcPzG2ix5945T+4fVi85u4Ov+Ee5Vw0yyD6raNuNseuJ94K33fiWHuFZ7BIrYceuxW9+fryANhazCpjpM/j35STe5md1oaM/V27SfqFa9LSTP9mojaVfdu3nnVQ427XcM1kfvD+HSPOZDK3MZrMrVRdqso53D+43c0oo+aHp0ImtNxlqPQgF2nZjJNaF1HaDiGRopOLd1VEjPdg+ONieTvwhHulV99tEtCvSPyXrHMvbawZbPX5blUzZtS7Syqb5RiL16wiPOdS5Et9gn9lf+3Q2F8N+Qj0RLffvqJ198KassZnVnWwev+uJ35mnaXryajm/+k1erRJ5eGM2aFBCrl4tZx/maZK/pefV2ziS7I575Kg3v3yHnuyrK38/+c1pq+/84tWVmQeNCMmS8eZne2SWdj1x+CZ2iifz/ix4OzrJz50f3CDyM2218cFdzlOqB7/8+CVLzuyfzOPr6Hr7++YHd91EUmYT0GI/7Hb2d3fgtbPGnZfNdgadw63Y6dXr8IrJEb7QN542VtwZMAggpWdVHpCynbzBWqJocSA7pPhCJfq1iD+yFuSSb7VNFJ2fYtHrtNe1mVV7LLnCGvvR7368kewYVrHPvmc8D1AObPzghqU3zr7+IuOdP9n22xn3kHWUgUsAvqXnV+zCwU+eJ/9XMjlUyCU5Su7Hdg6avxGdeabNWDMosJYLLXqgvywdNcj0cqzarpGYWx1JNWTpuGyyMRFVLvN5kvVxZF3bO8vILEbnuubH+xuOsd/03s6vCyQMYj9wzbAfY1eCEhJ2bI/yUSI/WpBEfwl83WSW2cF0gqyXsyvrpGhDY/6fGa8QRCRDJZIebOK/f1Ef/79iRjathSTfMLuJ1EcjhvFpNuDekPhGT9ME9ml6NGEYAx8GnI//hHq0/D/IQa5h4h7ua1c8bHzx6k5+GTvxwhNf3PH0jbK65drHyPl94++DnMHpHZ4xfp55X/i16fzmiSPnROuWkd3kKbXTX+ya/D/4Ene9ebG8lnzxzkn2LzX+Z/IUP2PJl+8IdC62tXGIuu4XAp3EffLjn+xlDRusS1HNgv9BLgDPv6bFc1YvEFrsxtF3nDesrk7s2GjccU+Ns6JsmBW7rAOQAUHNghtJxLNiY5Cg9o/vvKmuo1aYgZ1YS+Mza8ai86PVLVl/JfYqZetodryg0e1n39hMylYpdrJj0Gs/2eLKZrUpbOfxF6DY2eLcA+IKym1p5uGI2n+ufrny680z4+Tyb7skW9OzsTI4YBrN352uaWpLGH39aRkf5E3WU5/R8G1+ek4ZsfUikSP0upDbso7+joT8NaWaRevpb139VOZnUlOP9UNLLD+2H53oSMuf+66Pdog0dTXRWMzoy2bF4JBCRDJEElOtq3/N1XUkeMieEYOGEYsolwRaw7E04I9lJKJKtUchstk+IzaZxD5l5nGyozdDF31jrvLMDu28pl6lPLG+LGcfDHbK5g8HmR6+R1wwjDsvdvl1VvWekvXnzX8u/ij36ptKskTAGRnP/BSW7Jcm3yk+Sd7XGH8f/emox7NUw6vYnXUA/CkMx12+G1pcu544XFhjlu7AD7LP3/nlh6xCLj4/M/6R1xnY/ooIktzRiGfDxW/8tr5BPp9y6t0vWEf1ax96mlZfPa9l24aV1bt/FEMlCVLsrBZKtjQNieyWZvp0oR6OONREbhafJLU6mY1VLuSxWNRag0mRmJHKuv+EkzNZb40NUXns1KmXB5ebSXt+NDQ/msR8ZVYPNRF2hQrjh6gQkUDlsRvuL1bcqdwU3vnBLjEyn69Np+0C9OrIZrQ3kWiN/Xc94eyyV1Ynz5NsP99iLfGmm7K05rlEeZMld73WqMMr3hRfV9CwKnZ2w21szJpLJH8PbhTj8iF357QvNm0tYjMGb9ISDh6ij0avUi+cpeSncv7Yv3QXbSbzuMbXkFuCNw2rz9Cb5yt5ySm52CshEW9N0TtAZ6As+2pw0U7xdanKnyy9mTQ6oyJFxpas1U2EmEJ7E44giEig8vgzO7ITifVn1fz7k4/50DdVvKl2sCDXRXrzaj71U/FXWbDnEq3eFfJPbdEohn+yrEvHHU9Pk99PW22vI6mM4VPsvFpoiei0Yf0Fvr2WNRO0x4O9F04etL1GaXDkis9PZVpteIVE9tV7pllP4dIwV3+TB92gQ/qMdwnFXhmJNO1akdI6XhAkbiBX7g7RM4NId4gxJalIspFII215ESmarA4xJECJJY+JrwePefRBHK4QkYQg83bC+OuGKO//UTkTWNWbe88Sulun3hmyhsLAbTT+ahbUs6ujvLdjPeMeXlqOWl9nu5KrQtpoCuCbLO18aoz/bolBj6tgqxN+sRfQRuPv2sfY1TH4FuTtNZ32wi8+P5Vptbls9j0kKNR2Etln+bP33hHfBKD3Rykbr2JnNW326rcgeDVA0F6impqmTekE7eBp9fdk3fxjSdFvI69MulNvqVGoTwwUmGxAvm00LG9GxzKr80pRctkB2lhUWiLFQUQy5A51RbNGYlbAniKliET+2kj9OunoS02wvkudWu/aSmKdH59vKeZhhAM/UOdi7fdm7wRWtWD28SR3n8U2H9D7YGOJ6I/p69qHnr5oVyEPswTjlyzrpWF2/yQn8TK22lw7b4mx67Wc8/Q2zIqd9YF984O7Aj6fpfrod99V52LhVNDXELu01wjF56cyWH/nsw/K/OT4S3jdcs6xasvz79mOx4IKx1+QYmdfFvOsTS57hP6TanU9ueVV305rDqyHYli3iVT/bj5EH6z1aV7JPBNNGIllrq9xOtXb1pqKdcd5DFJQssHRp3Ndn5GhWA2KeWLf31VUqw3rqtIYKX83wwAQkQwR670grw4kW7UHcb1lxLtGtDeL2J5391HTtJTcDSSiPBH9fSQ1cxrIMan1wa4ocmvInpBUaqqD3RvN+McbjZXmXOx5S7Nu/Kobf0yf2RHN+T++flphzQdWP4Ds0aeV6m7ZaYNdaGVHCnl6pU88bh6v9/koscqd8kmWjKLvlhCj+IO1bEQ50Ac+3S4Jw63YWYsDe2hczEv/AsWFZMZ7PrHmYo+gy+ZC84UZtNeO7PFghmIsYLL1fzK3ddH5KZ7Zd4f1MZKLlgtl9RDyy7ueMFa/WXADDatWUTvw+vMtPb9il4p+1oY/QlIC9nJS9kwvO53ObM92x1KtEdbzIpJtczavJMyOG9Ejyexgu1rvIWeknTbqdg7KJ1mCJFsUkvnBdELvSiKfRuY1QDK36yPZIlptTqX7+9xfVTUEqi5cuCA+QskOHjw4depUMWA609vcHa/7RsAoZOiwFsdEWj+6xgj2sgRylTUvh2OXfG9E4D4ZJUCxD2Mf/e677I04QXt3hSvTVR1NWI/dVlCOPp5T53GepNkY6M5aUcjIR68LJOqqfMG6Qh3J2MXfzRcN+8ceIVyXNSwdbwy/14fD0Pqsf+UHuwqoIAkXazqJJdeEc9UczfZ3RT3e5T00EJGMYbzqMuwfe4SwfW36GxXpHAMjxoEfHF7xpvUS+uGMvSKdVe4qLx+Dsjjl+turQwoRydjGWzpDemEwDBeiq4r+HlgYK+gr5y9a/WbZ3tJWUTPb2VOtI7mtWX9JiV14ldb0t1etN7qGA/1Iysm9HwkAAADkgzoSAAAACB8iEgAAAAgfIhIAAAAIHyISAAAACB8iEgAAAAgfIhIAAAAIHyKScrr00ks//fRTMQAAAACB4X0k5XT+/PkTJ06cO3dODAMAAEAwiEgAAAAgfGi1AQAAgPAhIgEAAIDwISIBAACA8CEiAQAAgPAhIgEAAIDwISIBAACA8CEiAQAAgPAhIgEAAIDwISIBAACA8CEiAQAAgPAhIgnd3tVVVQtePCOGRrSTmxdUSYs2j4pVyotuvtX7xEA4wiv2vU/TZY6SvbdwdPWf3isGCnZm8yJaeiHvPADDCSISKJ9rWrZdoPZ0ii9GO3JRmb1y4abv3CaGwzHmin24mLVkU2PH7DEbkAGUHSKSyttH7qJdLdh8UkwCI9Hepycu3rpqz5aWCeKLMWfWEzQS2vbAiCgAUSfhEkColUxVq81KjzMv0q/V6e11QiQW3Luqr2ViUfUcE1q20NJbEW44K/GVFQqq+PEoPY6XGOcoeVq/KLmfDGWu7Ml6bU1tLTir1lDMYtK2mu0s7ahrVFfEkR89ZWc9pUjcuRaUSNlR5tq6uNZ9eibrnx/3YncpOkaWkjqX4FOAxdf80WMChsjpTQsNo3OPGBL2rDKMxs2nxdCoQG/WF24aVavkdGJTo2Gs2iuGhoMxUexFOb2ZbKvGTXvpJrMfa3vJ8Wd+yY5QYxU/RNlcapHSQ5WwpcCqpsQsIxRbhcZNJ9gA27EdpykP3qVnH9SmtC9Fy4CJT0NpxeuzNdmoQNuCb1yP45dtaGu7sxWxDVpLYRNbxWWbV4x130lYmazaa0uBotmzJWINEj7J2lLT5w1S7JJemDQdW2mbxBaR6fiWbR6ISIYS25X1Pc/c0nwrMvYdVxnluU+4Ume0L9c62gllp6QHyao9YizJCT/85Oz0ezox25UZ7TgR6Fi37/kRKNjLwYN/fjifZL1WkxU7OWZ8it2f5zqOjmLntNxq5WPlhBWjSlt9QS15gp0lhcKKvRhk9XmxsNXRjyDnIWmdeek6dm7atFBmnqRDBx3HoEuy/uTGpWwlw6nl4zIBL+GyRcMs/1pqdIdxzZiNX+k5E2HZFpvbsa86kxLT7FHmovy2praIfJSsOmjp+JeP32rSleIzsuNFzxhNln/DNrfvgcnSNJfim2zJxS7ZcuVTXL67QYHQajMs9LVMnNi/gG1AsnVXzlZq8PY+XTWxZYbY2ic2GS0TXaqd3Zx5ccHEFsPcNU9PWavUpO1d/ajxIzGG7KZ9i69Va00PrH30+GN0r1q5dtH3tjWwaKljh8wTmbhqtiH28FVbF08MVsdLawVnHZD52bOqY3bgymG//Pgm67+axspZVROPPcZGsmJ3rRp1t3dHh9HYMM/ZXDF6iv3k5gXXLjbM08qJ2rXKjLy9hp+sbSY8wLu1cPRs1bj5Ry3XiLGskn/2AZnsns6Vsz1qs8vmthUXvFrWTu7YttVYdc8sMUiLa+1KUtb9O+SeUDuvwVi8kWTwzOZnD2xa0lI7zeg7dlyM5K6Zt2ChOkteor2GXTyc9q6umr3SOr8/dvxR2255Zkd/H/ln5WvlKbYzu7b1GavmWY1HZE1pGWzblW+FfEtv72srjYUL5pnb3dj7kxaS7ZU76OHgOHz2/WTxVkPZ22krwOyOxk3PttSKYclna1bSgeNWaZw5fsAwZtRaq9Z3XDmrHD/WZyysZdmmG9qzVY52/1phlV0BfJOlvPIToNgltikbNy0JnMHDSgGd5AVU1FYSuz0MBdeAlIaTatyqhrTO8Fwb68sRDntT7zbYWZJ9tjLGFsribn4FUlbBNT9ui6apaVGzI5Z355+fgpJVV9O/2PPyXsooKXYiyJQsY9rto47mU8+SI5OOHLpjx45TwKLmtB2A0deR5828KaeDpMzpXKz6ii1LfKkrbOcxuZZwviIl2OLyTBOcvkX45tjjfeus8Cs9/VwnVkpua30dRelpqVl7hWfZskRsew4vGYv37kFz67XJHCmLZNnqOAufJSWmZ59djhq/xfFD3re0vWZ3/d4zP/mL3eTMEvtGoe1+LGWRE/45787jAXUkw4Lr3TbhuH0xJtTOoPG6EgJ7qZ3SaJA76SD3/dfQRBWNC+6Q2ZnmEuiqd0VB87NvB4m4rWSJa2ob9Vjem3d+CkrWvpqexZ6X4ybJMnqKnU1pq1UqzMnN32vpW/WoekfrrFuqrV3oqHVwIesVbMp2u0w77q2dcpokKG/Kzxw/bDROqSX3so91rlz76DbDe28JflTmx/aKlbP8+gbyWqjyd4mlnRPX1p64sO0Be8VEPs7Ss9BaumuPP+aeYdoHk9VTarUF7AZ91WOF95jW6+dYVaJeA2d2UKUVMCf0Kgqzi+61i/s696j9tWmy5ELbMZuM5DWg6rrQ+kLWwZmMnd1BrsrbrBrBsqDVReQaPy9gfUWA/LgXu8mtgmTWClGqFIlmyC6qdfHm1cys9GjF6hMBM2uHiGRYoxVuBtvMplkrxbh86FFE4l96TDJ6XT09TVhmB020WOwSTtsdLOSwFyOLlzfZIV5NYvQUOz3LkBsjc/ZC21bObH6Untm16xCrzuXnSmkirTcOF2tIMvZ6PjQ0655VfVtnWBdItYK6/Mipn1YwkDM+U0JEqPF90oScamjrnlHM1dS39GijM22Pdr3ykThm4rYGx9WLB7J7i2vRUM1aQSsAeDuRIFobiRMLtpEdWz085VP0xB6DnHStkmdBlWjBZI2t2ow0ypm1ktUZiKtywIb1QEiYSM75CzedDnyNz5cfj2K3sPa1zsd89oQJD/yI7KJWSyXdByYuNliNlAiGimyKRUQyrNEbbpfKusBnjdtEXEvr7pQOBOQAm0iPeT6SsNfIlR27iXSpzCzxPs8/2aFfTWH0FLu8MWJn9oI6fJx58Xv00WjbWY9VANhq2qn8Z1v7BVUooOuPG14PNGvbAuWuV2l3l+gGLf0CGZysEKIV4OT6V5agxF7JZK4vr9WbrcUNx49vZfVD/vxKb0LtNLrz055PZj2W2b1A1ANpcYysd3QLZItGc6h1AbFc0/KjzWo/Lc2sJ2gsLnrS7FtNDluy0/KskpiGtnd0zOYhHTmoZ3fQJgyWYVrI5Kjva/leeeJIcqWnt6AFvGLALz9+xc6HqGA9SNj23Xqc1W3uXU3uc0jMxDNJDha632q9IYNDRDKslas2mBxF9Ooo7u1Yz7gyvdfL0X/NQ/DGgoL4JVvO1bQJuF1GT7GTswwNSgLvip63uQHbaJwq02rDOqXqt4NmuxK9KgfkPK2XB7lrZ0GJrdjJVYcEYz7NOgWZcMcCet+jNq45G/tEi4YekvqVHq1YotGwcmFT2qBnzSPHhXYssKOjc94s1luWxvESiQZkPXHBt91sifqKFI5tXBZISezwF4EOq8ZuVDc9u40sx0FHypzWaJI70gKiYd/8eBe7GCTyV5AwdEOLGVmgqTU08/booqoSEZEMb7d9Z9NCcpNURA0YuadU52I7kNhpeHi7bQc/Zlila5HNB6yBU+8o4IE2xpPwvFxV0JJfsuVbTafb5lm3UJrRU+zksqde82gMFPSi63ObO6Hl0VXkelPOau2SiPzINSWbj76E90duDRAcq1Hgt4YmHmvq1SpF27daLRx+TdWLnS2OXKXL9KyN3Enkfkv2zFkrtcejRDYIrQUkT+nxc5f5oBCraTCDVPq6262LvyfXVLxs8IlZNAgTwaYgOmDSjwVWU4m6DW1FLGLsd9zSZCsiO7LwiG3ls2ZtHH8WSQQ6LPDqY09jcfyRIq3zXzGKCkcI//x4FrsUrIJElI+YkQemHWvNkwxLpNheemyjw9DQ+58LtOre0a9ba6mh99mqoN2YtUYBvaqc5UQgy1LyQG+FeT0/m50ti2WJfcn7UVu0FgE2mZ1j1RTePeEt/vlhvJP1Xk3tM8US0YrdH90o7vln+ZRGarEz2o6nzaWtoyRKL29+/Fen/OyL45SF0sKXrNW07yGcy37C0lca4/JxzY9SvHoBuuyTfIIClhiAuq2day3z7HaAuJcep+7wjgxr5eCWMmMvcN+tqZ8qbfuVbafVlmjbae0lYF+onlu1BAilEOynbk6cwF0PIlFK7jPKlH2T9csP5VfsLEv2jcjYSsBclqBtaKLonbOK/CfSAMiLRe4zRCPl2MaKwpCty5WFYh/G9j5dNfuwbEQHgBKg1QagKKyuu2xd2GCECt6CBgD5ICIBKNKsJ04X28sHRgXR5eI06q4AygIRCUDRJrRs2bPK3t0Pxoq9G+2v0gKAUqAfCQAAAIQPdSQAAAAQPkQkAAAAED5EJAAAABA+RCQAAAAQPkQkAAAAED5EJAAAABA+RCQAAAAQPkQkAAAAED5EJAAAABA+RCQAAAAQPkQkAAAAED5EJAAAABA+RCQAAAAQPkQkAAAAED5EJAAAABA+RCQAAAAQvqqtW7eKjwAAAAChMIz/HzAm0F9VIHpqAAAAAElFTkSuQmCC"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![10M.png](attachment:10M.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>It's also better to save this value in a variable to use it in other parts or even calculating errors if needed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Absolute Error for Population Mean Estimation based on 100 sample's of size 1 is :0.163547199563083\n"
     ]
    }
   ],
   "source": [
    "true_pop_mean = -0.00041534\n",
    "mean_abs_error = abs(true_pop_mean - kappa_mean)\n",
    "print(f\"The Absolute Error for Population Mean Estimation based on {n_sample} sample's of size {sample_size} is :{mean_abs_error}\") \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color=#4C009B >\n",
    "$$\\textbf{Approximate Population mean:(10M sample size)}$$\n",
    "    <font>\n",
    "<br>\n",
    "$$\\boxed{\\mathit{\\mu = 4.1534 \\times 10^{\\,-\\,4}}}$$\n",
    "        <br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style = \"font-family:Times;\">\n",
    "    <font size=\"3\">\n",
    "We can also examine that weather this is a good approximation or not by drawing a 10 times larger sample size (100M for ex.) and a sample size 10 times smaller (1M for ex.) and observing the size of convergence steps to the true population mean. (n = infinity(population size))<br>It's very important that the sample size that we're using as a reference and approximation of $\\mu$ should be considerabaly larger than the total instances we use in each part of our survey sampling.(in our case 2K * 100 = 200K)\n",
    "    </font>\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color=#2480B6 ><font>\n",
    "## **C) Calculate the *unbiased estimation* of the standard deviation of your sample.**\n",
    "<font color=#000000 ><font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style = \"font-family:Times;\">\n",
    "    <font size=\"4\">\n",
    "- The argument <b>'ddof'</b> in the method <b>'np.var'</b> used in the code below, replaces the default 'n' in the divisor by 'n-1', <b>making the variance estimation unbiased.</b>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The popualtion variance estimation (unbiased) based on 100 is: 21.378344830457927\n",
      "The  std (unbiased) is: 4.6236722235100025\n"
     ]
    }
   ],
   "source": [
    "kappa_var_est = np.var(kappa_samples,ddof=1)\n",
    "print(\"The popualtion variance estimation (unbiased) based on\",n_sample,\"is:\", kappa_var_est)\n",
    "kappa_std_est = np.sqrt(kappa_var_est)\n",
    "print(\"The  std (unbiased) is:\", kappa_std_est)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style = \"font-family:Times;\">\n",
    "    <font size=\"3\">\n",
    "- Like the previous part we can calculate a very good estimate for the population variance and std by giving a very large number to n_sample and storing it an a variable for later use!<br> In my case I used the same simulation that I used for population mean approximation with 10M samples. <font color=#E31339 ><b><br>P.S 2) I have not used this 10M sample  estimation ( as true population variance, std ) for obtaining confidence intervals or other problems as well as \"P.S 1\"!</b><font> <font color=#000000 ><font></b>"
   ]
  },
  {
   "attachments": {
    "true%20variance,std.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![true%20variance,std.png](attachment:true%20variance,std.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "The Relative Error for Population Variance Estimation based on 100 sample's of size 1 is     :5.720865566144587 %\n",
      "\n",
      "\n",
      "The Relative Error for Population std Estimation based on 100 sample's of size 1 is     :0.6274125238483899 %\n"
     ]
    }
   ],
   "source": [
    "true_pop_var = 20.2215\n",
    "var_abs_error = abs(true_pop_var - kappa_var_est)\n",
    "var_rel_error = var_abs_error / true_pop_var\n",
    "\n",
    "true_pop_std = 4.4968\n",
    "std_abs_error = abs(true_pop_std - kappa_std_est)\n",
    "std_rel_error = std_abs_error / true_pop_var\n",
    "\n",
    "print(f\"\\nThe Relative Error for Population Variance Estimation based on {n_sample} sample's of size {sample_size} is     :{var_rel_error*100} %\") \n",
    "print(f\"\\n\\nThe Relative Error for Population std Estimation based on {n_sample} sample's of size {sample_size} is     :{std_rel_error*100} %\") \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color=#4C009B >\n",
    "$$\\textbf{Approximate Population Variance & Standard Deviation :(10M sample size)}$$\n",
    "<p style = \"font-family:Times;\">\n",
    "    <font size=\"4\">\n",
    "    $$\\mathit{\\sigma^{2} _{pop} = 20.2215}$$<br>$$\\mathit{\\sigma_{pop} = 4.4968}$$<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style = \"font-family:Times;\">\n",
    "<font color=#0F60BE>\n",
    "   <font size=\"4\">\n",
    "       - <b>Unbiased standard deviation estimation:</b>\n",
    "    </font>\n",
    "</font>\n",
    "\n",
    "<p style = \"font-family:Times;\">\n",
    "    <font size=\"3\">\n",
    "<font color=#000000 ></font>\n",
    "First Lets look at the biased estimation for std:\n",
    "- The Maximum Likelihood Estimation (MLE) for standard deviation <b>(Biased</b>):<br><br>\n",
    "$$\\mathit{{\\displaystyle \\boxed{ s_{n}={\\sqrt {{\\frac {1}{n}}\\sum _{i=1}^{n}\\left(x_{i}-{\\bar {x}}\\right)^{2}}}}}}$$<br><br>\n",
    "$\\textit{Proof of biasness:}$<br><br>\n",
    "This estimator is derived by taking the square root of the biased estimation for variance so it should probably be biased too, as taking a square root doesn't act as a proper bias correction factor but first let's take a closer look to the MLE (Maximum Likelihood Estimation) for variance which is Biased:<br><br>$$\\boxed{\\mathit{s_n^2 = \\frac {1}{n} \\sum_{i=1}^n  \\left(x_i - \\overline{x} \\right)^ 2 }}$$\n",
    "         <font size=\"4\"><b>How much bias does the MLE of Varince have?</b><br><br><br>\n",
    "${\\displaystyle {\\begin{aligned}\\boxed{\\operatorname {E} \\left[\\sigma ^{2}-s_{n}^{2}\\right]}&=\\operatorname {E} \\left[{\\frac {1}{n}}\\sum _{i=1}^{n}(x_{i}-\\mu )^{2}-{\\frac {1}{n}}\\sum _{i=1}^{n}(x_{i}-{\\overline {x}})^{2}\\right]\\\\&=\\operatorname {E} \\left[{\\frac {1}{n}}\\sum _{i=1}^{n}\\left((x_{i}^{2}-2x_{i}\\mu +\\mu ^{2})-(x_{i}^{2}-2x_{i}{\\overline {x}}+{\\overline {x}}^{2})\\right)\\right]\\\\&=\\operatorname {E} \\left[{\\frac {1}{n}}\\sum _{i=1}^{n}\\left(\\mu ^{2}-{\\overline {x}}^{2}+2x_{i}({\\overline {x}}-\\mu )\\right)\\right]\\\\&=\\operatorname {E} \\left[\\mu ^{2}-{\\overline {x}}^{2}+{\\frac {1}{n}}\\sum _{i=1}^{n}2x_{i}({\\overline {x}}-\\mu )\\right]\\\\&=\\operatorname {E} \\left[\\mu ^{2}-{\\overline {x}}^{2}+2({\\overline {x}}-\\mu ){\\overline {x}}\\right]\\\\&=\\operatorname {E} \\left[\\mu ^{2}-2{\\overline {x}}\\mu +{\\overline {x}}^{2}\\right]\\\\&=\\operatorname {E} \\left[({\\overline {x}}-\\mu )^{2}\\right]\\\\&=\\operatorname {Var} ({\\overline {x}})\\\\&={\\boxed{\\frac {\\sigma ^{2}}{n}}}\\end{aligned}}}$<br><br><br><b>Therefore the Expected value of the biased Estimator is:</b><br><br>\n",
    "$${\\displaystyle \\boxed{\\operatorname {E} \\left[s_{n}^{2}\\right]}=\\sigma ^{2}-{\\frac {\\sigma ^{2}}{n}}=\\boxed{{\\frac {n-1}{n}}\\sigma ^{2}}}$$\n",
    "<br><br>\n",
    "\n",
    "             \n",
    "[Calculation Source: Wikipedia, Bessel Correction](https://en.wikipedia.org/wiki/Bessel%27s_correction#Proof_of_correctness_%E2%80%93_Alternative_3)\n",
    "\n",
    "             \n",
    "<p style = \"font-family:Times;\">\n",
    "<font size=\"3\">\n",
    "<br><br><br>\n",
    "- The corrrection coefficient factor\n",
    "$\\mathit{(\\frac{n}{n-1})}$\n",
    "is called the Bessel Correction Factor.As a result the Unbiased Variance Estimator is derived from multiplying the Biased estimator ($\\mathit{\\,s_n^2\\,}$) by the \"Bessel correction coefficient factor\"<br><br>\n",
    "$$\\mathit{\\boxed{s^2} = \\left(\\frac{n}{n-1}\\right)\\,s_n^2 = \\boxed{\\frac { \\sum_{i=1}^n  \\left(x_i - \\overline{x} \\right)^ 2}{n-1} }}$$<br><br><br>\n",
    "Primarily, it seems that by taking the square root of the unbiased variance estimator, ($\\mathit{s^{2}}$) we can obtain an unbiased estimation for standard deviation but by calculating the expected value of the derived estimator we observe a slight bias that fortunately effects very low sample sizes and tends to zero by increaseing n. So in our case which n = 100, This estimator can be assumed as an unbiased estimator:<br><br>\n",
    "\n",
    "$$\\boxed{\\displaystyle s={\\sqrt {\\frac {\\sum _{i=1}^{n}(x_{i}-{\\overline {x}})^{2}}{n-1}}}}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color=#2480B6><font>\n",
    "## **D) Answer the following questions.**\n",
    "<font color=#000000><font>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "    \n",
    "$\\textbf{Q1) What is an unbiased estimator?}$\n",
    "><p style = \"font-family:Times;\">\n",
    "<font size=\"3\">\n",
    "The definition for an unbiased estimator is an estimator which it's expected value equals the true value of the estimated parameter.For example; sample variance is a stochastic estimator for the population variance. This estimator is biased if (n = sample size) is used in the denumenator and unbiased if (n-1) is used instead. This correction is called the \"Bessel Correction\" and corrects the bias in the population variance estimation but also increases the MSE (mean squared error)<br><br>$ \\textit{If ${\\hat{\\theta}}$ is an estimator for estimating true parameter $\\theta$}, \\textit{ ${\\hat{\\theta}}$ is called an \"Unbiased Estimator\" if :}$<br><br>$$ \\operatorname {E} ({\\hat {\\theta }}) = \\theta  $$<br><br>\n",
    "$\\textit{Otherwise ${\\hat{\\theta}}$ has an estimation bias that is calculated as follows:}$<br><br>\n",
    "$$ {\\displaystyle \\operatorname {Bias} ({\\hat {\\theta }},\\theta )=\\operatorname {E} _{x\\mid \\theta }[\\,{\\hat {\\theta }}-\\theta \\,]} $$\n",
    "<br><br><br>\n",
    "    \n",
    "    \n",
    "$\\textbf{Q2) In what situations the maximum likelihood estimation of the variance of a distribution can severely contaminate the estimation}$\n",
    "><p style = \"font-family:Times;\">\n",
    "<font color=#4C009B>\n",
    "   <font size=\"4\">\n",
    "       - <b>Maximum Likelihood Estimation (MLE):</b>\n",
    "    </font>\n",
    "</font><p style = \"font-family:Times;\"><font color=#000000><font size=\"3\"><b>(MLE)</b> is a method of estimating the parameters of a probability distribution by <b>maximizing a likelihood function</b>, so that <b>under the assumed statistical model</b> the <b>observed data</b> is <b>most probable</b>. The point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate.<p style = \"font-family:Times;\">\n",
    "<font color=#4C009B>\n",
    "   <font size=\"3\">\n",
    "       - <b>Maximum Likelihood Estimation (MLE) for Variance Estimation and it's issues:</b>\n",
    "    </font>\n",
    "</font><p style = \"font-family:Times;\"><font color=#000000><font size=\"3\">As I mentioned mathematically in the previous part the <b> Maximum Likelihood estimator</b> for variance <b>underestimates</b> the true population variance by <b>\"Bessel Correction Coefficient\" factor</b> and in order to <b>correct</b> this bias we <b>multiply the estimator by this factor</b> and obtain the <b>Unbiased Variance Estimator</b> for Population's Variance and std.<br><br><br><b> <font color=#4c009B><font size=\"4\">Reasons we shouldn't use MLE for variance estimation:</b><br><br>\n",
    "    1) We observed that the <b> bias </b> of <b> MLE for variance </b> increses by decresing n in a hemographic way. So using MLE for variance estimation <b>causes large ammount of error in low sample size cases</b>.<br><br>2) <b>MLE</b> can be <b>sensitive</b> to the <b>starting samples</b> we are choosing as its the optimal value for omtimizing the likelihood function.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color=#2480B6><font>\n",
    "## **E) Now, draw 2000 samples of size 100 and store their means in an array You're going to use this array in the next questions.**\n",
    "<font color=#000000><font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "sample_num = 2000\n",
    "sample_size = 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "kappa_samples_2k_100 = my_kappa(sample_num * sample_size,student_id).reshape(sample_num,sample_size)\n",
    "means_2k_100 = np.empty(sample_num)\n",
    "for i in range(sample_num):\n",
    "    means_2k_100[i] = np.mean(kappa_samples_2k_100[i])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\textit{Assuming ' k ' samples, each consisting ' n ' realizations from a Population size 'N':}$$<br>\n",
    "$$ \\textit{The sample mean ($\\bar{x}$) and population mean ($\\mu$) are defined as follows:}$$<br>\n",
    "$$ \\bar{x}_{j}=\\frac{1}{n}\\sum_{i=1}^{n}x_{ij},\\quad j=1,\\ldots,k. \\\\ \\mu=\\frac{1}{N}\\sum_{i=1}^{N}x_{i}$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br><br><br>\n",
    "<font color=#CF3A69><font>\n",
    "# Problem #2 - Data Visualization and CLT\n",
    "\n",
    "<font color=#2480B6><font>\n",
    "## **A) Draw a sample of size 2000 from my_kappa distribution. Then, using matplotlib package, depict the histogram of your sample.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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9NEcDj6BZJ8N0f5oeVD9O8+PZ24EPV3Mpg37OpLno+ZntvnQJzWfSo4Atqmqjn71Jvk9zfurFND9ovRr4NU0HR/18meaz76SezzWA69tzHzdpu22bgE7rWo5JtqP5vLwd+Gdgr7tORefWiY5oVtU1bQj8PvD1JE/YlB8tpa4xAEq6m6pal+TfaM672ugRro3M6+j2iNtJSZ5bVV9L8laaywe8mqYJ5XNouyEf5ySaZkefoAkap9GEj/FeRdP9/xtpmjAdUlWn9Yz/c5oOKcZ6lPswTYA7dAov4QFtjUXT7HAVzSUJPlRVk53jdBHNUcb30QSYa4CP03wpHPNamt43v0lzNGVnBreGpgv5d9E0yTufpjfO3/VMcyjN618J/Iqma/rl3L1zipNpmme9B9iW5ijBK8YvrKquT/Jk4J9omgbfQXOO4xt7zh+bqrFLDfQ7j3HMeTTrdQXNF+w1NF/eP9jWM8j2NB0b28bupqpuaL9gH0XTZPWBNNvA99m0oD+ZqazfuWh34PM9j3eh6XUV7t7B0n2ZfBtZRbN//gNNs8vraY4ivQ2gqq5Nc03A9wKn0jRRfy1Nc8lh+iea13AiTdP5Y8dq6Keqqj2a/TaabWspzbZ1IU1T8an4Ac1+uoymc5v/oOnBdaKLv+/a/v3OuOEn0PRIPJvb7Xi7cVfnRt8eN+473LVt3ENV/bT9IeBbNJfRePq4z0BJ4+TuLWckdV3b89sa4Liq+tsR1bAa+EJV/dUk0zyJ5ovC/zNgL6WaA5K8kuZ6a7vWEC8KPkxuY6OV5pqkq2i2kV+Mup6JJCmayzF8eNS1SNJUeARQEgBpur7/Y5ojZg+iuVaeNFOWAx+Yq+FPc8JymvOQ52z4k6T5yAAoacx/ozl35DrgNeObEbU9Z07Ye2ZVrZ/Z8rSQVNWrR13DqLgvTU1VfYbmenWdk+YEuImuMwlwZ9mES9ImsgmopClJcjxwwCST7DxBxyGSergvaWPaDpn69dQ5ZsLOkyRpYwyAkqak7bVxogtfA1y0CR2BSJ3jvqSNSfIgJu8Y6oqqunG26pG0sBgAJUmSJKkjFtw5gNtss00tW7Zs1GVIkiRJ0khccMEFN1TVtv3GLbgAuGzZMs4/f1rXI5UkSZKkeSvJmonGTdgLmSRJkiRpYTEASpIkSVJHGAAlSZIkqSMMgJIkSZLUEQZASZIkSeoIA6AkSZIkdYQBUJIkSZI6wgAoSZIkSR1hAJQkSZKkjjAASpIkSVJHGAAlSZIkqSMMgJIkSZLUEQZASZIkSeoIA6AkSZIWrCVLl5FkJLclS5eN+uVL97B41AVIkiRJM2XtVWtYec6GkSz74OUea9Hc41YpSZIkSR1hAJQkSZKkjjAASpIkSVJHGAAlSZIkqSMMgJIkSZLUEQZASZIkSeoIA6AkSZIkdYQBUJIkSZI6wgAoSZIkSR1hAJQkSZKkjjAASpIkSVJHGAAlSZIkqSMMgJIkSZLUEQZASZIkSeoIA6AkSZIkdYQBUJIkSZI6wgAoSZIkSR1hAJQkSZKkjjAASpIkSVJHGAAlSZIkqSMMgJIkSZLUEQZASZIkSeoIA6AkSZIkdYQBUJIkSZI6wgAoSZIkSR1hAJQkSZKkjjAASpIkSVJHGAAlSZIkqSMMgJIkSZLUEQZASZIkSeoIA6AkSZIkdYQBUJIkSZI6wgAoSZIkSR1hAJQkSZKkjjAASpIkSVJHjCQAJlmU5D+SnN4+3jrJmUl+1v7dqmfaw5OsSnJ5kmeMol5JkiRJWghGdQTwL4Gf9Dw+DDirqnYFzmofk2Q3YAWwO7APsDLJolmuVZIkSZIWhFkPgEl2Ap4NHNszeF/ghPb+CcDze4afVFXrquoKYBWw12zVKkmSJEkLySiOAH4AeAuwoWfY9lV1DUD7d7t2+I7AVT3TrW2HSZIkSZIGNKsBMMlzgOuq6oKpPqXPsOoz34OSnJ/k/Ouvv35aNUqSJEnSQjXbRwD/BHhektXAScBTknwauDbJDgDt3+va6dcCS3qevxNw9fiZVtUxVbVnVe257bbbzmT9kiRJkjRvzWoArKrDq2qnqlpG07nLt6rq/wCnAQe0kx0AnNrePw1YkWTzJDsDuwLnzmbNkiRJkrRQLB51Aa13AScnORC4EtgfoKouSXIycCmwHjikqu4cXZmSJEmSNH+NLABW1dnA2e39G4GnTjDdUcBRs1aYJEmSJC1Qo7oOoCRJkiRplhkAJUmSJKkjDICSJEmS1BEGQEmSJEnqCAOgJEmSJHWEAVCSJEmSOsIAKEmSJEkdYQCUJEmSpI4wAEqSJElSRxgAJUmSJKkjDICSJEmS1BEGQEmSJEnqCAOgJEmSJHWEAVCSJEmSOsIAKEmSJEkdYQCUJEmSpI4wAEqSJElSRxgAJUmSJKkjDICSJEmS1BEGQEmSJEnqCAOgJEmSJHWEAVCSJEmSOsIAKEmSJEkdYQCUJEmSpI4wAEqSJElSRxgAJUmSJKkjDICSJEmS1BEGQEmSJEnqCAOgJEmSJHWEAVCSJEmSOsIAKEmSJEkdYQCUJEmSpI4wAEqSJElSRxgAJUmSJKkjDICSJEmS1BEGQEmSJEnqCAOgJEmSJHWEAVCSJEmSOsIAKEmSJEkdYQCUJEmSpI4wAEqSJElSRxgAJUmSJKkjDICSJEmS1BEGQEmSJEnqCAOgJEmSJHWEAVCSJEmSOsIAKEmSJEkdYQCUJEmSpI4wAEqSJElSRxgAJUmSJKkjDICSJEmS1BEGQEmSJEnqCAOgJEmSJHWEAVCSJEmSOsIAKEmSJEkdYQCUJEmSpI4wAEqSJElSRxgAJUmSJKkjDICSJEmS1BGzGgCTbJHk3CT/meSSJEe2w7dOcmaSn7V/t+p5zuFJViW5PMkzZrNeSZIkSVpIZvsI4DrgKVX1x8CjgH2SPA44DDirqnYFzmofk2Q3YAWwO7APsDLJolmuWZIkSZIWhFkNgNW4vX147/ZWwL7ACe3wE4Dnt/f3BU6qqnVVdQWwCthrFkuWJEmSpAVj1s8BTLIoyYXAdcCZVfUjYPuqugag/btdO/mOwFU9T1/bDhs/z4OSnJ/k/Ouvv35mX4AkSZIkzVOzHgCr6s6qehSwE7BXkj0mmTz9ZtFnnsdU1Z5Vtee22247rFIlSZIkaUEZWS+gVXUzcDbNuX3XJtkBoP17XTvZWmBJz9N2Aq6exTIlSZIkacGY7V5At03ywPb+fYCnAZcBpwEHtJMdAJza3j8NWJFk8yQ7A7sC585mzZIkSZK0UCweZOIke1TVxdNY3g7ACW1PnvcCTq6q05P8ADg5yYHAlcD+AFV1SZKTgUuB9cAhVXXnNJYvSZIkSZ01UAAELkpyAXAccGLbjHPKquoi4NF9ht8IPHWC5xwFHDVgnZIkSZKkcQZtAvpUmqNx7wGuTnJikr2T9OusRZIkSZI0hwwUAKvq21V1APBg4FCaSzKcAaxJ8s4kD52BGiVJkiRJQ7BJncBU1a+r6riqegLwcGA18Dbgp0m+k+QFQ6xRkiRJkjQEm9wLaJJlSY4AvgE8HvgacBBwLfC5JO8fSoWSJEmSpKEYKAAmuW+Slyf5NrAKeCnwcWBpVT23qj5RVS8CXgMcOPxyJUmSJEmbatBeQH8JLAJOAZ5WVWdPMN15wI3TqEuSJEmSNGSDBsDDgM9U1S2TTdReK3DnTa5KkiRJkjR0AwXAqlo5U4VIkiRJkmbWoOcAHpfkcxOMOzHJscMpS5IkSZI0bIP2Aro38IUJxn0RePr0ypEkSZIkzZRBA+C2wE0TjPsVsN30ypEkSZIkzZRBA+Aa4AkTjHsCsHZ65UiSJEmSZsqgAfB44K1JDkmyJUCSLZMcDLwF8BxASZIkSZqjBr0MxLuBhwIfAv45ya+B+wEBjmnHS5IkSZLmoEEvA7EBeFWSo4GnAFvTXPD9W1X10xmoT5IkSZI0JIMeAQSgqi4HLh9yLZIkSZKkGbRJATDJw4GdgC3Gj6uqr023KEmSJEnS8A0UAJPsBnwO2I3mvL/xClg0hLokSZIkSUM26BHAjwGbAfsBlwJ3DL0iSZIkSdKMGDQAPhpYUVWnz0QxkiRJkqSZM+h1AH9On/P+JEmSJElz36AB8M3A25LsMhPFSJIkSZJmzqBNQP8R2BG4LMlq4ObxE1TVXkOoS5IkSZI0ZIMGwIvbmyRJkiRpnhkoAFbVK2eqEEmSJEnSzBr0HEAA0liSZHmS+w27KEmSJEnS8A0cAJMcDPwXsAb4HvCIdvgpSd4w3PIkSZIkScMyUABM8tfA+4CPA08B0jP6bODFQ6tMkiRJkjRUg3YCcwjw9qp6T5JF48ZdDjx8OGVJkiRJkoZt0CagDwYumGDcBrxIvCRJkiTNWYMGwFXAEycY9wTg0umVI0mSJEmaKYM2Af0AsDLJHcAX2mHbJTkQeBPw6mEWJ0mSJEkankGvA3hskq2AtwNHtoO/BvwGOKKqPjvk+iRJkiRJQzLoEUCq6ugkHwWWAw8CbgJ+UFW3DLs4SZIkSdLwDBwAAarqNuCMIdciSZIkSZpBAwXA9iLwk6qqlZtejiRJkiRppgx6BPDDk4yr9q8BUJIkSZLmoIEuA1FV9xp/A7YGXgL8J7DbTBQpSZIkSZq+TToHsFdV3Qx8LskDgI8BT5ruPCVJkiRJwzfoheAncwWw5xDnJ0mSJEkaoqEEwCQ7AG+mCYGSJEmSpDlo0F5Ar+euzl7GbAbcH/gdsN+Q6pIkSZIkDdmg5wD+C/cMgL8D1gJfr6obh1KVJEmSJGnoBgqAVXXEDNUhSZIkSZphw+wERpIkSZI0hw16DuAV3LMJ6ISqapeBK5IkSZIkzYhBzwH8ArACuC9wJnAdsB2wN/Br4HNDrU6SJEmSNDSDBsBfAT8Hnl1Vvx4bmGRL4HTglqr6+yHWJ0mSJEkakkHPATwEOLo3/AFU1e3Ae9vxkiRJkqQ5aNAA+ABg+wnGPRjYcnrlSJIkSZJmyqBNQE8Djk5yK/CVqlqXZHPgecC7ga8Mu0BJkiRJ0nAMGgBfBxwPnAxUktuA+wOhCYevG2p1kiRJkqShGfRC8LcAL0iyO/BYmuagvwTOq6pLZ6A+SZIkSdKQDHoEEICqugS4ZMi1SJIkSZJm0KCdwJBkuyTvTnJWksvbo4Ek+cskjx9+iZIkSZKkYRgoACbZC/gZ8L+B1cDDgM3b0TsAbx5mcZIkSZKk4Rn0COD7gW8DDwdeQ9P5y5hzgb2GVJckSZI0ry3ebHOSzPptydJlo37pmsMGPQfwfwL7VtWGJBk37kZgu+GUJUmSJM1v6+9Yx8pzNsz6cg9ePvBZXuqQQbeOW4BtJxi3C3DtZE9OsiTJt5P8JMklSf6yHb51kjOT/Kz9u1XPcw5Psqo93/AZA9YrSZIkSWoNGgBPBY5MskvPsEqyDfBXwCkbef564M1V9UjgccAhSXYDDgPOqqpdgbPax7TjVgC7A/sAK5MsGrBmSZIkSRKDB8DDgFuBS4HvtsM+ClwO/BZ4+2RPrqprqur/a+/fBvwE2BHYFzihnewE4Pnt/X2Bk6pqXVVdAazC8wwlSZIkaZMMeiH4XyV5HPAy4KnAr4GbgGOBT1XVuqnOK8ky4NHAj4Dtq+qadhnXJBk7l3BH4Ic9T1vbDpMkSZIkDWjKATDJFsBpwD9U1SeAT2zqQpNsCXwReENV3XrP/mTumrTPsOozv4OAgwCWLl26qWVJkiRJ0oI25SagVfU74LHAtM7BS3JvmvD3maoaO2fw2iQ7tON3AK5rh68FlvQ8fSfg6j61HVNVe1bVnttuO1EfNZIkSZLUbYOeA3gad52fN7D20hGfAH5SVe8bN98D2vsH0HQ2MzZ8RZLNk+wM7EpzvUFJkiRJ0oAGvQ7gGcDR7VG6r9Fc9uFuTTKr6muTPP9PaM4f/HGSC9thbwPeBZyc5EDgSmD/dl6XJDmZptOZ9cAhVXXngDVLkiRJkhg8AH66/btfexuvmKSJaFV9n/7n9UHTqUy/5xwFHDVAjZIkSZKkPjYaAJN8A3h9VV0O7EwT4J5K03vnbTNbniRJkiRpWKZyBPBpwAMAqmpNeyH2Y4DHVtWamSxOkqRRWbJ0GWuvmv1/czsteQhXXbl61pcrSeqGQZuAjuCjUw8AAA4ySURBVJnwug2SJC0Ea69aw8pzNsz6cg9ePmj/bJIkTZ3/ZSRJkiSpI6YaAO9x8fUJhkmSJEmS5qipNgE9I8n6ccPO6jOMqtpu+mVJkiRJkoZtKgHwyBmvQpIkaZaNqqMfsLMfSaOz0QBYVQZASZK04Iyqox+wsx9Jo+OnjyRJkiR1hAFQkiRJkjrCAChJkiRJHWEAlCRJkqSOMABKkiRJUkcYACVJkiSpIwyAkiRJs2zxZpuTZNZvS5YuG/VLlzRiU7kQvCRJkoZo/R3rRnINQq8/KMlPAUmSJEnqCAOgJEmSJHWEAVCSJEmSOsIAKEmSJEkdYQCUJEkjtWTpspH0iClJXWQvoJIkaaTWXrXGHjElaZb4ySdJkiRJHWEAlCRJkqSOMABKkiRJUkcYACVJkiSpIwyAkiRJktQRBkBJkiRJ6ggDoCRJkiR1hAFQkiRJkjrCAChJ0hyyeLPNSTLrtyVLl436pUuSZsHiURcgSZLusv6Odaw8Z8OsL/fg5f4mLEld4Ke9JEmSJHWEAVCSJEmSOsIAKEmSJEkdYQCUJEmSpI4wAEqSJElSRxgAJUmSJKkjDICSJEmS1BEGQEmSJEnqCAOgJEmSJHWEAVCSJEmSOsIAKEmSJEkdYQCUJEmSpI4wAEqSJElSRxgAJUmSJKkjDICSJEmS1BGLR12AJEkavcWbbU6SUZchSZphBkBJksT6O9ax8pwNI1n2wcttkCRJs8VPXEmSJEnqCAOgJEmSJHWEAVCSJEmSOsIAKEmSJEkdYQCUJEmSpI4wAEqSJElSRxgAJUmSJKkjDICSJEmS1BEGQEmSJEnqCAOgJEmSJHXErAbAJMcluS7JxT3Dtk5yZpKftX+36hl3eJJVSS5P8ozZrFWSJEmSFprZPgJ4PLDPuGGHAWdV1a7AWe1jkuwGrAB2b5+zMsmi2StVkiRJkhaWWQ2AVfVd4KZxg/cFTmjvnwA8v2f4SVW1rqquAFYBe81KoZIkSZK0AM2FcwC3r6prANq/27XDdwSu6plubTvsHpIclOT8JOdff/31M1qsJGn2LFm6jCQjuUmStBAtHnUBk+j337f6TVhVxwDHAOy55559p5EkzT9rr1rDynM2jGTZBy+fC7+RSpI0XHPhv9u1SXYAaP9e1w5fCyzpmW4n4OpZrk2SJEmSFoy5EABPAw5o7x8AnNozfEWSzZPsDOwKnDuC+iRJkiRpQZjVJqBJTgSeBGyTZC3wDuBdwMlJDgSuBPYHqKpLkpwMXAqsBw6pqjtns15JkiRJWkhmNQBW1UsmGPXUCaY/Cjhq5iqSJEmSpO6YC01AJUmSJEmzwAAoSZIkSR1hAJQkSZKkjjAASpIkdcTizTYnyUhuS5YuG/XLl8TcvhC8JEmShmj9HetYec6GkSz74OUed5DmAvdESZIkSeoIA6AkSZIkdYQBUJIkSZI6wgAoSZIkSR1hAJQkSZKkjjAASpIkSVJHGAAlSZIkqSMMgJIkSZLUEQZASZIkSeoIA6AkSZIkdYQBUJIkSZI6wgAoSZIkSR2xeNQFSJIkaeFbvNnmJBl1GVLnGQAlSZI049bfsY6V52yY9eUevNwGb1Iv9whJkiRJ6ggDoCRJkiR1hAFQkiRJkjrCAChJkiRJHWEAlCRJkqSOMABKkiRJUkcYACVJkiSpIwyAkiRJktQRBkBJkiRJ6ggDoCRJkiR1hAFQkiRJkjrCAChJkiRJHWEAlCRt1JKly0gy6zdJkjRci0ddgCRp7lt71RpWnrNh1pd78HJ/p5QkaZj8zypJkiRJHWEAlCRJkqSOMABKkiRJUkcYACVJkiSpIwyAkiRJktQRBkBJkiRJ6ggDoCRJkiR1hAFQkiRJkjrCAChJkiRJHWEAlCRJkqSOMABKkiRJUkcYACVJkiSpIxaPugBJ0tQsWbqMtVetGXUZkiRpHjMAStI8sfaqNaw8Z8NIln3wchuMSJK0EPgfXZIkSZI6wgAoSZIkSR1hAJQkSZKkjjAASpIkSVJHGAAlSZIkqSMMgJIkSZLUEQZASZIkSeoIA6AkSZIkdYQBUJIkSZI6wgAoSZIkLSCLN9ucJLN+W7J02ahfuqZg8agLkKT5ZsnSZay9as2oy5Akqa/1d6xj5TkbZn25By/32NJ8MC8CYJJ9gA8Ci4Bjq+pdIy5J0oiNOoT5j1WSJM1Hcz4AJlkE/AuwN7AWOC/JaVV16WgrkwSjDWKjCGFgEJMkSfPXnA+AwF7Aqqr6BUCSk4B9AQOg1KNrQcwQJkmSNLj5EAB3BK7qebwW+F8jqmWTjfLL+U5LHsJVV64eybK7xmaJkiRJs29U38Hm4/fsVNWoa5hUkv2BZ1TVq9rHLwP2qqrX90xzEHBQ+/ARwOWzXujobAPcMOoiNCtc193huu4O13V3uK67w3XdHXN5XT+kqrbtN2I+HAFcCyzpebwTcHXvBFV1DHDMbBY1VyQ5v6r2HHUdmnmu6+5wXXeH67o7XNfd4brujvm6rudD263zgF2T7JxkM2AFcNqIa5IkSZKkeWfOHwGsqvVJDgXOoLkMxHFVdcmIy5IkSZKkeWfOB0CAqvoa8LVR1zFHdbLpa0e5rrvDdd0druvucF13h+u6O+blup7zncBIkiRJkoZjPpwDKEmSJEkaAgPgPJTk6CSXJbkoyZeSPLBn3OFJViW5PMkzRlmnpi/J/kkuSbIhyZ49w5cl+W2SC9vbR0dZp4ZjovXdjnPfXqCSHJHkv3r252eNuiYNT5J92v12VZLDRl2PZlaS1Ul+3O7L54+6Hg1PkuOSXJfk4p5hWyc5M8nP2r9bjbLGqTIAzk9nAntU1f8AfgocDpBkN5peUncH9gFWJlk0sio1DBcD+wHf7TPu51X1qPb22lmuSzOj7/p23+6E9/fsz57zvkC0++m/AM8EdgNe0u7PWtie3O7L8+7yAJrU8TT/g3sdBpxVVbsCZ7WP5zwD4DxUVd+oqvXtwx/SXBsRYF/gpKpaV1VXAKuAvUZRo4ajqn5SVZePug7NjknWt/u2ND/tBayqql9U1R3ASTT7s6R5pqq+C9w0bvC+wAnt/ROA589qUZvIADj//V/g39r7OwJX9Yxb2w7TwrRzkv9I8p0kfzbqYjSj3LcXvkPbZv3HzZcmRJoS993uKeAbSS5IctCoi9GM276qrgFo/2434nqmZF5cBqKLknwTeHCfUX9TVae20/wNsB74zNjT+kxvN69z3FTWdR/XAEur6sYkjwG+nGT3qrp1xgrVUGzi+nbfnucmW+/AR4B30qzTdwL/RPPjnuY/993u+ZOqujrJdsCZSS5rjxxJc4YBcI6qqqdNNj7JAcBzgKfWXdfyWAss6ZlsJ+DqmalQw7KxdT3Bc9YB69r7FyT5OfBwwBPO57hNWd+4b897U13vST4OnD7D5Wj2uO92TFVd3f69LsmXaJoBGwAXrmuT7FBV1yTZAbhu1AVNhU1A56Ek+wBvBZ5XVb/pGXUasCLJ5kl2BnYFzh1FjZpZSbYd6wQkyS406/oXo61KM8h9ewFrvzSMeQFNZ0BaGM4Ddk2yc5LNaDpzOm3ENWmGJLlfkvuP3QeejvvzQncacEB7/wBgopY8c4pHAOenDwOb0zQtAPhhVb22qi5JcjJwKU3T0EOq6s4R1qlpSvIC4EPAtsBXk1xYVc8AngD8XZL1wJ3Aa6tq/InJmmcmWt/u2wvee5I8iqZp4GrgNaMtR8NSVeuTHAqcASwCjquqS0ZclmbO9sCX2u9mi4HPVtXXR1uShiXJicCTgG2SrAXeAbwLODnJgcCVwP6jq3DqclfrQUmSJEnSQmYTUEmSJEnqCAOgJEmSJHWEAVCSJEmSOsIAKEmSJEkdYQCUJEmSpI4wAEqSOi3J6Ul+PMn4Dyf5VZLNNzKfJyWpJHsMv0pJkobDAChJ6roTgT2S7D5+RJJFwAuBU6pq3axXJknSkBkAJUlddyrwG2BFn3FPprm484mzWpEkSTPEAChJ6rSquh04HXhxn9ErgGuBa5KclOSqJL9JckmSNySZ8P9okmVtk9DnjBt+fJLzxw3bI8lXk9zW3j6f5MFDeHmSJN2NAVCSpOYI365JHjM2IMm9gRcAJwMPBi4HDgaeBXwcOBJ463QXnORhwL8DWwAvA14B7A58JUmmO39JknotHnUBkiTNAf8G3ExzxO+CdtgzgK2BE6vqB8BZAG0o+z5wX+DVwD9Oc9nvAH4JPLOq7miXcRFwGU3Y/Oo05y9J0h94BFCS1HltBy9fAl7Uc9TtxcAa4IdJtkhyZJJVwDrg98BRwM5Jpvtj6tPaZW9Isrid3xXAamDPac5bkqS7MQBKktQ4EVgKPD7JFsC+NEf/Cng38FfAMTRH5R4L/H37vC2mudxtaJqS/n7cbRdgyTTnLUnS3dgEVJKkxrdoOnxZAewA3J+7ev/cH/hQVb1nbOIkz97I/H7X/t1s3PCtxz2+ieYI4LF95nHDxsuWJGnqDICSJAFVdWeSz9OEvR2Bn1TVRe3o+9A0/QT+cH3AfpeN6HUdzZG8R/Y8b0vg8TRNS8ecBewBXNAebZQkacYYACVJusuJwKE0vX++vWf4mcAh7TmANwGHAJtPNqOq2pDkVOCNSdbQdDLzZuC34yY9AjgX+GqS42iO+u0I7A0cX1VnT/M1SZL0B54DKEnSXX5A0/lKgJN6hr8e+B7wL8BxwMVMrffPQ2ku8bCyfe6JNE1N/6Cqfgo8juZi9MfQ9Eh6JM0Rx1Wb/EokSeojtjaRJEmSpG7wCKAkSZIkdYQBUJIkSZI6wgAoSZIkSR1hAJQkSZKkjjAASpIkSVJHGAAlSZIkqSMMgJIkSZLUEQZASZIkSeoIA6AkSZIkdcT/D99N67/ffzYbAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1080x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "kappa_samples_2k = my_kappa(sample_num,student_id)\n",
    "plt.figure(figsize=(15,6))\n",
    "plt.xlabel('Value',fontsize=15)\n",
    "plt.ylabel('Frequency',fontsize=15)\n",
    "plt.title('my_kappa Distribution, sample_num = 1, sample_size = 2K ',fontsize=15)\n",
    "hist_2k = plt.hist(kappa_samples_2k, bins = 25, color = \"#96C6FE\",edgecolor = \"black\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color=#2480B6><font>\n",
    "## **B) Now, plot the histogram of the sample means you've calculate in problem 1 part E.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15,6))\n",
    "plt.xlabel('Mean Sample',fontsize=15)\n",
    "plt.ylabel('Frequency',fontsize=15)\n",
    "plt.title('Sample Means Distribution (2k_100)',fontsize=15)\n",
    "\n",
    "hist_means_2k_100 = plt.hist(means_2k_100,bins=25, color = \"#C7BBF7\",edgecolor = \"black\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color=#2480B6><font>\n",
    "## **C) Considering the 2000 realizations of the sample means distribution you've calculated in problem 1 part E, compute their mean and standard deviation.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean of 2K sample means distribution is:     0.008294934038888329\n",
      "The population mean estimation absolute error is:    0.008710274038888329\n",
      "\n"
     ]
    }
   ],
   "source": [
    "mean_2k_100 = np.mean(means_2k_100)\n",
    "print(\"The mean of 2K sample means distribution is:    \",mean_2k_100)\n",
    "pop_mean_abs_error = abs(true_pop_mean - mean_2k_100)\n",
    "print(f\"The population mean estimation absolute error is:    {pop_mean_abs_error}\\n\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "The variance of 2K sample means distribution is:     0.20450496237163424\n",
      "\n",
      "The estimation for the population variance based on 2000 samples with 100 size is:    20.460726600463655\n",
      "\n",
      "The population variance estimation relative error is:    1.1830309347162975 % \n",
      "\n",
      "\n",
      "\n",
      "\n",
      "The std of 2K sample means distribution is:     0.4522222488684455\n",
      "\n",
      "The estimation for the population std based on 2000 sample's with 100 size is:    4.522222488684455\n",
      "\n",
      "The population std estimation relative error is:    0.565346216964386 % \n",
      "\n",
      "nThe Ratio of std of population and std of sample means is:      9.943783197867715 that we expected it to be close to 10.0\n"
     ]
    }
   ],
   "source": [
    "var_means_2k_100 = np.var(means_2k_100)\n",
    "pop_var_estimation = np.var(means_2k_100,ddof=1)*sample_size\n",
    "pop_var_rel_error = abs(true_pop_var - pop_var_estimation)/true_pop_var\n",
    "\n",
    "\n",
    "print(\"\\nThe variance of 2K sample means distribution is:    \",var_means_2k_100)\n",
    "print(f\"\\nThe estimation for the population variance based on {sample_num} samples with {sample_size} size is:    {pop_var_estimation}\")\n",
    "print(f\"\\nThe population variance estimation relative error is:    {pop_var_rel_error*100} % \\n\\n\\n\")\n",
    "\n",
    "std_means_2k_100 = np.sqrt(var_means_2k_100)\n",
    "pop_std_estimation = 10* std_means_2k_100\n",
    "pop_std_rel_error = abs(true_pop_std - pop_std_estimation)/true_pop_std\n",
    "\n",
    "print(\"\\nThe std of 2K sample means distribution is:    \",std_means_2k_100)\n",
    "print(f\"\\nThe estimation for the population std based on {sample_num} sample's with {sample_size} size is:    {pop_std_estimation}\")\n",
    "print(f\"\\nThe population std estimation relative error is:    {pop_std_rel_error*100} % \")\n",
    "print(f\"\\nnThe Ratio of std of population and std of sample means is:      {true_pop_std/std_means_2k_100} that we expected it to be close to {np.sqrt(sample_size)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style = \"font-family:Times;\">\n",
    "    <font size=\"4\">\n",
    "        The <b>2000 realizations</b> of the sample means are <b>i.i.d random variables</b> themselves as they are computed from 2000 i.i.d samples, therefore they can be considered as i.i.d samples from a population themselves but with a <b>much lower deviation</b> (because the mean operator has affected them and now these sample means are much more closer to the true population mean than 2000 i.i.d samples drawn from the main distribution. In fact the <b> standard deviation of the sample means are reduced by a factor of $\\mathbf{\\sqrt{n} = 10}$ </b>compared to the main distribtion.)<br><br> We can now compare the true population derived in Part 1 with this estimation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color=#2480B6><font>\n",
    "## **D) Answer the following questions.**\n",
    "<font color=#000000><font>\n",
    "\n",
    "- #### $\\textbf{Q1) What do you think is the main characteristic of the second histogram?}$\n",
    "<p style = \"font-family:Times;\">\n",
    "    <font size=\"3\">\n",
    "It's tending towards Normal Distibution as CLT issues.<br>Applying an operator, based on summation on i.i.d samples of any arbitrary distribution will generate a Normal distribution because of the fact that summing random variables result in convolving their pdf(pmf)'s and by convolving same distributions that are independent from one another we obtain a gaussian function that's interpreted as a random variable(statistics) with a normal distribution (the MGF will look uniform like a white noise spectrum) <br><br>\n",
    "\n",
    "\n",
    "- $\\textbf{Q2) Interpret the results of part C. Do these results have any association with your estimation of the mean of my_kappa distribution?}\\\\ \\textbf{Explain.}$<br><br>\n",
    "\n",
    ">Each of the <b>Sample Means</b> are an <b>Estimation</b> for the <b>Population Mean</b> as each sample is a representative for the whole population.(The <b>Accuracy</b> of this Estimation <b>grows with increasing the Sample Size</b>). As the samples are drawn randomally, <b>Sample Means are in fact \"Random Variables\"</b> and have a distribtion.<br><br>According to the <b>\"Central Limit Theorem\"</b>, As <b> n (number of samples) increases</b> in a sampling procedure, the distibution of Sample Means in a population <b> tends toward a normal distribution</b> with the <b>average of population mean</b> (as a result of <b>Unbiasness</b>) and \"std = sample_std\", even though the original random variables dont have a normal distribution. (in our case they have kappa distribution)<br><br><b>The Effect of a larger n on the similarity</b> of our histogram to a <b>normal distibution</b> is demonstraed by an idea in Statistics called the <b>\"Weak Law of Large Numbers\"</b>.It calims that by <b>increasing  the amount of n</b> (sample size or the times any stochastic trial thats repeated) the <b>result of a repeated trial converges to the expected value we considered for it</b> using our prior beliefs or a probabilistic model.<br><font color=#CF3A69><font><b>In this Case the larger our sample number gets, our histogram converges to the normal distribution we expected from CLT.</b><br><br><font color=#000000><font>Dividing a Population to a set of enough Samples with sufficently large size to Demonstrate a good Approximation (Estimation) of the Population Mean using the conclusions of CLT is the key idea of the Sampling Procedure and benefits of a Good Sampling.\n",
    "\n",
    "\n",
    "#### Comparing the two histograms(A,B):\n",
    "\n",
    "<p style = \"font-family:Times;\">\n",
    "<font size=\"3\">\n",
    "In the Distribution for part A, we have drawn one sample with the size of 2000 from our distribution. The histogram of these values should represent our main random variable distribution(my_kappa), and doesn't have the conditions for applying CLT (no sample means are calaculaeted and the only mean calculated is the mean of our only sample), so the term sample mean is a definitive value not a random variable and we dont expect the distribution of that one and only sample to be normal but we excpect it to model our main distribution.<br><br>In Contrast,the Distribution derived for part B, represents how the sample means for each sample are distributed along the population mean as their average. The conditions of CLT theorem are completely satisfied in this case as the stochastic we are using (sample mean) has a sum-based definition and our samples are i.i.d, it will that tend to a normal distribution by increasing the sample numbers (n),as a result of convolving i.i.d RV pdf's.\n",
    "   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color=#CF3A69><font>\n",
    "# Problem #3 - Confidence Interval\n",
    "\n",
    "<font color=#2480B6><font>\n",
    "### **A) Construct a 95% confidence interval on the sample means of my_kappa distribution. Your result, obviously, consists of two numbers: a lower bound and an upper bound of the calculated interval.**\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lower Interval Bound: -0.878044386750974 Upper Interval Bound: 0.8946342548287507\n"
     ]
    }
   ],
   "source": [
    "low,m, up = mean_confidence_interval(means_2k_100,0.95)\n",
    "print(\"Lower Interval Bound:\",low,\"Upper Interval Bound:\",up)"
   ]
  },
  {
   "attachments": {
    "Confidence%20interval.jpg": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style = \"font-family:Times;\">\n",
    "    <font size=\"3\"><br>In the figure below, 95% confidence interval for a standard normal cdf is illustrated.\n",
    "        \n",
    "![Confidence%20interval.jpg](attachment:Confidence%20interval.jpg)\n",
    "        \n",
    "<p style = \"font-family:Times;\">\n",
    "    <font size=\"3\"><br>What we do in Calculating Confidence intervals for a given estimator and data is summarized in the following steps:<br>- 1) Obtaining the corresponding z-score value for the significance level <br>- 2) Multipying the sample mean std which acts as the true population std divided by $\\mathit{\\sqrt{n}}$ <br>3) Adding and subtracting the result "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color=#2480B6><font>\n",
    "### **B) What does this interval mean?**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style = \"font-family:Times;\">\n",
    "    <font size=\"3\">A confidence interval (a,b) with a certain level of confidence (c) is an interval that includes the true parameter we are estimating with a chance of c percent. In other words this definition implies thats there is (1-c) probability that the interval we've constructed doesnt include the true parameter (in our case the true population mean).<br><br>This interval is symmetric relative to the estimated value we have found \n",
    "(The estimated value always lies in the middle of the interval)\n",
    "        <br> What confidence interval calculations imply is that we convert any approximately normal shaped distribution derived from our estimator to a standard normal and use cdf values related to the standard normal to obtain an alpha-level confident interval beside the estimation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color=#CF3A69><font>\n",
    "# Problem #4 - Estimating The Parameters of Some Observations\n",
    "<font color=#2480B6><font>\n",
    "#### **A) Draw 100 samples from my_omicron distribution. After observing each realization, calculate the sample mean of the realizations you've observed so far. In addition to that, construct a confidence interval for your estimation at 0.1 significane level. Finally, plot your estimations in a bar plot alongside their confidence errors as whisckers of each bar. Your final plot should be similar to this:**<br><br><br>\n",
    "\n",
    "<img src=\"https://support.content.office.net/en-us/media/68efe29e-f30c-4c6f-95cf-9cff7dde1131.jpg\" width=\"400px\" alt=\"no internet connection!\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "student_id = 810196607\n",
    "n_sample = 100\n",
    "significance_level = 0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "omicron_samples = []\n",
    "omicron_means = []\n",
    "intervals = []\n",
    "middle = []\n",
    "for i in range(n_sample):\n",
    "    omicron_samples.append(my_omicron(student_id))\n",
    "    omicron_means.append(np.mean(omicron_samples))\n",
    "    l,m,u = mean_confidence_interval(omicron_means,1-significance_level)\n",
    "    middle.append(m)\n",
    "    intervals.append([m-l,u-m])\n",
    "    \n",
    "intervals = np.transpose(np.array(intervals))\n",
    "\n",
    "plt.figure(figsize = (20,10))\n",
    "plt.errorbar(range(0,100),middle, yerr=intervals, xerr = None,fmt = 'o-', capsize=3, capthick =2, color ='#AFB5EC' , ecolor= '#D6D6D6')\n",
    "plt.ylim(-10,15)\n",
    "plt.xlabel('Omicron Distribution Samples')\n",
    "plt.ylabel('Sample Means (Cumulative) Alongside Confidence Errors')\n",
    "plt.title('Converegence of Sample means towards final Estimated mean')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color=#2480B6><font>\n",
    "#### **B) How is your estimation changing over time? How is your confidence interval changing? Explain why.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style = \"font-family:Times;\">\n",
    "    <font size=\"3\">The repeated trial of calculating means and using them as an estimator of the population mean oveer iterations, shows us how the estiamtor converges to true population parameter as n grows.Also the Confidence Interval width's are decresing as we go further in sample size and this is cause the intervals include the term of $\\mathit{\\frac{\\sigma}{n}}$ in their calculation that tends to zero and decreases the interval width alongside the x-axis."
   ]
  }
 ],
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