tutorials/abigail_bootjack/boot_jack_solutions.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "apparent-baking",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.font_manager as font_manager\n",
    "%matplotlib inline\n",
    "font_prop = font_manager.FontProperties(size=16)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "offensive-slovakia",
   "metadata": {},
   "source": [
    "# Problem 1: A simple resampling example"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "thick-police",
   "metadata": {},
   "source": [
    "## 1a. Generate a random sample from a normal distribution, of 14 numbers, with a mean of 10 and a scale somewhere between 1 and 5. Call this array `star`.\n",
    "Think of this like the apparent magnitude of a nearby star that has a true apparent magnitude of 10, but we suspect that there's some variable dust component between us and the star, so we took a measurement every night for 14 days (two weeks)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "rational-scroll",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 9.97058069 11.4076584   9.90586506 10.94627636 12.98625071  9.97822775\n",
      " 12.32547381  9.15909382 13.57492281 10.32316197  9.498954   10.31809939\n",
      "  8.65893732  9.89578532]\n",
      "10.639234815927145\n"
     ]
    }
   ],
   "source": [
    "star = np.random.normal(loc=10, scale=2, size=14)\n",
    "print(star)\n",
    "print(np.mean(star))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "infrared-mailman",
   "metadata": {},
   "source": [
    "This isn't enough data that we feel comfortable just averaging the magnitudes and computing an error from the distribution, but the star now is not visible from the telescope, so this data is all we have to work with. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "secure-asset",
   "metadata": {},
   "source": [
    "## 1b. Resample the data 5 times, with replacement, to get 5 different arrays of the same length as `star`, and calculate the mean of each resample.\n",
    "Call your array of the mean of each resample `boots`. Hint: look up the documentation for `np.random.choice`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "pending-vacation",
   "metadata": {},
   "outputs": [],
   "source": [
    "boots = np.asarray([])\n",
    "for i in range(5):\n",
    "    temp = np.random.choice(star, size=len(star), replace=True)\n",
    "    boots = np.append(boots, np.mean(temp))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "distant-cinema",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[10.95636345 10.61977884 11.30538136 11.15618145 10.86080616]\n"
     ]
    }
   ],
   "source": [
    "print(boots)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "caroline-twelve",
   "metadata": {},
   "source": [
    "## 1c. Make and plot a histogram of the bootstrap means.  \n",
    "Also plot a vertical line at 10, the true magnitude of the star, and at the mean of your original data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "sufficient-radar",
   "metadata": {},
   "outputs": [
    {
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d+yU5dqtjw4B1X9fbNWnLxRfMrQq4JGv7In+d5OEDfV9P8uNJrt/dv9nd/9LdH+/ur3b3Gd396e7+7+7+4+6+e5Kjk7x1YKwrJvn3qrrRlOuH3VnbSbr7Q0l+a8Ill89o7X+gqp5YVd9bVdeuqkOr6jpV9X1V9ZQkH0ny/5IcssfHn5HkCwNjf2u79QMXsxO+ru2E/68AwMqrqu9L8soMf0/+jyQP7O5pH2cGzEB3n9vdp268lvZP3f3YJDfKxg1MEz700UmOm0OJK0UwA9bPWRP69nwxc7smjXfmlOfaV5Oe/y5/OYV5Jp2bfY8pjA+7W/d1vWVVdWBGv9Ad5+sZ/aAJi2JtJ6mqn0nykwPd709ydHf/w74eP9bd709y9yT/d+CSKyZ5UVUdsOliYd9Y2xu6+0+TPHsvl90syVOS/HeSz2QUuDglyX8meWKSG475mAuS/ESGd8b42hbKBYbthK9rC/+aBgCrrqpuk+S1SQ4euORdSX6wuwWhYYn1yJuTfE9Gu2MMeUJVfe+cyloJghmwfr4+oe+wKc81abxJdczS3l6EPbW7P7DdSbr7lCSfHOi+zXbHhz2s+7rejh9KcoWBvr/v7n3ZZQdmZe3XdlVdOcMBii8mOaa7P7/Zcbv7gu5+TJKh825vneSXNzsu7KO1X9u76+5fTfLUJFs9RnBP5yX5ie5+dZIrDVzzpSnNBYzshK9rO+JrGgCsqqq6eZJ/zfD34hOT3Lu7hSVhRXT3+d39uCRPG7hk/yRPn2NJS08wA9bPaRndQTbOlac816Txdmow411TnGtorKtU1aFTnAdOy3qv6+1wjAk72Wmxtn8hw3fG/lp3Dx1TsK8eneH/G/yqXTOYkdNibV9Mdz8xyQ8m+dw2h/pskrt094ur6nIZftF404EuYKJJX0/m9XVtx3xNA4BVU1U3SfLGjI4bHOfDSe7R3d+YX1XAHD0xybsH+r5/Yzcd9oFgBqyZ7r4woztMx7nqlKcbGu/8LOgutY3E7mkTLvnUFKc7eULfNac4D2tu3df1VlXVUUnuOtD9ju7+8DzrgT1Z20mSnx5o/2iSf9ru4Bv/LxjakeNaGR15AlNlbY/X3a9NcuMkv5HRkSWb8bWMzra9SXf/10bb9SZc/5FNFwhMMilUNa+va9sNdgEAY1TVDZK8KcPhyJOS3L27HRcIK6q7O8lvTbjkfvOqZdkJZsB6+vRA+1FTnmdovM919/lTnmszJoUvppnqPW1Cnx0zmLZ1X9db8dNJaqDPbhnsFGu7tjde/LnGQPe/bPxQOA3HT+i705TmgD2t7dqepLu/2d3PzKju2yd5UpLXJPlYktMzCpScl1EQ491J/jLJA5Jcs7uf3N3f3G24W0yYSjADpmvoa1oyxa9rG0ecDZ1pP82bLACAJFV13SRvTnK1gUs+leSu3f3l+VUFLMh/JvnKQN8d51nIMrM1L6ynkzL+C+X1qmq/jbv4puH6A+2fmNL4W/XxJLca6DtrivNMOk/v0lOcBxLrelOqav8kDx/oPjPJS+dXDUy0zmv71hP6/nNak3T3h6vq60muMKb7ltOaB/awzmt7rzaCV+/YeGzV0NeQD3f3GdsYF7ikzyb5dsb/nHvDKc4z9DUt2eFf1wBg2VTVdTIKZQzt/PzZjEIZ2z1iFFgC3X1hVb09yQ+P6Z72TSYry44ZsJ5OHGg/KMmNpjFBVR2S4e2D3zeNObbhfyb0TXMni0ljnTPFeSCxrjfr3hm+E/8fu/vseRYDE5w40L4Oa/tKE/qmfTfOUOJ/Ug2wHScOtK/D2p6XOw+0v2WeRcA66O4LknxwoHvS7jWbdfSEvnX4ugYAc1FV18golHGdgUu+mFEoY7NHEALLbehI1CvOtYolJpgB6+m9E/puM6U5bp3hrzEnTGmOrXrPhL4jpjjP5Sb0nT7FeSCxrjfrkRP6nj+3KmDv1nltHz6hb9rfR0/bQg2wHeu8tmeuqo5McpOB7n+dYymwToa+rt28qg6c0hzfM9B+VkY7EQEA21RVV80olHHdgUu+klEo4+T5VQXsEEM7zl9qrlUsMcEMWE8nZPiYjbtOaY6hcTrJf0xpjq16Z5JvDvQN3VW4FZPG+twU54HEut5nGz9gHjPQ/f7unvTLMpi3dV7b503om3Zg4oiBdjtcMSvrvLbn4cED7f8bwQyYlbcOtB+U5HunNMddBtrfNsUjoABgbVXVlZK8KcNHkX0tyd26++PzqwrYQa480D4U2GAPghmwhrr7/Ay/aHLvqtp/CtNM+qXnqVMYf8u6+9sZfv63neJUtxto/0x3f2uK88Dar+tNeniSAwb6XjDHOmCv1nxt/++EvqtOea6h8SbVAFu25mt7pqpqvyQ/O9D90u6eFPoCtu5NSYbCEUNfj/ZZVd0sw9up/9t2xweAdVdVl0/y70m+a+CS/01y9+7+8PyqAnaYaw+0f36uVSwxwQxYX68caL9KtnmXXlXdKKOtk8f55+2MPUUvH2i/UlUdvd3Bq+q6Gd7u7Z3bHR8GrPu63lc/NdB+TpJ/mGchsI/WdW1/ekLf901rkqr67iSX30INsF3rurZn7SFJjhrTfmGSZ823FFgf3f21JG8f6H7wRmhqOx46NHWGv54CAPugqg7PKOh484FLTk/yA939/vlVBewkVXXZDL8e99F51rLMBDNgfb08ydCuDb+8zbF/aaC9k7xom2NPyz8lOXug71FTGP/nJ/S9bgrjwzjrvq73qqrunOQGA90v7+7T5lYM7Lt1XdsnTui7X1XVlOa5/4S+/5nSHDDOuq7tmamqQ5L8/kD3K7v7pHnWA2vo7wfar5XkAVsdtKouk+SRA91v6+7PbnVsAFh3VXVokjdkONh9ZpJ7dvcJ86sK2IEemNExheOs+nGpUyOYAWuqu8/M8J3hx1TVls6Araojk/z0QPe/dveOuPO0u89K8sKB7h/feB5bUlVXy/CLRt9McvxWx4ZJ1n1d76OhtZkkz59bFbAJ67q2N+68/eBA902S/PB259i4K+jXJlzylu3OAUPWdW3P2J9l/Naq5yZ57JxrgXX0kiTfGOh78jaOafrVJFcc6HvuFscEgLVXVQcneU2Gj+Q+O8l9uvtd86sK2Gk2AlxDN0FcmOTVcyxnqQlmwHr7o4w/A7aS/OXGXSn7bOPO1edlODX3B5sr7zvjHllVPfB461bG3PCMJOPOmL5skr/exlarz09yxEDfC92Rz4yt+7qeNOcRGf5F7knd/bZZzAtTsq5r+2UT+v5kIwy5Hc/N8DEmH+vuD2xzfNibdV3bU1dVv5vkJwe6n9HdJ8+zHtjpZrGuN26AeM5A902TPG4Ldd4oyRMGuk/O8DGlsJaW4Xs2sHmzWNtVdekkr0pyx4FLvpnkmO4eOqoM2IZpr+uquvIMytz1teLFSa4+cMlruvsLs5h7FQlmwBrr7k9k+A7x707yd5u8o+WZSe4x0PeanfZLz+7+TIbPmb5Lkhdu5vnXyF8kOWbgkrOTPHVTRcImrfu63ouHZfgXVX81z0Jgs9Z4bT8vw0c9XDPJa6pq6AfDQVW1f1U9K8lDJlz2J5sdFzZrjdd2kqSqbrVxTu12xrh0VT0nyZMHLnnXhD5g+v44yVcG+o6rqh/a14Gq6ioZ3X039HXisd19wSbrA4C1V1WXyuio76GfHc5Jcr/udjwBLI8PVNWfV9W1pjXgxmtu/5LkvgOXXJDkd6c13zo4YNEFwCqrqgOz/QDUAVU19IvEPZ3b3ePuuJvk8UmOTXKVMX0PTPKGqvrJ7v7i0AAbd6E/J8mPDVxydpJf2WRd83Jckh9Kcr0xfQ9LcrWq+oXu/vikQarqqCT/L8OhjCR53KTPI8vBuv6Onbyuhwxt635eho82Yk1Y29+xo9Z2d59aVX+U4R/ybpXkxKr6lSQv25dfzlTV0Un+NMn3T7jsw0n+ZpPlsgNZ29+xo9b2bh6d5Eeq6u+S/GOSd+7r529jd7tjkzwtyY0HLvtykgd19/lTqJUdYhnW9Uag6lL7ePlQ+Ko2UeMF3T1uN8i56+7Tq+oxGX9U0/5JXlpVT0jyzEnft6vqdhndmXfUwCWv7+5/3nbB7BjW9lg7Zm0ny/F3xM6zDP9u1m1tbzzff0jygwOXnJfRTQz/tYnntK8u7O5zpzwmc2Zdj7UTvmcflOTnk/x0Vb0ho53lju/u0zc7UFVdNckjMtrx7tAJlz6ju9+/lWLXVXX3omuAlbWx3dCd5jjlXbr7rZv9oKq6W5J/y/A3028m+duM7lT5YJIzkhyS0fnu98nol51D24AnyY9399D52ftS35FJhs7C/o/uvvNWx94Y/+gk/51kaKvo8zLa1u3VSU7M6O6fC5NcNaM7Ge+XUbhj0jfpl3f3j2ynTnYG6/o7dvS6HjPfbZK8Z6D7Fd09dMQJa8La/o4dt7Y3tkx8e5Lb7OXST2d0x8/bknwiyf8mOTfJ5TLabvEOSe6d5K57GeecJN/X3SdstlZ2Hmv7O3bc2t4Y9wW5eHDyqxl9Hv4nyfuTfC7JaRkFSw7K6P/fN84oWPVDSSbdCXRGkjt39/u2Uhs71zKs66p6eOYb8Hthdz98Mx8wh5+z/zbDxwslyccz2jHoLUlOyejn7isl+Z6Mfhl0v4yOdRrni0lu2d2nbqdGdhZre6wdtbaX4e+InWcZ/t2s29rey1izNvXX/Jg/63qshX/PrqrTkhy+R/O5SU7I6PdaJyb5aEavl52+8dg/o+DF4UlukOToJLfPaEf5ve3e+bok93cjxObYMQNId7+pqn4ho3PWxzk4o7vZHr2F4Z+6nReB56G7T6yqB2WUIDxwzCWXSvIjG4+teHOSH9/ix8KWrPu6HuORE/qGtpCHHWcd13Z3f7uqjk3y1iTXn3DpUUl+a+OxVecneZhQBvO2jmt7wJWSPHTjsR1fTnLv7j5x2xUBW/XzSa6d0Yu649woo2NPNuv0jLZWF8oAAIDJDkzyvRuPaTo+yYOFMjZvu1vNACuiu/8iyc9l9Au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Tijd/Ux1YU8tmuvu/zexc4P0liw8kSvN3xN3nmNmvKf9h9wDg553G6sCUxPyT3H1ep0HM7FvEkAsprxAdHX8k3lB/AniG6NBfjijPvXMxlXXorg78wcw2d/eZnbarD5MpT8C5hkiOuYYYI/1pYCGiA+dtRCKHV9zWv4h/953F9AjwPPAc8e9dghhGYRLxRvcupBNcdiUqH3yrYhteZWbvB9q9kfoK8cP1GcQwD48BLxEdpKsS++n9wIq91lmYKAldVlGma0VH/29o39F/CzEE0FXAQ8Sx5cSx9aZe7S2rDDIWOMPMNnH3ezI2PbcngGuJ4+cOInnq+WKaRxxDywIbAVsCe5AeQmQT4IfEUDs5LQccw/z76hHi2Dif2D9PEm9+rkSUjN+bdCfJOOLc38DdH8vUTgNOYf5S+9OBs4nj/l5iSKLxxHG+CfBhIrEl5ftmdpe7X5KpnTOI69AdxH7/B69dN2YRx/OSRPLaJsS1KTUcy5JEB/Qkdy9LIuzWWGLftp5bTwF/IPb5P4l9PpNIingTsd+TQ8AM0fN+GaJSTOvwW38hvos/Ag8T38VY4nq6NXFcpZKPFiE6z1JDq41EhzH/9/Ekce85nzh3nyDuocsTHe77E/fvMpsSlTd+UlQRO5P5h8u5BTgHuIK4LjxDHFdrADsSw0UtkYj/PTM7192f7ehf17fniOtCz73gfl67Lswp2rE0sAFRvewDxHlXZg3g19Q4vorqA7+jfVLuncR19XLieeIZIiluReCdwJ7AW1vW+RExlFvTfsz8SRnPEvv7QuAu4viaRdxj1yMqEe1D+t98hJmd4+73NdJi6UqR1HUWsFqbj00j7j3nEfeVJ4jzp+dY3Zt4zurts8R1J2dbFyfOlze3+diTxL3lCuI+8wzwInFurQS8izi33pJY/6Nmdr+7d/33hIiIiPQjd9ekSZMmTZo0adKkaVhOxBAeXjI9AFib9XZOrOfAJhXbsH6bWOtk+ndOSsSfB6xRIc7ebdrqwK+ANTuMtR7xA2Mq1o+7+HdOS8Sa0/L/twJbdhhzoTbL/lrEu4/oQNqwizYvCxxLJEiUtX0WsHqX+315otMh9R3fAmzUyXcAfAN4uWX95xNxD+uireu0iedEsss2HcZaBvhpm1i3A6NynFt1J6JDwInEoO8CWwALVIyxGDGeeOv+6T1t3mX7pibite6rOcDhwOg+4hnwX0TyT6qtF3XRzikdttOJTsNlO4j5LtLXFCc6bZfsoq2HFOvPLL7fXYFxFWOMIq7Hj7dp35e63Oep77L1OjoLOApYpIOYpddRBvl53+b4f7Hl/x8APtBhzH2LfZ9q5zs6iDGGSPjomT6WiHVyy+f6nLo5ZupMRMdpWdtnAnNbjr8+jzdeu8ak7qmPEZ3sZ7XMvx/YtYP2LksMhZHaf0d0+T38uFj/OeB/iYSmttfTkhhjgYP6OKf27rJ9RrzRn4r7GPDBDmOVXbtSbb6yYju3ScRpPWfnAN8Blugg5trAbW3+7Sd2+Z1OS8RbrY/1Fmo5b49MxDmSaud/8nm3TnsrfB9TEvGndhHrsDb762ViaJI+7wfAh4jkw3bHUs80rcvz6sI2bf03cT3r8xmhiDW5pL090ytU/BtVkyZNmjRp0jQwk4YyEREREZFhqRi3/AOJxb9yd2+z+kXEm1VlUkOjlHL3vxCJAmWmVInVRirOVe5+fycBzGxF4CeJxTOAfdx9f3fv6E0yd/8r0fEwNfGR/zSz1FuvVfWuBPgHYDN3v7aTFd395TaLbybeXF/b3Q9z99urNszdn3T3/wbeTXyPrRYCvlw1buHbpN/sPQfY1N1v66CNL7v714H3Ep2xPXKUf6coLT+1TbzvAVu7+5WdxHP3p9z9E0SViFdKPjKRGF9+MLib6FRd1d0PdffrvEIFGwB3f8HdDycqKZQNjQSRWJNT7301G3ivu3/N3ee0W8nDccTb3c8lPrZDMbRFDq3H1NfcfU93f7KvFd39MuJN9NR5vQKRjFLV08V6q7j7FHc/xytWB3L3ue5+GvGG7Y2Jj33ezBbton0pva+jM4Cd3P0r7j69rxXLrqND/LzvXSnjJmBjd/9dJyu6+ynAbkRiZJmPdBBjtrvP6pmITuYyr/T+XCdTJ/+GfjKW16qozAR27+R463WN+WziI8sTSaS79Zp3M9FheU5fjSquHe8jEhvL7G9m1lecEg8RSVsru/tB7n5pX9fTkrbNcvf/JRJ+U89ih3XZvsmkqwjdC0xy99M7CVRcuyYRyTA9sjxPtNH7nJ0O7OLuX3D35/pa0d3/AWxHJOOW+UDma21f7Xm55Zydm/jo3Irnf7vn3SGjqOzyxcTiWcC73f0Id099b69y998QVTMe6jW7tVJSHZ8E3pNYdjtxXh3XyTNCce07iThPHyj5yALACV2e/yIiItKPlJghIiIiIsPVB5m/hHWPX7Vbsfgx79eJxXubWdWxt09MzN/fzNqVd++TmY0hyqdX2W6Z71Leyf8KsKe7n1qxaT3f44HABSWLFyB/Z/IVwPs9U3l/dz/A3X/n7mWdgFVj/ZEoQ1zmw1V/9DezNYH9EouvBvbq5Efp3tz9ciIRJbcDSZf3/5a7f75qWwHc/QTSSS1fNLPU+d9v3P0Qd/9Fjg4Rd7+TSHYqO77fVRwTTdi3SGLomLv/mRjGJ3UuHtlA58FP3P2IKiu4+/NEQlJZJwfAx81slYoxp7r71909lURTJdazRKfOP0sWT6CZ89WB3YprVh3D4by/G9jO3Z+uspK7Xwz8LLF4z8FwbRpk9nH38yqucyzppNcP9frvacC7quzDopP0k8S50GoVompDJe7+HXc/xt1frLpuSawHgW2J4Q5arU0M09Cx4jn0a4nFTxLnwKMV2/gIkexQ6dzJwIE93P2iSivFtbanMk2rhUknekv/+xqR1NzKgQ+5+1VVgrn7Q0Ty9LMZ2vYqM1sS+GZi8V3AO9099eyR5O7/JJ4Fy64lG5D+W0NEREQGCSVmiIiIiMhwdWBi/rXe2VjRUxPzFwf2qNiWU4nSuq1WJH4MrON9wJIl818kSvr3yczWJUpPl/myu1/YZdtwdycqepT9OL+jma3VbewWM4CPdNPR11+K77HsjdPxRCd2Ff9N+d9zs4GPdpuc4u7nAqd0s24ZMxtNusPnAuArNTdxNHBlyfxlSCcsDVlFcsYPEoub6KT/TaeVAlp5VK1JtXUdYsioXKYBn+tmRXd/guiELTMK+HSXbcqiSB5JVYL4YAOb/Km7X1onwDA572cTnXwvdbn+kZRXzRhHvKEt4ZfuflbVlYpni2P7+hiwn7u/0EX8m4FrEou3qhovN3d/GPhqYnHV68KuwOqJZYcWiSCVufs00pUNmnJ0t9cvd78RuDixeIvumyS5mNnypK/xp3RSFaeMu99N+nzq1ucprxTzErBzJ9VcUoq/Y1PPJgd3G1dERET6hxIzRERERGTYMbN1SJdkPqmTGB5DkKRK3KeSPlKxniWGligzpUqsEqmhVU5397KhM8p8kvK/De4j3bHaseLN8f9NLJ5cN37h2G7ePBsAqe9hu04DmNkoXv9GcG/HFm/T1XEIrx/SpI5dgZVL5s8FPlN0rnWtWD9VeSXXsTXYpIYc6vgY6tBM4NCaMY4EHk8sm1Izdm+HeI1hGoq3q89PLN63bmWjuor2lQ1LtaWZlb053K2ZdD+0Um/D4bw/rUiE6kpRYeDKxOJJ3cYdZuYCX6+x/h9ID/MAcJF3OKxZQiq5dcMaMXOaSnTytqp6L9g3Mf9m+qgw14FfAn0OqZbJC8BRNWOkqsPpnB0c9gbGlMyfQf0koJ8Bf64ZA4DivvyxxOJjvMNhJvtwEuXPBZs3WEFNREREMlBihoiIiIgMR6nEiZnAbyvEmZqYv62ZrValQcSP02V2NbMJFWMBYGYrADskFnc0jEnxZvM+icVHecUx0Nv4CeVvD++YIbYDv8gQpz9cT3QetHpbhRibEm+Gl6n9PRQVBM6tG6cwJTH/1GJc99rc/UrKx4bftNtzazAr3l7+W8miKsdQJ84qSnx3zd2nk76O7tjFsFBlHgYqv3Ff4rjE/GWBrTPEr6usctE4YN2M2zijzlu8vUxJzB9K5/0PM8RIJQVMzBB7ODi7qPzQleJYvbfNR1LndKduTsyfWDNuFkUy2pUli9YohlHoUzEcXuo58heZkqj+r06MCk7spjpKi9Q5u27xvCwD6/2J+WdWHW6nVTFs4fF1YvSyC7BUyfyXgO/l2IC7zyOdqJvjbysRERFpiBIzRERERGRYKd5s3i+x+OyKP9qeCpQlJhjV3/a+lOhAbLUQ6WFE+rIfUPYm9z/c/foOY2wJLFEyfw55OjsBcPcngb+ULJpoZmXbr+LmDoenGXDFD7+PlCx6U4W38lPjx9/s7vd017L51H1LlqLTPfXmbtmQLnX8sWTeggyCkvMNKSstv5iZrZRxG79uOM5Y0pWNqjit6KCo6zLgicSy1DnXn1LDCbwl4zZOqxtgmJz3j7r7HTVjQPrt6+UyxB4OLsgQ4++J+bOByxuKvULNuDmlrgudJmxtSgyn1mo20NUwViV+U8RrWqrqURXTKE+eHU35sIHST8xsYWCTxOJczyu/Jc+xmhqe8AJ3fzFD/B5l90CAbTJuQ0RERDJTYoaIiIiIDDc7kv7RfGqVQO7+NOkfeqeYmVWINY90Z3dqOJK+pEq2d1Qto7BtYv5Vmd6c7q0sWcSAt9aM+6ea6/e3p0vmjSFdBaPVRon5V3XXnGSsWm/KApsRne+tZhCd4DmlEpEmZt7OYFF2DAHkSsyYTSST1ebufyU6u8pslmET52WI0ZM0VVaVAvK0s66m9znkuZYOh/P+mprr90i9wb14pvhDXacJpO2kkqludfeX6wQuEnlnlixaqKg0MRjUvS6knif+XAzDV5u7/5vy6jY5vQLcUDdIUeEjNfyWztuB9TYiQabVy6QTFCopjtUc16XU31apYS279Wdgesn8iZm3IyIiIhmNGugGiIiIiIhklhrG5FG66xSaCuxWMn9V4q3gKjFPBL5cMv9tZrZe0YHZETN7O+VvRL5CtWoHqXGz76wQo1OpTqp1gKtrxL2lxrqVmdkaxFum6xfTqsCivaZuy10vS7pDoLfUG/K3d7nd+bj7i2Z2P/DGGmFSx9Zd7p777dl2x9agY2YrEtUi1icSk9bg9cfQQl2GXjZLA+FvGYcxArgDWK1k/noZYue8Vt2RmF+7nWa2CFHJoee68SaiWlHPPi97a70Tufb5NHd/JkOc4XDeZxluhfI370EdvBCJf+2GIelUWackwD8zxO6JXzbk0uLAU3WDF0OO9L4urA0sxmvXhbIkp050el1o/HmiV7xUEkgOjxZDZ+Wg83ZwSt2Hm3he2abblc1saWDlxOKsf1u5+zwzewJYpGXRamY2poF7roiIiGSgxAwRERERGTbMbBlgp8Tik7ssd38B8eN7WTWDA6iQmOHu95rZNZSXWZ8CHFKhXVMS8y+uOM7ymxPz764Qo1OpTr831IybKuWdTdF5MpkYdmbjhjbTacds6k3Y3G+k/pV6iRnD4djKxszGA/sSx9DWNFPBstvO/VZ3ZIrT407KE9zWqBn3AXd/vmaM3lKdJsuZ2Xh3n1ElWFFVaRdgH2Bn8u2f3nLFzHUdHQ7nfZZKAcBLiflNHAdDzQtFlZq6Uudkrn2Yit/1PjSzUcBewIeBd9N9Mmc7g/F5okm59jfovB2sUs8Ld2TeTt14qWGEXiFfwlhvzzD/s7oBK5KuViYiIiIDSIkZIiIiIjKc7E/6B+6Tugno7nPM7FTg0yWL9zCzJSoO+XEi5YkZ+5rZF919bl8BzGws8KE28TtSdBqmOrB+bmY/7zRWTRNqrp96u7E2M1sA+BhwFLBUU9sp9FklwcwWI/0G7b/zNqd2vNQbg/uY2T41Y3eq7rGVhZntCRwDrNLwprqttNHq4Uxx+oqXGnaqbtwm4q0A3NdpIDPbEPgxURmlSbn2ea7r6HA475/L0Yg2Oh4GbRjLmVA1EPG72odmti1wHOlKFbl0el1YLjF/sD1P9OW5huODztuBlnpeeCTzdurGS90DFwRmVRgFs64JKDFDRERkUGriDR0RERERkYFyQGL+ze5+V424UxPzxxJvv1fxO8rfxlsO2LHDGLsRJfBbPQP8oUJbFgcGwzjpZWXCq2ikA8bMJgCXAz+l+aQM6OxH/3ZvbOZOUKn7vZZVmelvdY+tWsxsrJmdTpz3TSdlQL6OoxczxemROjaXqBm3v9oJFdpqZp8nhlhqOikD8u3zXNfR4XDee5ZWSDtNf8eDah+a2QJm9gPimaLppAzo/LqQeqYYbM8TfRlU+1sakRpKJvexWjfeYLgHwgA//4qIiEiaEjNEREREZFgws7eT/rG7q2oZPdz9DtIl7lPJIKlY04lO2jJTOgyT2uapFccTHiw/2tUt491nlZGqzGwR4FLgHblj19QukSZVfrtbdcdrHwzHVxMl4jtiZgsCZxAl64ea/uroSFV/qRu3iXgdtdXMvgh8l6H3e0uu6+iIPu9FEn4CHDzQjSiReqYYbM8TIqkqMIMtiWgw3ANB90EREZFBS0OZiIiIiMhwcWBi/hzgrGL4jzpOBTYomb+xma3n7lXGzz6R8iSMnc1saXd/OrWima0EvCux+JcV2gCD5++BwVge+jhgUpvlToxDfS3wF+AB4HGinPZ0opMz1dF5CeXD2XRiTptl48lbQWDhmusPhuNrII+trwI79fGZvwPXAH8G7ieOoWeIY2gO6WPo58C+eZpZKvfbx/Myx+sxqNppZtsA3+zjY48BVwK3AfcSZdOfJs7dl4l9Xvbv2g84oU77+slIP+9FXsfMJgMf7+NjDwBXEc8V9xHXiaeJe8Fs0vf+rwJfqdG8VNx21bm6Ufd5QiQl9/W+brzBcA8E3QdFREQGrcHysCAiIiIi0jUzGwd8MLF4NPnHH251IPDZTj/s7leb2b3Ami2LRgP7AD9qs/r+lL+JfWdR2aOKWRU/PyKY2Sakq5fMA44FfuDuD3YZv86b9DPaLFuMvIkZqbLRnRqxx5eZrQx8qc1HTga+6e53dxm/6R/cF8scL3Us1T1G+qud0Edbi/P6ONKdITcA/wNc7u6VE0rMbKiU6h+x571IKzNbmKigk3IBcJi739xl/K7a1UvqmaI/r60inXg5MX/RzNupe+zrHigiIiJtKTFDRERERIaDPRnYH333NbMvuHu7agatpgJHlsw/gPaJGZMT86tWy4D2nfibkh6+JbdX+mk7nfpMYv4sYFd3v6Rm/Andrujuz5vZy5SXdF6SvElIXbezkDq+DiU6sPvDQHVmf5LyfeTAAe5ea3gl6u+bvvRXp1zdkuH92XnYV1u3B9ZLLDsBOMjd6wwX0vQ+z2Ukn/cirfYFlk0s+5q7H1Ezft3rwpOJ+UvWjNtqqFy/pDl1h/d6LjE/93NA3Xipe+BfgE1qxq6iytCWIiIi0o+UmCEiIiIiw0FqGJP+sgywM3BWhXVOAg5n/h8qNzCzDd399tYVzGwLYO2SWLOBX1fYNgDuPsvMngaWLlm8krvfVDXmUGdmCwG7JhZ/KUNSBtTv8HgYeGPJ/LcQP/zmkupk7tRDwNtL5q/i7sP9jcK9EvOPzZCUAfk7zVq9oZ/iPdZQ3Cbi9dXW1D6/hfpJGdD8Ps9lJJ/3Iq1S14VzMiRlQP3rwkOJ+W+pGbdV3ecJaV7TCW1L1Fw/dQ9eqWbc3PFS59TqugeKiIgI1M9WFREREREZUGa2OvCOgW4HFZND3P1h4LLE4ikV55/r7s9U2X4v9yXmr9VlvKFuEjCuZP7zwPF1g5vZokQiTx13JeZPrBn3VWa2COXJH1WMyGPLzFYE1ihZNI/2Je2rKIuf08TM8TZIzH+gZtzVzSzn27Kpdj7l7i/1se5WifnHZEjKgPrnY38Zkee9SCszWxDYLLH425k2U/e60PjzREPxJL+ZifnjM8Wvm0R0f2L+xJpxW21Yc/3UPXARM1u+ZmwREREZBpSYISIiIiJD3YFA7UG2M3ivma1QcZ3U8CP7mNmY3jPMbBzpNy+7Gcakxy2J+e+sEXMoWycx/zJ3T41vXcWmwII1Y9yWmL91zbi9bUn9vxdTx9YWRWWS4Sp1DN3u7o/WDW5ma5EujZ/LW8xsdMZ4qYSHuhVerE3sbnTVTjMbRTpZ5vxaLXrNFpniNG2knvcirVahPNHzGXe/sW5wMxtP/U7k1PPExFxJb2a2OPDWHLGkUanhuhbNFL9ucl7qPpz7eWVizfX/AbyQWDZS/7YSERGRXpSYISIiIiJDlpktAExOLD7X3S33RJTiLStFuyCwf8V/wtnAsyXzlwJ2aZn3fsrHPX4MuLjidnu7OjF/m+LH9JEmVc3i4Uzxc/woe3li/mZmtmaG+FD9WC5zLeWlsRcBtssQf7AaCsdQXxYi0z4yszeTTlqo3TkJ7JQhRs/95L2JxX21c0nKE66ed/fUePMdM7N1gBXrxuknI/W8b9K8xHz9pje4NX0v2Ir6Q1TfQPkz7ULAB2rG7vHBIp50p7/O/1QyQa4hw7asuf6twJyS+WOA7WvGBsDMliJd5aYj7j4PuC6xeLc6sUVERGR40B9xIiIiIjKUbQ+snFj26yY26O7Pk34D+oCKsV4GTkssntJh7F+5+ytVttviQqCsEsRo0kkvw1nqrbtUieeOFW+LVxryJuF64N+JZR+pG9zMlibDj8fu/jjpDu2P1o0/iDV2DBU+kSlOXz6cKc4+ifmzSXdeVLG3meWomvROIFX1KJUM1aPpff6fmeI0bgSf902anZifa4gBacagvy64+yzg0sTiXOdr7eeSEa6/zv/HE/NrV6Uysw2pmVzo7jOIRKIyqeeMqj5E+ryt4uzE/J00nImIiIgoMUNEREREhrJUJ/d04NwGt3tqYv46ZrZ5xVgnJua/p+fHOzNbFdg28bmpFbf3OsXb3GcmFn/VzHKVMB4qyiqYQLrDtop9yTAEhbvPAX6bWHywmaWqE3Tqu5SXX+/G1MT83c2s1luJg1hjx5CZbUf+8dRT9uhieKbXKUrtp5LKLiw6WupahfkrDHXjoMT8p4Gr+lg3tc+XLoY56ZqZLUnFpL9BYGpi/nA+75uUGmJgqX5thVTV5L1gbfJc9yCdyLypme1dJ7CZ7Q9sUieG9Nv5f3ti/lYZYn82QwyA3yfm725mK9UJbGYLki8J8ndA2fPNeOCwTNsQERGRIUqJGSIiIiIyJBWdVbsmFp+VqcMv5XzgucSyShUR3P0WysdNHkV05ENUrih7I/x6d7+7yvYSfpiYv0ybZcPVU4n529QJamZvAI6uE6PFsZQPFzAWOKHb8bbNbAfmr9ZSxynAM4llx5vZIhm3NVikjqFNzKzrhJfiu/pZt+t3YWHgOzVjfIn0W7In1Yzd2zFmNqbblYuEl90Si09197nt1i/uN2X3nFHUL99+POXDWA1mI/G8b9Jjifnr9GsrpKrUvWBVM1ut26BFB/JU8v2meybwUGLZMWbWVaWDoqM853PPSNVf5/+tifnvKJ5hu1JUy/hgt+u3+A3lFUTGUf9Y+xTwlpoxAHD3Z0k/43zEzFLJ9iIiIjICKDFDRERERIaqfUiPWZ2qaJFFMQRJqsrEXma2cMWQqaoZBxQl+lNDiqTWq8Td/0T633OgmX05x3ZamdmCdTqqG5J6Y3BVM0slArVlZmOJjsoJXbeqhbvfBZyeWLwdcErRedMxM9uCeBsxx7AQwKsd1t9ILN4AOL1uRYGUAaz28nfSHQf/0U1AM1uASMp4Y412dWPfGsf924FDEovvA87pulXzWxP4VjcrFmPKH59Y/Arwow5Dpa4dn67cqIKZfQLYq9v1B8oIPe+b9E/KE/FWMLMsHYmSn7s/BTycWNz1dQE4CshWeaaownVUYvEKwGVmtkyVmGa2HPBHMlQJE+5JzH+bmS2RcTu3UZ5guADwP90ELK7Hp5NneBDc/UniebrMh8zsA93ENbP1gMO7bli5I4gKjq1GAWea2bqZtweAmQ21RE4REZERR4kZIiIiIjJUpSpTPAlc1g/bT5V+XhTYs2KsU4A5JfPXJTo2y4ammEF6OItufJZ0ueSjzOynuZIozGyCmR0KPABMyhEzF3e/F7g/sfjHZrZylXjFD6QXUbPiRsLngRcTy/YCru6k087MRpvZF4lx5nsnFb1Uv4lAdHrfkli2I3CFma2SY0PFv+XDZvYn6nV8dc3dXwKuTSw+3MwqjddeVD85Dfhw3bZ1wYDTzKxSKXMzezNRWWhs4iNfc/d5dRvX4rNmlkoEKVVUbrgAWCvxkV+6e+p60OrixPzdzKzyUCRmdjDwk6rrDSIj6rxvUnFNKausBXBk1SQ86VeXJOYfZGbvrhLIwjHAF+o3az4/J10x4c3ArWb2vk4CmdluxLm/dq/ZuZ4nRqJ7KK/SN5qMyQTFdeaMxOKPmdl7q8Qzs2WJ5JzU/bVbRwCzEstOMbN3VQlmZqsT9++sCQ3u/hjw1cTiJYBrzWyPXNszs4lmNhW4PldMERERaYYSM0RERERkyDGzicDExOLf9lV2PpMrgUcTy6oOZ/IU0YlZ5puJ+b939xeqbKePNvwL+Cjlb+UCfBy43cymmFmqUkmSmS1uZnub2W+IN0i/A1RKcuhHJyfmr0QkO3Q0NEHxg+sdwDt6zXbg37Va1xPI/WHgk20+sjmxz84xs/3MbN0iKWYhM1vFzLYys28TP/p/i6jo0ONfwE8ztXMusDfp4X+2BO4ws6+a2dJV4xedstub2Y+Jdv8a2Ljb9maSOoYWA/5YdFz1ycy2ITq4WqsmpIaJyKX3W57jgEvN7EuddACb2UeBG4GlEh+5yt1zVTVqfRv1aDM7pRjqqq3iPL4N2CTxkaeBr1Roy2lA6t7z8+L47uT7W8PMzgR+wOur1zS9z7Maoed9k1LPCLsBN5vZJ83sbWa2rJktbGZjy6Z+bK+E1L1gNHCWmX2skyDFc+8VRBJtb1muC0Wi3D6kEyhWBs4xsxvM7LNmtqGZLVech8ub2UZm9jkzuxE4i3he6jGXLisuyKv75sLE4v8ysyvN7AAz28DMljaz8Ynzv5Nn958n5i9AHK/7Jpa/qkgg2gv4E6+/JpdVj6jM3aeR/ttoDHChmR1hHQxvZmaTieeA3sP1pJLUu3EscG5i2QTg92b2WzPr6t5lZuuY2aFmdgNRtWsy6YRYERERGSQaKR0pIiIiItKwj7RZlqpkkZW7zyuSDFp/JAfY2szWLKovdOpEooOlVeqZPcswJr25+xlm9gXgu4mPrFNs9ztmdjFwHfFD4DPAs0TVj8WLaSmi4sdbidL1G5OplHE/+D7wX0BZ5+5qwDVmdilRnvkm4HFi6IplgTcQQ4nsBqxfsv5xxPfxjpJllbn7KWb2VqJ6RpnRwPuKqVOziA7VHVKbrRArVnC/12JIjIsp/9F4AvEW5FfM7BLi2Or5bp8lOosWJY6tJYg3MDcgjq+3F/MHk5OBL1I+BvxSRAfHTcXnbiCSlWYCSxOl47cGdgU2LVn/D8R3khriKIdvAYfy2ve6ENER8lEzO5XoJH4IeIo4T94AbE907K3XJu6zwP4Z23kW8Vb223vN2wfY0czOIN7+vZdIohtXtHMTovrItqRfVnHgI0XSXEeKY/wkyu9PCxLH90fN7JfAVUW7nie+4+WAjYh9/m6ic6m3h4BjgB922p7BYASe9036OXGdL3sm2BD43w7jZBuqSvrm7lea2R+J54JW44ETiuo4JxKVlv5FVMJaElieuAe8j/Lr1a3EuZVluDl3v8fM9iauq6kksk0pvy+183kiSbV0sxVjjVTHE89lZd5BZ8+U/yKeYZPc/Vozu4CoatRqIeBkMzuI+FvrauJa/TKwDJGM0/P82/oc8Chx/0r9fVHVN4ln1C1Klo0iKlUcaGanA+cBDxIVFScQSRjbEs8BZVXlDiGdoFKJu3txTl1OOgn0A8AHzOw2IvnqOuL54FkisXEMr/1t9QZe+7tqEjGMm4iIiAwxSswQERERkSGleOMrVdL/fne/sR+b82vKEzMAppAuYVvmAuAJooOuLw8QFTuyc/ejzWwu0QmY6sBZFtivmIYdd3/BzD4FtHurf/tiquIqorM7NeRBt75AJGAcnCHWbODD7n6Dmb2nzWcqc/eri5hnE52sZcZSPZFk0HH3V8zsP4hhlVIJSW/n9QkFnbgLOIBIHmrSo8Q17Pe8vjNwDeK6VuXa1mM2sIe7P1i7da/pecv7RiKppccE4GPF1I2vuvsfuljvK8R1ITVEx6rANyrGnA68n/IOpEFvJJ33TXL3B8zsB6ST8GTw+hRxjUolEq0LHF0x5uNEh27WBD13P9fM9gF+xfwJYt042t1/aGbbJpZ39Twx0rj7NWb2O2KfN+0/gL+RPl6rJudMB3YnjvMsimesPYjE1rLhHiESMD5TTJ36FpmHw3T3lyyGLTqb9sMablRMn8u5fRERERl8NJSJiIiIiAw1u1FeyQDad6Rn5+63AXcnFk82s46ft4uy76mS162muntjbxm6+w+AnYm3y0Ykdz+N6h2o7VwH7OruL2eMCcQbee7+GaITus447o8C73b3s4r/T4233fW/wd2vIn7Qv63bGEOFu19NDAGU61y9C9jB3bMMhdMXdz+bqByTo/0zgd3d/coMsV7H3e8DdiE9ZEZV33D3VJn0vtryRNGWFzO15QXiunFzpngDYiSd9w37MvDbgW6EVOPudxPDUc3JFPJR4l7wQKZ4r+PupxMVBabVCDML+G93P7T4/+zPEyPQgUSCb6Pc/RHgg8CMDOGeB3Zx9z9liPU67v4k8E7gH5lC/pJqw5d1zN2fJyp8/BBViRERERnxlJghIiIiIkPNgW2W9WtiRh/bXIkoSV9FJ8OTOHBSxbiVufsFRCniE4BXGtjEvcDXgb80EDsLdz+M6Fiv03HgRAnqdxY/zDbG3X9BvFX/K6p1AE0nKjCsW3Sg9lgi8flnu2pgwd3vITppDyVfZ3pvzwA/YRB0YLr7icSbonX3/e+Bzdz9ofqt6py7/4ToUHyuRph/AFsU15RGFJWStgTuqRHmBWCf4ryv05Y/E5VQ/l4nDvBnYFN3v7xmnEFhJJ33TSkSOD9EVM25b4CbIxW4+yXE2/KP1Ax1FbBJcZ1pjLtfTwzH9g2q3fPnEferDdz9uF7zl0h8vtbzxEji7tOBdxEVFR5reFsXE3/D1EkE/Svx3HJllkaVcPd/AZsR1Si6NYeokvWRhpPeZxdJ1NsQwxDl9gpRke/Qvj4oIiIiA0uJGSIiIiIyZJjZSsSPkmVud/e7+rM9hXbJIO2SSObj7n8H+nqr7PLih8jGuftT7v5xYC3ge0Tp7K7DAbcXcbZw97Xc/fCmkxXqcvcTgLcBvyM6HDpeFbgQ2NzdP+nu/VKu293/5e6TgZWJ8ulnAv/kteSSeUQH9J1EhZb9gJXc/XMl+2JpytU5DnraOcfdjybGO/8sUTa7jmnA/xFJECu6+0Hunustylrc/RxiPPBfUL1s+7XAju6+50CdK+5+BlGC/JdUa/8zxNunG7j77U20rTd3/xswEfhase1OzSaOnTe7e5bkvuJetEnRlqcrrn4fUalk0gDd0xozks77phQVkqYS9+XNiWPsbCLJ8UmiUkGVe5X0kyLZYSIxVNz0iqvfCezr7tsUFQ0a5+7Ti0S1NxAJQScW7ejd9hnEM8bZxHBqaxT3q9bzsLHniZHE3ee6+/eJ4bK2A44CziMSAZ8hnvWyJBe4+3XEdeYHVLv3P04kB2zUH/cwd/+3u+9O3AeqJHs7cC5xrz2qkcaVbTSqqW0MvLfYfp2/D6YTQ2EeDKzs7u9x9zNrN1JEREQaZQ0mg4qIiIiIZGVmG5Eeg/46d7+0P9vTw8w+DUwoWTTL3b/d3+1pipkZ0dm4FTAJeCNRGWQxYCzx4+KLxfQU8ab83cQPxte6e5XO0kHHzNYAdiLedlsXWIrY73OJf/NDxL/3GuACd38wEWccsGDJopnu3kR1kp7tjgJe6fSNQDN7FFihZNGbi9LsWZnZmkRZ6o2BNxHJJUsC44gf0HuOrWeJiit3E8N73Oju9+duTxPMbAVimKBtiGSNpYh/oxM/sD9CVH24Abgw9T2b2ULA6JJFs4q36jttz1RgcsmiA4rO39bPLwfsSnQIrU90Do0HjBhG537iTdCLgHPcfVanbemjnVMoryh0krtPKfn8OGBH4D1ER+iaxHVqAeI69RDRgXMpcEZREr0RZja+aMu2RCWN5Yj9Por4znqulbcClwDXl52jxfk7tmQTc7yBIZL6y0g470VamdkEXrsXTAKWIa4LCxD3gseJ68JNwEWp5DYzGwOMKVk0u8mE0J6h+ty9oyQgMzuNSO5o9Z/u/tOcbRsszGwasGrJotXdfVr/tqYeM1uaGIpjB+Lev3QxGVER7D7gDiJJ4JL+SkYuY2abE38rbgasTTynL0icV49R/E1CPKM0MhxQFWa2KPFMtSnwVuKYWR5YmHjOe4m4B74APEg8I95NfN9/qvLMJyIiIoODEjNERERERETkdcxsVcrHl58NLKwfgoeHqokZiRiVOui6UTUxo02cUTp2RUT6l5k9QFTKabW1u1/Tz80RERERERkwowa6ASIiIiIiIjLo7JGYf5s6tqW3JhMyctOxKyLSv8xsQ8qTMuYSQ9yJiIiIiIwYCwx0A0RERERERGTwKCogfCqx+Ir+bIuIiIgMaZ9OzL/Z3af3a0tERERERAaYEjNERERERESkt08AaySW/b4/GyIiIiJDk5lNBPZOLNbzhIiIiIiMOErMEBEREREREQDMbAPgmMTiv7r7rf3ZHhERERl6zGxR4HRgTMni2cCp/dsiEREREZGBp8QMERERERGRIczMvmFmW2WI807gj8DYxEe+U3cbIiIiMjiZ2WQz29fMFqwZZ1XgGmDtxEdOdvfH6mxDRERERGQoUmKGiIiIiIjI0LYdcLWZXWNmU8xsiSorm9nKZnYscDGwVOJjN6O3W0VERIaztYCTgX+a2aFmtlqVlc1sETP7HHArsEHiYy8CX6/VShERERGRIWrUQDdAREREREREstiymH5mZlcCNxGdI/cBzwLPA+OAJYHlgU2BrYHtgdFt4r4EHOju8xpruYiIiAwWqxNVsr5jZjcD1xHPE38HngGeI172W5JI6NyIeJ54DzChj9ifdvdHmmm2iIiIiMjgpsQMERERERGR4WUM8O5iqmsusJ+7/zVDLBERERlaNi6mHI5x9xMzxRIRERERGXI0lImIiIiIiIiUeRHYw93PGuiGiIiIyJDlwOHufshAN0REREREZCCpYoaIiIiIiIi0uhz4uLvfO9ANERERkSHrXuAgd79koBsiIiIiIjLQVDFDRERERERkaNsPOBS4CZhXI85c4HxgB3ffTkkZIiIiI8oxwIHEs8CsmrFuAz4GvEVJGSIiIiIiQRUzREREREREhjB3fwA4GjjazBYD3g5sCqwFrAqsDCwKjAfGEgkYM4AngQeBvxBJHZe4+7P9/g8QERGRAVc8A5wInGhmY4ANgc2AdYnniVWAJYnniXHEECUzgX8DDwF3AbcQzxPT+rv9IiIiIiKDnbn7QLdBREREREREREREREREREREZFjSUCYiIiIiIiIiIiIiIiIiIiIiDVFihoiIiIiIiIiIiIiIiIiIiEhDlJghIiIiIiIiIiIiIiIiIiIi0hAlZoiIiIiIiIiIiIiIiIiIiIg0RIkZIiIiIiIiIiIiIiIiIiIiIg1RYoaIiIiIiIiIiIiIiIiIiIhIQ5SYISIiIiIiIiIiIiIiIiIiItIQJWaIiIiIiIiIiIiIiIiIiIiINESJGSIiIiIiIiIiIiIiIiIiIiINUWKGiIiIiIiIiIiIiIiIiIiISEOUmCEiIiIiIiIiIiIiIiIiIiLSECVmiIiIiIiIiIiIiIiIiIiIiDREiRkiIiIiIiIiIiIiIiIiIiIiDVFihoiIiIiIiIiIiIiIiIiIiEhDlJghIiIiIiIiIiIiIiIiIiIi0hAlZoiIiIiIiIiIiIiIiIiIiIg0RIkZIiIiIiIiIiIiIiIiIiIiIg1RYoaIiIiIiIiIiIiIiIiIiIhIQ5SYISIiIiIiIiIiIiIiIiIiItIQJWaIiIiIiIiIiIiIiIiIiIiINESJGSIiIiIiIiIiIiIiIiIiIiINUWKGiIiIiIiIiIiIiIiIiIiISEOUmCEiIiIiIiIiIiIiIiIiIiLSECVmiIiIiIiIiIiIiIiIiIiIiDREiRkiIiIiIiIiIiIiIiIiIiIiDVFihoiIiIiIiIiIiIiIiIiIiEhDlJghIiIiIiIiIiIiIiIiIiIi0hAlZoiIiIiIiIiIiIiIiIiIiIg0RIkZIiIiIiIiIiIiIiIiIiIiIg35fzA0dR4TgdtrAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 2400x1200 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(8, 4), dpi=300)\n",
    "plt.hist(boots, bins=4)\n",
    "ax.set_xlabel(\"Average apparent magnitude\", fontproperties=font_prop)\n",
    "ax.set_ylabel(\"Number of resamples\", fontproperties=font_prop)\n",
    "ax.tick_params(axis='both', which='major', labelsize=16, \n",
    "               top=True, right=True, bottom=True, left=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "authorized-glory",
   "metadata": {},
   "source": [
    "## 1d. Calculate the variance and standard deviation of `boots`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "prompt-voice",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.2372499233691391\n",
      "0.2372499233691391\n"
     ]
    }
   ],
   "source": [
    "boot_var = np.var(boots)\n",
    "boot_stddev = np.sqrt(boot_var)\n",
    "print(boot_stddev)\n",
    "print(np.std(boots))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "psychological-reservation",
   "metadata": {},
   "source": [
    "This standard deviation from the bootstraps, `boot_stddev`, gives you 1-sigma errors on the original mean of the data `star`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "commercial-bermuda",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.64 +- 0.24\n"
     ]
    }
   ],
   "source": [
    "print(\"%.2f +- %.2f\" % (np.mean(star), boot_stddev))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "chicken-aquatic",
   "metadata": {},
   "source": [
    "## 1e. Try with N log N resamples. \n",
    "From the lecture, N log(N) (where N is the number of samples in the original data set) is the number of bootstrap iterations you need to do to be able to assume a Gaussian distribution of the resamples. Redo steps 1b, 1c, and 1d here. Print the mean from your data and the 1-sigma error. \n",
    "Notice how the histogram and variance change when you use the correct number of bootstrap iterations. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "inappropriate-klein",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 2400x1200 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "boots = np.asarray([])\n",
    "boot_num = np.ceil(len(star) * np.log(len(star)))\n",
    "for i in range(int(boot_num)):\n",
    "    temp = np.random.choice(star, size=len(star), replace=True)\n",
    "    boots = np.append(boots, np.mean(temp))\n",
    "    \n",
    "boot_var = np.var(boots)\n",
    "boot_stddev = np.sqrt(boot_var)\n",
    "\n",
    "fig, ax = plt.subplots(1, 1, figsize=(8, 4), dpi=300)\n",
    "plt.hist(boots, bins=10)\n",
    "ax.set_xlabel(\"Average apparent magnitude\", fontproperties=font_prop)\n",
    "ax.set_ylabel(\"Number of resamples\", fontproperties=font_prop)\n",
    "ax.tick_params(axis='both', which='major', labelsize=16, \n",
    "               top=True, right=True, bottom=True, left=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ignored-chemistry",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.64 +- 0.43\n"
     ]
    }
   ],
   "source": [
    "print(\"%.2f +- %.2f\" % (np.mean(star), boot_stddev))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "stable-fitting",
   "metadata": {},
   "source": [
    "## 1f. Now try again with way more bootstraps than N log(N). \n",
    "Again redoing steps 1b, 1c, and 1d here.\n",
    "Most of these are unnecessary and just take up computational resources, but with a small set like this, you can play around."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "dangerous-search",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.64 +- 0.38\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 2400x1200 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "boots = np.asarray([])\n",
    "boot_num = 1000\n",
    "for i in range(int(boot_num)):\n",
    "    temp = np.random.choice(star, size=len(star), replace=True)\n",
    "    boots = np.append(boots, np.mean(temp))\n",
    "    \n",
    "boot_var = np.var(boots)\n",
    "boot_stddev = np.sqrt(boot_var)\n",
    "\n",
    "print(\"%.2f +- %.2f\" % (np.mean(star), boot_stddev))\n",
    "\n",
    "fig, ax = plt.subplots(1, 1, figsize=(8, 4), dpi=300)\n",
    "plt.hist(boots, bins=20)\n",
    "ax.set_xlabel(\"Average apparent magnitude\", fontproperties=font_prop)\n",
    "ax.set_ylabel(\"Number of resamples\", fontproperties=font_prop)\n",
    "ax.tick_params(axis='both', which='major', labelsize=16, \n",
    "               top=True, right=True, bottom=True, left=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "patient-report",
   "metadata": {},
   "source": [
    "## 1g. Use a larger sample set.\n",
    "14 data points is a pretty tiny sample set. Pretend that the star was visible again and you were able to hire an undergraduate student for the summer, so you got another 86 days of magnitude data for the star. \n",
    "Resample with bootstrap (using N log N) and see what your error is. Print the original mean of this new data set and the 1-sigma error you get from the bootstrapping."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "ranging-pepper",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.23 +- 0.19\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 2400x1200 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "star = np.random.normal(loc=10, scale=2, size=100)\n",
    "boots = np.asarray([])\n",
    "boot_num = np.ceil(len(star) * np.log(len(star)))\n",
    "for i in range(int(boot_num)):\n",
    "    temp = np.random.choice(star, size=len(star), replace=True)\n",
    "    boots = np.append(boots, np.mean(temp))\n",
    "    \n",
    "boot_var = np.var(boots)\n",
    "boot_stddev = np.sqrt(boot_var)\n",
    "\n",
    "print(\"%.2f +- %.2f\" % (np.mean(star), boot_stddev))\n",
    "\n",
    "fig, ax = plt.subplots(1, 1, figsize=(8, 4), dpi=300)\n",
    "plt.hist(boots, bins=20)\n",
    "ax.set_xlabel(\"Average apparent magnitude\", fontproperties=font_prop)\n",
    "ax.set_ylabel(\"Number of resamples\", fontproperties=font_prop)\n",
    "ax.tick_params(axis='both', which='major', labelsize=16, \n",
    "               top=True, right=True, bottom=True, left=True)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "loaded-reservoir",
   "metadata": {},
   "source": [
    "Notice the correlation between the number of points in the original sample, the number of bootstrap iterations you do, and how accurate and precise your result is."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "located-workshop",
   "metadata": {},
   "source": [
    "# Problem 2: Black hole 'happiness' variance as a function of X-ray counts\n",
    "Congratulations! You are a scientific crew member aboard a starship only 1 kpc from the Milky Way galactic center. Your chief scientific officer wants to test a hypothesis that stellar black holes are sentient and have feelings. You're go"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "loving-canyon",
   "metadata": {},
   "source": [
    "## 2a. Over a few kiloseconds, you take 40 observations of X-ray photon counts of a nearby black hole X-ray binary.\n",
    "The mean photon count rate is 3000. As you define your data array `photons`, remember that X-ray counts are Poisson-distributed!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "micro-frame",
   "metadata": {},
   "outputs": [],
   "source": [
    "photons = np.random.poisson(lam=3000, size=40)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "paperback-quick",
   "metadata": {},
   "source": [
    "The chief scientific officer gives you the following function to calculate the value of black hole 'happiness'. You want to estimate the variance on the 'happiness', but can't do propagation of errors. Perhaps we don't know if there is a little unknown correlation or bias."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "spanish-heavy",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1496.9528846153846\n"
     ]
    }
   ],
   "source": [
    "def bh_happy(data):\n",
    "    temp1 = np.mean(data)\n",
    "    temp2 = np.mean(np.diff(data))\n",
    "    happiness = (temp1 + temp2) / 2\n",
    "    return happiness\n",
    "print(bh_happy(photons))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "sonic-boating",
   "metadata": {},
   "source": [
    "## 2b. Compute the jackknife estimate of the black hole happiness.\n",
    "Resample (N-1) samples without replacement, where N is the number of original samples, and calculate the black hole happiness. Do this N times, and call your array of happiness estimates `jacks`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "virgin-teach",
   "metadata": {},
   "outputs": [],
   "source": [
    "jacks = np.asarray([])\n",
    "jacks_num = len(photons)-1\n",
    "for i in range(int(len(photons))):\n",
    "    temp = np.random.choice(photons, size=jacks_num, replace=False)\n",
    "    jacks = np.append(jacks, bh_happy(temp))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "obvious-playback",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1498.2611336  1499.94230769 1499.04824561 1496.12483131 1498.06072874\n",
      " 1498.47165992 1498.12955466 1498.1379892  1496.68353576 1499.25641026\n",
      " 1497.33265857 1497.35458839 1495.25168691 1496.02294197 1497.86504723\n",
      " 1496.38225371 1498.54251012 1496.11605938 1496.37854251 1499.71929825\n",
      " 1499.02192982 1497.45614035 1497.93353576 1497.73987854 1498.65789474\n",
      " 1499.86403509 1499.53879892 1498.87719298 1498.34008097 1496.00910931\n",
      " 1496.83164642 1497.99932524 1499.10020243 1497.89304993 1496.41160594\n",
      " 1496.90789474 1497.54588394 1496.24493927 1497.42037787 1497.62483131]\n"
     ]
    }
   ],
   "source": [
    "print(jacks)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "sunrise-peoples",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 2400x1200 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(8, 4), dpi=300)\n",
    "plt.hist(jacks, bins=10)\n",
    "ax.set_xlabel(\"Black hole `happiness` (unitless)\", fontproperties=font_prop)\n",
    "ax.set_ylabel(\"Number of resamples\", fontproperties=font_prop)\n",
    "ax.tick_params(axis='both', which='major', labelsize=16, \n",
    "               top=True, right=True, bottom=True, left=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "upper-dance",
   "metadata": {},
   "source": [
    "## 2c. Compute the variance of `jacks`, the jackknife estimate of the variance of black hole happiness"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "exact-tanzania",
   "metadata": {},
   "outputs": [],
   "source": [
    "jack_var = np.var(jacks)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "proof-niger",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Jackknife variance estimate:  1.4190835424754318\n"
     ]
    }
   ],
   "source": [
    "print(\"Jackknife variance estimate: \", jack_var)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "wound-apartment",
   "metadata": {},
   "source": [
    "## 2d. At which number of jackknifes does it converge?\n",
    "Redo part 2b and 2c again, making `jacks` different lengths (doing the N-1 jackknife resampling J times). Try for values of J < N, J > N, and J >> N (you already did J = N in 2b!). Can you find approximately where the variance converges? Plotting histograms may help along the way, if you like visual information."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "spiritual-jamaica",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "rolled-booth",
   "metadata": {},
   "source": [
    "# Problem 3: literature search!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "hired-maple",
   "metadata": {},
   "source": [
    "Look on ADS to find an example of a paper using the jackknife or bootstrap technique for a research topic related to your astro sub-field. See if you can figure out what their original data is, what their 'estimator' or function is (it might just be the mean of the data set), why they applied the bootstrap or jackknife, and whether they used one of the alternative approaches (like block jackknife or smooth bootstrap)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "maritime-bradley",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "southwest-measurement",
   "metadata": {},
   "source": [
    "# Bonus problem 4: \n",
    "Let's say for problem 1 that the first 7 days of stellar magnitude measurements had distribution scale of 2, but the next time the star was visible, the seeing was worse from the telescope site, so the next 21 days of measurements had a distribution scale of 4. Define a probability `p` associated with each magnitude measurement in `star` that you use in the resampling, instead of the standard uniform sampling. How does this change the histogram and variance? (for future reference, uniform sampling should be fine for most use cases, this is just to play around and get a better intuition for how the inputs affect the output)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "perceived-depression",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "dangerous-brush",
   "metadata": {},
   "source": [
    "# Bonus problem 5: bootstrap resampling from a 2-D array"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "contemporary-british",
   "metadata": {},
   "source": [
    "2d array, your result is the average along the rows, but there's some mild correlation between adjacent columns. Resample the columns to get the 1-sigma error for each data point in the mean 1D array!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "specified-banks",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "absolute-camcorder",
   "metadata": {},
   "source": [
    "# Bonus problem 6: try the 'delete-d' or 'block' jackknife technique\n",
    "Use the setup from problem 1 or 2 (or something similar you come up with). Remember, jackknife works best for small sample populations with linear statistics or estimators (like means), not as well for non-smooth and/or non-linear cases."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "universal-arnold",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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