{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <style>\n",
       "        .output_wrapper, .output {\n",
       "            height:auto !important;\n",
       "            max-height:100000px;\n",
       "        }\n",
       "        .output_scroll {\n",
       "            box-shadow:none !important;\n",
       "            webkit-box-shadow:none !important;\n",
       "        }\n",
       "        </style>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import sys\n",
    "sys.path.insert(0,'..') # allow us to format the book\n",
    "\n",
    "# use same formatting as rest of book so that the plots are\n",
    "# consistant with that look and feel.\n",
    "import book_format\n",
    "book_format.set_style()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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JsxdUVW/V6XNN16QOH7ObBvuaFeY3QOH+AxTmP0CRAQMUHeit2CBvDfJyl8lkuia1AP0ZgQDo4xqbbfqyol5fltfpUGW9jlQ26EhVvSrrrP90XxeTFOBtlr/XV7/sB5rd5OXhKk/31oe768UeAZNJJpNks0s2u10tdkPWFrvON9nU2GxTg7VFtReaVXexp6GmoUlNNrvqrS2qP9WiwlPnLluDr6ebhll8NNwyUMOCfTQyxEejw/zk5+Xe3acK6NcIBEAf0myz68vyeuWXnlF+aa0OnKzVkaoG2ezGZbcf5OWu6EBvxQR6KWKQl8L8ByjM31MWX08N9jFrkJeHXF165te5YRiqa2zRqXqrquoadbK2sbWH4swFFZ8+p6Lq86qoa1RdY4tyi88ot/hMm/0jBg1QQpifxkT6aXzkII2J8JO3mY80oKtMhmFc/pOiF6mrq5Ofn59qa2vl6+vr7HKAXqO+sVmflZzV7uM12nP8jPaVnZW1xd5uu0BvD40K89Ww4Iu/tC0+GjLYW/5eHk6o+spdaLLpePU5Halq7dk4XFmvgoo6lZ6+0G5bF5M03OKjSbEBmhgToEmxAbL4ejqhaqB3udLvUAIBcB1pbLYpt/iMdh2r1s6jNdpfdlb/+OPf19NN46IGaVykv8aE+2l0uK9CfD371HX42vPNOlBeqy9O1Cq/9KzyS87qZG1ju+3igryVOjRQU4YEKWVIYK8PQEBPIBAAfURR9TltOVSlrYdPKaewRo3NbXsAIgMGtP4ijgnQhJgAxQV5y6WHuvl7s8q6Ru0tOqM9Rae1+/hpFVTU6eufbi4maWykv6YPH6wZI4I1JtyvX54n9D8EAuA61WKz67OSs/qooFIfFVS2G2wX7GPWlKFBSh0SqNShQQr3H+CkSnu32vPN+uR4jXYdrdbOYzU6WtXQ5vWggR66aWSwbo63KG1YkLw8GH+AvolAAFxHrC027Tpaow++qFB2QWWbW/7cXEyaGBOg6SMGa8aIwRph8elT3f/XSnntBW09dEpbD5/SjiPVqre2OF4zu7kobdhgzUwI0S3xFu5gQJ9CIAB6uaYWu3YcPaW/7CvXRwcr23xB+Q1w100jg3VLvEXThgfJx5MvqO7U1GLXnqLTjl6Yrw9SdHMxKXVokO4cE6rbRofIbwDnHtc3AgHQC9nthj45XqP38k7qgwMVqr3Q7Hgt2MesbyWE6FujQzQpNkBurswsfi0YhqEvK+r1wRcV+uCLCh2qrHe85uHqomnDg3T3uHDdEm/RAA9mVcT1h0AA9CKHKur1bl6ZNuafVPnXRsMP9jHrjhtCdeeYUCVGDWKQWy9w7FSD/rq/XO/vP6nDlV+NOxhodtNto0N0T2K4UuIC+bvCdYNAADjZmXNN2rjvpP6cW6bPT9Q62n083XTnmFDdNTZMybGBPTbxD67e4cp6bcw/qQ35J1R25qvLCmF+nro3KUL3JkYoJsjbiRUC/xyBAHACu93QzmPVemtPqbIPVKrJ1nqLoJuLSTeNDNY9ieGaMSKYBX2uM4ZhKLf4jN7NO6G/7Dup+savxntMig3Q/RMjNTMhlEsK6JUIBMA1VFnXqD/tKdW6vaVtfkmOCvXVdyZE6F/GhilwoNmJFaK7NDbblH2wUu98VqZth085Joby8XTTrHHheiA5SvGhfE6h9yAQAD3Mbje042i13vy0WB8VVDnWC/D1dNOs8eG6b0KkEsL9nFwlelJ57QX9eW+Z/pRb2uZOhfFR/npgUpTuGhtGbxCcjkAA9JCz55v09t4y/eHTYhXXnHe0T4wZpAeSozQzIZQvgX7Gbje061iN1u4u0YcHKtRyMRz6DXDXfRMi9L3kaMYawGkIBEA3O3CyVq/vKtJ7+ScdCwj5eLrp3sQIPZAcpeEWHydXiN7gVL1Vb+eW6o+flrS5fDRt+GDNTY3R9OGDuUMB11SPBoKsrCz9+te/Vnl5uUaPHq2XXnpJaWlpl9323Xff1bJly5Sfny+r1arRo0fr2Wef1W233dbtbwbobi02uzYfrNRrO4u0u+i0oz0+1FdzUqJ197gwprzFZdnshrYertKanGJtPXzKsa5CTKCX5qTE6F8nRMiXCadwDfRYIFi3bp0efPBBZWVlacqUKXr11Ve1YsUKHTx4UFFRUe22X7hwocLCwnTjjTfK399fq1ev1n/913/p008/1fjx47v1zQDdpfZ8s97aU6LXdxU5VtFzdTFpZkKIHk6NUVL0IKYPxhUrrjmnN3KKtW5vqeMOhYFmN31nQoQeTo1RdCCXE9BzeiwQJCcnKzExUcuWLXO0xcfHa9asWcrMzLyiP2P06NGaPXu2fvazn13R9gQCXCtF1ee0audx/Tm3TOebbJKkAG8PfS85St9LjlaIn6eTK8T17Jy1RevzTui1XUWOxZZMJumWeIsemRqrSbEBBE10uyv9Du1UX2dTU5Nyc3P19NNPt2lPT0/Xrl27rujPsNvtqq+vV0BAQGcODfQYwzC0p+iMVmwvVHZBpaNrd2SIj+ZNidW/jGOkOLqHt9lN358cre8lR2n7kWqt2nlcWw6dUvbBSmUfrNSYCD/Nnxqr228IlTtTV+Ma61QgqK6uls1mk8ViadNusVhUUVFxRX/Gb37zG507d0733Xdfh9tYrVZZrVbH87q6us6UCVyRFptdHx6o1PJtx7Sv7KuZBG8aGaz5U2OVOiSQX2voESaTSdOGD9a04YN1tKpeq3YW6Z3cMu0vq9UTb+XrVx8c0twpMbp/UpQGmhmjgmujS//S/vFD0jCMK/rgXLt2rZ599lm99957Cg4O7nC7zMxMPffcc10pDfinzje16O29ZVqxo9Bx77jZzUX3JEZo/tRYDQ0e6OQK0Z8MDfbRf3z7Bj2ZPkJ/+KRYa3KKdOLsBb3w1wL9z9+P6IHkKM2bEiuLL5er0LM6NYagqalJXl5eevvtt/Xtb3/b0f7EE08oPz9fW7du7XDfdevWae7cuXr77bd1xx13fONxLtdDEBkZyRgCXJXT55r0+q4irckp0pnzrasMDvJy15yUGD2YEq0gZhJEL9DYbNOGvBNavr1QhafOSZLcXU369vhw/XBanIYGc3srOqdHBxUmJSUpKyvL0TZq1CjdfffdHQ4qXLt2rebNm6e1a9dq1qxZnTmcJAYV4uqUnj6vFdsLtW5vqRqbW+cPiArw0g/SYvWvSZHMP49eyW439Pcvq7R82zHtKTrjaL91lEU/njFEiVGDnFgdric9MqhQkhYvXqwHH3xQEyZMUEpKipYvX66SkhJlZGRIkpYsWaITJ05ozZo1klrDwJw5c/Q///M/mjx5smOswYABA+Tnx7Su6DlfVtTplS3H9Jf95Y5phW8I99OPpsdpZkIoqwyiV3NxMenWURbdOsqi3OLTenVroTZfHHyYfbBSk2ID9OPpQzRjxGDGuqBbdHliol/96lcqLy9XQkKC/vu//1vTpk2TJD388MMqKirSli1bJEkzZsy47KWEhx56SK+99toVHY8eAnTG3qLTytpyTP/3ZZWjberQIGVMH6IpQxkoiOvX0aoGLd92TOvzTqjZ1vrRPTLERz+eMUR33BAqN+5MwGUwdTH6FcMwtOXQKWVtOeroXjWZpNsTQpUxfYhuiKA3Cn1Hee0FrdpxXH/8tETnLs6XERXgpR9Nj9O9iRHcJos2CAToF2x2Q3/9vFzLthxTQXnr7akeri66NylcP5w2RLEsKIM+7Oz5Jq3JKdbqnccdA2UH+5j1yNRYfW9yNLcsQhKBAH2ctcWm9Z+d0Ctbj6no4oqDXh6u+l5ylB5Ji+MWLfQr55tatG5PqX6/rdAx1bavp5seTo3Rw1NiFeDt4eQK4UwEAvRJ55tatHZ36wdfRV3rB5+/l7vmpsbqodRo+XvxwYf+q6nFrg35rUH50i2LA9xd9UBylH6QFsfU2/0UgQB9Su35Zq3JKdKqr3WNWnzN+kFanL47KUredI0CDja7oQ8PVOh3Hx/VgZOtl9LcXU3616QI/WjaEMVwKa1fIRCgTzhVb9XKHcf1h0+K1WBtXSUuKsBLP54xRPckhsvsxuApoCOGYWjbkWr97v+OOpbvdjFJd44J06M3DtHIED5P+wMCAa5rZWfOa/m2Qq3bUyprS+tkQiMsPnr0Rm6vArpiT9FpZX18VB8fOuVouyU+WI/eOJRJjvo4AgGuS0er6rVsS6Heyz+hlouTCY2P8tdjM4bqppHBcmEyIeCqfHGiVsu2HtOmz8sdK3umxAXqsRuHMk9HH0UgwHVlf9lZZX18TB8erHB8SKUNC9KjM4ZqchxrxAPdrfBUg17Z2naSo7ERfvrxjKFKH2UhfPchBAL0eoZhKKewRsu2HNP2I9WO9ttGW/TojKEaG+nvvOKAfuLk2Qv6/fZCrd1d4ljrY2jwQGVMH6K7x4XJnctz1z0CAXotu91QdkGlsrYc077Ss5IkVxeT7h4bph/PGKJhFlZzA661mgarVu8s0us5RapvbB3AG+4/QD9Ii9XsiVEsAnYdIxCg12lqseu9/BN6dVuhjlY1SJLMbi6aPTFSP0iLU2SAl5MrBFDX2Kw3PynRyh3HVd3Qugx9gLeHHk6N0ZwU5vq4HhEI0Gucs7borT2lWrn9q1nUfMxu+n5KtOZNidVgH7OTKwTwjxqbbXo7t0zLtx1T6ekLklpnA31gUpTmp8Uq1G+AkyvElSIQwOlqGqx6fVeRXs8pVu2F1smEggaa9UharB5IjpKvp7uTKwTwz7TY7I71Qr6sqJfUOsnRrHHh+tH0OA0N5hJfb0cggNOU1JzXih2F+tPeUscgpZhAL/1gGiuxAderSyuKLtt6TLuPn3a03xJvUcb0OE2ICXBidfgmBAJcc/vLzurVbYX62+flujiFgG4I91PG9CH6VkKIXLmNCegTPis5o1e3HtPmg5WO24QTo/z1w2lDdOsoC//XexkCAa4Ju93Qx4eqtHxboT792q+G6cMH60fT45QSx0QnQF917FSDVmwv1Du5J9Rka+0NjA3y1vypsfrXJHoDewsCAXpUY7NN6/NOaOWO4447BtxcTPqXsWH6wbQ4xYfy9wT0F1X1jXp9V5HeyClW3cVbFgO8PfT9ydF6cHI0A4edjECAHlHdYNUbOcX6wyfFqjnXJKn1joEHkqP08JQYRh4D/dg5a4v+tLdUK3ccV9mZ1jsTPNxc9O1x4ZqfFqvhzDHiFAQCdKuC8jqt2nFc7+WfdHQNhvsP0NwpMZo9MVI+3DEA4KIWm10fHKjQ77cfd0w+JrVORz5/aqymDRvM1MjXEIEAV81mN/Txl1VatfO4dh2rcbSPjfDTI2lxmpkQwqqDADpkGIZyi89oxfbj2nywwjHYeMhgbz08JVb3JobLy8PNuUX2AwQCdFldY7Pe3lum13cVqeT0eUmta6jPTAjVvKkxSowaxEBBAJ1SUnNer+cUad2eUjVYW8cZ+Hq66f5JUXpwcjQzlfYgAgE67XBlvdbkFOndz07ofJNNUut/2O9OitKDKdGKGMR/WABXp/7iD441OUUqqvnqB8fN8RY9lBLDEsw9gECAK9Jss+ujg5Vak1OsnMKvLgsMtwzUw6mxmjU+jC49AN3Obje05XCVVu8sarPa6ZDB3npwcrTuSYpgNtNuQiDAN6qsa9Ta3SVau7tElXWtC5i4mKT0USGakxrN/AEArpmjVQ16I6dIf84t07mLvZNeHq66e1y4vj85SqPD/Jxc4fWNQIB27HZD249W64+fFuujgirZLo7wCRroofsmROp7k6MV7s9tgwCco76xWevzTuiNnGIduTi/iSSNj/LXA5OidOeYMJZh7gICARyq6hr1dm6Z3tpT4li1TJImxgzS9ydH61sJITK78Z8MQO9gGIY+PX5ab3xSrA+/qFDLxR8vvp5u+vb4cN0/KYrJzzqBQNDPtdjs2nbklNbuLtX/fflVb4CPp5vuTYzQA8lRTBICoNerqm/U23vLtHZ3iWOyI0kaG+mv706M1J1jwzTQzDinb0Ig6KcKTzXo7dwyvZNbpqp6q6N9QvQgzZ4YSZcbgOvSpUueb+0uUfbBSkevwQB3V90xJlT3TYjUxBhuib4cAkE/UtfYrL/uL9c7uWXaW3zG0R7g7dHavTYxUsPoDQDQR1Q3WPXuZ2V6a0+pCk+dc7THBHrpnsQI3ZMYzm3SX0Mg6ONabHZtP1qt9Z+d0IcHKmRtaZ1O2MUkzRgRrPsmROimkRZ5uDGTIIC+yTAMfVZyRn/aU6b395903KEgSSlxgbonMVzfSgjp91OrEwj6IMMwtK+sVhvyTuj9/SdV3dDkeG24ZaDuTYzQrPHhsvh6OrFKALj2zllb9MEXFXrnszLlFNbo0jeb2c1Ft46y6Nvjw5U2bHC//JFEIOhDjlTWa+O+k9q476SKL87sJUmB3h66a2yY7kkM1w3hflw7AwBJJ85e0PrPyrQ+74SOfe2Sgr+Xu2YmhOpfxoZpUmyAXPvJAksEgutc4akG/XV/ud7fX65DlfWO9gHurq1pNzFcU4cGyZ3FhQDgsgzD0Bcn6vRuXpne31+uU18baB3sY9btN4TqzjGhSowa1KdXXyQQXIeOVtXrb59XaNMXFSoor3O0u7uaNH34YN01Nky3jrIwlTAAdJLNbuiTwhptzD+pTV+Uq76xxfFaqJ+nbhsdottvCFVS9KA+13NAILgOGIahz0/UavOBSn1woEJHvzYzl5uLSVOGBumOMaG6bVSI/Lz696AYAOgu1habdhyp1vv7y5V9sNKx+qIkBQ00K320RemjLEodEtQnxhwQCHopa4tNnxae1t8LKrX5YKXKaxsdr7m7mjR1aJBmJoTq1lEWDfL2cGKlAND3NTa3hoNNX5Tro4OVqvtaz4GP2U0zRgbrlvhgzRgefN3+MCMQ9CKn6q3acqhKHx+q0tZDp9rcGuPl4aoZIwYrfVSIbhwZLL8B1+c/OAC43jW12JVTWKMPD1Qo+2BlmzEHri4mTYoJ0M3xwbpxZLDigryvm4HcBAInstkN5Zee1bbDp/TxoSrtL6tt8/pgH7NuHhmsW+ItmjosSJ7uzBwIAL2J3W4or/Sssg9W6u8FlW0WW5KkqAAv3TQyWNOHD1ZyXECvHttFILjGSk+f186j1dp+pFo7jlar9kJzm9cTwn1144hg3Rxv0Zhwvz49ohUA+primnP6qKBKH39ZpU+P16jZ9tVXp4eriybFBihtWJCmDgtSfIhvr/qMJxD0sOoGqz4prFHOsRrtPFqtoq/NDyC1rsqVNmywpg8frBkjBiuYyYIAoE84Z23RzqPV+vjQKW07fEonzl5o83qAt4dShwQqdUiQUoYEKibQy6mXFwgE3exUvVW7j5/W7uM1+qTwdJu5AaTW60vjI/01ZWiQpg0frLERfnJjjgAA6NMMw1Bh9TltPXRKO49W65PCmjbjxKTW2xonxwUqOTZAyXHXPiAQCK6CYRgqrjmvPUWnlVt8RnuKTreZ7eqSkSE+ShkSqClDgpQcF9Dv58sGgP6u2WZXfulZ7ThSrZzCGuWVnGlzeUFqnRRpYkyAJsQM0oToAMWH+vToD0gCQSecs7bo8xO1+qzkjD4rPqv80jNt1gm4ZGSIjyPhJccGKHCgudtrAQD0HReabMotPqNPCmu0+/hp5ZeeVZPN3mYbLw9XjYnwU2LUICVGDdL4KP9u/X4hEHyD2gutywXvKz2rfWVndbiyXvZ/OAseri66IcLPkeAmxgySvxfzAgAAuq6x2ab80rOO3ufc4jNtZk2UpLggb/3fkzO67ZhX+h3ae++T6EHWZpueWf95m7ZQP0+Nj/K/mM4GaXSYL7cDAgC6lae7qybHBWpyXKCk1tsbj1Q1KK/kTGsvdclZjYv0d0pt/TIQBPt66q6xYYoO8NLYSH+NjfDjLgAAwDXn4mLSiBAfjQjx0f2ToiS1zmXjDP0yEEjS/353vLNLAACgHWctrsR9cQAAgEAAAAAIBAAAQAQCAACgLgaCrKwsxcbGytPTU0lJSdq+ffs3br9161YlJSXJ09NTcXFxeuWVV7pULAAA6BmdDgTr1q3TwoULtXTpUuXl5SktLU0zZ85USUnJZbc/fvy4br/9dqWlpSkvL0/PPPOMFixYoHfeeeeqiwcAAN2j0zMVJicnKzExUcuWLXO0xcfHa9asWcrMzGy3/VNPPaWNGzeqoKDA0ZaRkaF9+/YpJyfnio7ZGxY3AgDgetQjMxU2NTUpNzdXTz/9dJv29PR07dq167L75OTkKD09vU3bbbfdppUrV6q5uVnu7u0XBLJarbJarY7ntbW1klrfFAAAuHKXvjv/2e//TgWC6upq2Ww2WSyWNu0Wi0UVFRWX3aeiouKy27e0tKi6ulqhoaHt9snMzNRzzz3Xrj0yMrIz5QIAgIvq6+vl5+fX4etdmqnwH9dxNgzjG9d2vtz2l2u/ZMmSJVq8eLHjud1u1+nTpxUYGNhta0jX1dUpMjJSpaWlXIb4B5ybjnFuOsa56RjnpmOcm45117kxDEP19fUKCwv7xu06FQiCgoLk6urarjegqqqqXS/AJSEhIZfd3s3NTYGBgZfdx2w2y2xuu/Sjv79/Z0q9Yr6+vvwj7ADnpmOcm45xbjrGuekY56Zj3XFuvqln4JJO3WXg4eGhpKQkZWdnt2nPzs5WamrqZfdJSUlpt/3mzZs1YcKEy44fAAAA116nbztcvHixVqxYoVWrVqmgoECLFi1SSUmJMjIyJLV298+ZM8exfUZGhoqLi7V48WIVFBRo1apVWrlypZ588snuexcAAOCqdHoMwezZs1VTU6Pnn39e5eXlSkhI0KZNmxQdHS1JKi8vbzMnQWxsrDZt2qRFixbpd7/7ncLCwvTb3/5W9957b/e9iy4wm836+c9/3u7SBDg334Rz0zHOTcc4Nx3j3HTsWp+bTs9DAAAA+h7WMgAAAAQCAABAIAAAACIQAAAA9cNAkJmZqYkTJ8rHx0fBwcGaNWuWDh065OyyeoVly5ZpzJgxjkkwUlJS9Le//c3ZZfU6mZmZMplMWrhwobNL6RWeffZZmUymNo+QkBBnl9VrnDhxQt///vcVGBgoLy8vjRs3Trm5uc4uy+liYmLa/bsxmUx67LHHnF2a07W0tOj//b//p9jYWA0YMEBxcXF6/vnnZbfbe/S4XZq6+Hq2detWPfbYY5o4caJaWlq0dOlSpaen6+DBg/L29nZ2eU4VERGh//zP/9TQoUMlSa+//rruvvtu5eXlafTo0U6urnfYs2ePli9frjFjxji7lF5l9OjR+uijjxzPXV1dnVhN73HmzBlNmTJFN954o/72t78pODhYx44d67GZV68ne/bskc1mczz/4osvdOutt+o73/mOE6vqHX75y1/qlVde0euvv67Ro0dr7969mjt3rvz8/PTEE0/02HH7/W2Hp06dUnBwsLZu3app06Y5u5xeJyAgQL/+9a81f/58Z5fidA0NDUpMTFRWVpZeeOEFjRs3Ti+99JKzy3K6Z599Vhs2bFB+fr6zS+l1nn76ae3cuVPbt293dim93sKFC/X+++/ryJEj3bZmzfXqzjvvlMVi0cqVKx1t9957r7y8vPTGG2/02HH73SWDf3RpaeWAgAAnV9K72Gw2vfXWWzp37pxSUlKcXU6v8Nhjj+mOO+7QLbfc4uxSep0jR44oLCxMsbGxuv/++1VYWOjsknqFjRs3asKECfrOd76j4OBgjR8/Xr///e+dXVav09TUpD/84Q+aN29evw8DkjR16lT9/e9/1+HDhyVJ+/bt044dO3T77bf36HH73SWDrzMMQ4sXL9bUqVOVkJDg7HJ6hc8//1wpKSlqbGzUwIEDtX79eo0aNcrZZTndW2+9pdzcXO3du9fZpfQ6ycnJWrNmjYYPH67Kykq98MILSk1N1YEDBzpcwKy/KCws1LJly7R48WI988wz2r17txYsWCCz2dxmivf+bsOGDTp79qwefvhhZ5fSKzz11FOqra3VyJEj5erqKpvNpl/84hf67ne/27MHNvqxRx991IiOjjZKS0udXUqvYbVajSNHjhh79uwxnn76aSMoKMg4cOCAs8tyqpKSEiM4ONjIz893tE2fPt144oknnFdUL9bQ0GBYLBbjN7/5jbNLcTp3d3cjJSWlTdvjjz9uTJ482UkV9U7p6enGnXfe6ewyeo21a9caERERxtq1a439+/cba9asMQICAozXXnutR4/bbwPBT37yEyMiIsIoLCx0dim92s0332z88Ic/dHYZTrV+/XpDkuHq6up4SDJMJpPh6upqtLS0OLvEXueWW24xMjIynF2G00VFRRnz589v05aVlWWEhYU5qaLep6ioyHBxcTE2bNjg7FJ6jYiICOPll19u0/bv//7vxogRI3r0uP3ukoFhGHr88ce1fv16bdmyRbGxsc4uqVczDENWq9XZZTjVzTffrM8//7xN29y5czVy5Eg99dRTjKj/B1arVQUFBUpLS3N2KU43ZcqUdrc1Hz582LEYHKTVq1crODhYd9xxh7NL6TXOnz8vF5e2Q/xcXV257bC7PfbYY/rjH/+o9957Tz4+PqqoqJAk+fn5acCAAU6uzrmeeeYZzZw5U5GRkaqvr9dbb72lLVu26IMPPnB2aU7l4+PTboyJt7e3AgMDGXsi6cknn9Rdd92lqKgoVVVV6YUXXlBdXZ0eeughZ5fmdIsWLVJqaqr+4z/+Q/fdd592796t5cuXa/ny5c4urVew2+1avXq1HnroIbm59buvow7ddddd+sUvfqGoqCiNHj1aeXl5evHFFzVv3ryePXCP9j/0QpIu+1i9erWzS3O6efPmGdHR0YaHh4cxePBg4+abbzY2b97s7LJ6JcYQfGX27NlGaGio4e7uboSFhRn33HNPvx938nV/+ctfjISEBMNsNhsjR440li9f7uySeo0PP/zQkGQcOnTI2aX0KnV1dcYTTzxhREVFGZ6enkZcXJyxdOlSw2q19uhx+/08BAAAgHkIAACACAQAAEAEAgAAIAIBAAAQgQAAAIhAAAAARCAAAAAiEAAAABEIAACACAQAAEAEAgAAIAIBAACQ9P8BqS4s+Y+pkQEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from kf_book.gif_animate import animate\n",
    "from stats import gaussian\n",
    "import matplotlib.pylab as pylab\n",
    "from matplotlib import animation\n",
    "import matplotlib\n",
    "\n",
    "def plt_g (mu, variance):\n",
    "    xs = np.arange(2,8,0.05)\n",
    "    ys = [gaussian (x, mu, variance) for x in xs]\n",
    "    plt.plot (xs, ys)\n",
    "    plt.ylim((0,1))\n",
    "\n",
    "\n",
    "mu = 2\n",
    "sigma = 0.6\n",
    "def ganimate(frame):\n",
    "    global mu, sigma\n",
    "    if frame < 25:\n",
    "        mu += .2\n",
    "    elif frame == 25:\n",
    "        mu = 5\n",
    "    elif frame < 37:\n",
    "        sigma -= 0.05\n",
    "    else:\n",
    "        sigma += 0.05\n",
    "\n",
    "    plt.cla()\n",
    "    plt_g(mu,sigma)\n",
    "\n",
    "animate('04_gaussian_animate.gif', ganimate, \n",
    "        frames=80, interval=50, figsize=(6,4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src='04_gaussian_animate.gif'>"
   ]
  }
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