From 011064d39aabd1214aefbcbcd25b17664406f98c Mon Sep 17 00:00:00 2001 From: Alan Grissett Date: Wed, 28 Jan 2015 06:54:27 -0500 Subject: [PATCH] Finished notebook. --- coin_flips.ipynb | 490 +++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 490 insertions(+) create mode 100644 coin_flips.ipynb diff --git a/coin_flips.ipynb b/coin_flips.ipynb new file mode 100644 index 0000000..11ce342 --- /dev/null +++ b/coin_flips.ipynb @@ -0,0 +1,490 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:9f5587ac07c16928617394d9682be6a7c93f29f527c8cff71582b27bfc26d02e" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import random\n", + "import statistics as st\n", + "import matplotlib.pyplot as plt" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 2 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "%matplotlib inline" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 3 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def flip_coin():\n", + " \"\"\"If > .5 Heads, else Tails\"\"\"\n", + " return random.random() > .5\n", + "\n", + "def flip_coin_n_times(n=100000):\n", + " \"\"\"Flips coin n-times and returns list of counts at intervals of 2^n flips\"\"\"\n", + " heads = 1\n", + " tails = 1\n", + " record_count = 0\n", + " data = []\n", + " \n", + " for flip_count in range(n):\n", + " if flip_coin():\n", + " heads += 1\n", + " else:\n", + " tails += 1\n", + " if flip_count == 2**record_count:\n", + " data.append((heads, tails))\n", + " record_count += 1\n", + " data.append((heads,tails))\n", + " return data" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 4 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\"\"\"Flip coins 100000 times and find the difference\"\"\"\n", + "data = flip_coin_n_times(100000)\n", + "difference = [abs(flip[0] - flip[1]) for flip in data]" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 5 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\"\"\"Set up and show the plot of difference\"\"\"\n", + "x1 = [\"2^{}\".format(n) for n in range(len(data))]\n", + "fig = plt.gcf()\n", + "fig.set_size_inches(15.5,10.5)\n", + "plt.plot(difference)\n", + "plt.xticks(range(len(x1)), x1)\n", + "plt.xlabel(\"Number of Flips\")\n", + "plt.ylabel(\"Heads - Tails\")\n", + "plt.title(\"Difference Between Heads and Tails\")\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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l+WhV3b27bx5XjQAAACtpIw3kScbc8trd24cP902yd5Irhs/nWwA+Ocnp3b2juy9MckGS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\nbEMVj/kG8LWysw9w/b8PmEE+7n4z8k59kxbKfx4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+ "text": [ + "" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\"\"\"Calculate the ratio of heads to tails from data\"\"\"\n", + "ratio = [flip[0]/flip[1] for flip in data]" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 7 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\"\"\"Set up and show the plot for ratio\"\"\"\n", + "x1 = [\"2^{}\".format(n) for n in range(len(data))]\n", + "fig = plt.gcf()\n", + "fig.set_size_inches(15.5,10.5)\n", + "plt.plot(ratio)\n", + "plt.xticks(range(len(x1)), x1)\n", + "plt.xlabel(\"Number of Flips\")\n", + "plt.ylabel(\"Heads / Tails\")\n", + "plt.title(\"Ratio Between Heads to Tails\")\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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R1UiSJDUH50RKUhemT8/h0QApSZJUG0OkpLbmUFZJkqQNY4iU1NYMkZIkSRum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\npbQqIj4MXAP0Ay5JKc2IiA9Unv9Bo95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nZ+THXS4n2133tirmK0nS+0RKRe05\nI0mSGi0iprPqAXokSeo1d2eVJEmSJFXNLZGSJEmSpKq5JVKSJEmSVDVLpCRJkiSpapZISZIkSVLV\nLJGSJEmSpKpZIiVJkiRJVbNESpIkSZKq9v8Bh18aZz/jb0gAAAAASUVORK5CYII=\n", + "text": [ + "" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "From the above graphs we can see that as the sample size increases the size of the random swings may increase and heads or tails may occur hundreds more time, but in relation to the total number of iterations these swings are small. As the sample size increases the ratio of heads to tails approaches 1." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\"\"\"Set up and show scatter plot of difference using a log scale for the x-axis\"\"\"\n", + "x2 = [2**n for n in range(len(data))]\n", + "fig = plt.gcf()\n", + "fig.set_size_inches(15.5,10.5)\n", + "plt.xscale(\"log\")\n", + "plt.xlabel(\"Number of Flips\")\n", + "plt.ylabel(\"Heads - Tails\")\n", + "plt.title(\"Difference Between Heads to Tails\")\n", + "plt.scatter(x2, difference)\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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ETwAAAIYaHjyr6j5V9adV9daquqGqXjAt31NV+6vq+unnyXP7XFJV76qqG6tq5+gaAQAA\nGKe6e/xJqu7b3Z+qqlOSXJfkx5M8Mclt3f3iQ7Y9M8mrkjw+yelJXpvkMd1959w2vYi6AQAASKoq\n3V0nuv9Cutp296emyXsnuWeSj07zhyv8vCSXd/ft3X1zkpuSnD28SAAAAIZYSPCsqntU1VuT3Jrk\n9d39jmnVs6vqbVX18qo6dVr2iCT753bfn1nLJwAAAJvQolo87+zus5I8Msk3VdVSkpckeVSSs5Lc\nkuSyox1ieJEAAAAMccoiT9bdH6+qP0zy1d29cnB5Vb0syTXT7HuTnDG32yOnZZ9hz549d00vLS1l\naWnp5BcMAACwDa2srGRlZeWkHW/44EJV9dAkd3T3x6pqR5LlJM9P8o7ufv+0zXOTPL67nz43uNDZ\nuXtwoUfPjyZkcCEAAIDFWevgQoto8Twtyd6qukdmXXtf0d2vq6rfrqqzMutG++4kz0yS7r6hqq5I\nckOSO5I8S8oEAADYvBbyOpWTTYsnAADA4myK16kAAACwfQmeAAAADCV4AgAAMJTgCQAAwFCCJwAA\nAEMJngAAAAwleAIAADCU4AkAAMBQgicAAABDCZ4AAAAMJXgCAAAwlOAJAADAUIInAAAAQwmeAAAA\nDCV4AgAAMJTgCQAAwFCCJwAAAEMJngAAAAwleAIAADCU4AkAAMBQgicAAABDCZ4AAAAMJXgCAAAw\nlOAJAADAUIInAAAAQwmeAAAADCV4AgAAMJTgCQAAwFCCJwAAAEMJngAAAAwleAIAADCU4AkAAMBQ\ngicAAABDCZ4AAAAMJXgCAAAwlOAJAADAUIInAAAAQwmeAAAADCV4AgAAMJTgCQAAwFCCJwAAAEMJ\nngAAAAwleAIAADCU4AkAAMBQgicAAABDCZ4AAAAMJXgCAAAwlOAJAADAUIInAAAAQwmeAAAADCV4\nAgAAMJTgCQAAwFCCJwAAAEMJngAAAAwleAIAADCU4AkAAMBQw4NnVd2nqv60qt5aVTdU1Qum5Q+p\nqmur6q+ral9VnTq3zyVV9a6qurGqdo6uEQAAgHGqu8efpOq+3f2pqjolyXVJfjzJuUk+1N0vqqqL\nkjy4uy+uqjOTvCrJ45OcnuS1SR7T3XfOHa8XUTcAAABJVaW760T3X0hX2+7+1DR57yT3TPLRzILn\n3mn53iRPmabPS3J5d9/e3TcnuSnJ2YuoEwAAgJNvIcGzqu5RVW9NcmuS13f3O5I8rLtvnTa5NcnD\npulHJNk/t/v+zFo+AQAA2IROWcRJpm6yZ1XVg5IsV9U3H7K+q+pofWf1qwUAANikFhI8D+ruj1fV\nHyb5qiS3VtXDu/v9VXVakg9Mm703yRlzuz1yWvYZ9uzZc9f00tJSlpaWRpUNAACwraysrGRlZeWk\nHW/44EJV9dAkd3T3x6pqR5LlJM9PsivJh7v70qq6OMmphwwudHbuHlzo0fOjCRlcCAAAYHHWOrjQ\nIlo8T0uyt6rukdkzpa/o7tdV1fVJrqiqH0xyc5KnJkl331BVVyS5IckdSZ4lZQIAAGxeC3mdysmm\nxRMAAGBxNsXrVAAAANi+BE8AAACGEjwBAAAYSvAEAABgKMETAACAoQRPAAAAhhI8AQAAGErwBAAA\nYCjBEwAAgKEETwAAAIYSPAEAABhK8AQAAGAowRMAAIChBE8AAACGEjwBAAAYSvAEAABgKMETAACA\noQRPAAAAhhI8AQAAGErwBAAAYCjBEwAAgKEETwAAAIYSPAEAABhK8AQAAGAowRMAAIChBE8AAACG\nEjwBAAAYSvAEAABgKMETAACAoQRPAAAAhhI8AQAAGErwBAAAYCjBEwAAgKEETwAAAIYSPAEAABhK\n8AQAAGAowRMAAIChBE8AAACGEjwBAAAYSvAEAABgKMETAACAoQRPAAAAhhI8AQAAGErwBAAAYCjB\nEwAAgKEETwAAAIYSPAEAABhK8AQAAGAowRMAAIChBE8AAACGEjwBAAAYSvAEAABgKMETAACAoQRP\nAAAAhhI8AQAAGErwBAAAYKjhwbOqzqiq11fVO6rqL6vqOdPyPVW1v6qun36ePLfPJVX1rqq6sap2\njq4RAACAcaq7x56g6uFJHt7db62q+yd5S5KnJHlqktu6+8WHbH9mklcleXyS05O8NsljuvvOuW16\ndN0AAADMVFW6u050/+Etnt39/u5+6zT9ySTvzCxQJsnhCj8vyeXdfXt335zkpiRnj64TAACAMRb6\njGdVfWGSxyV507To2VX1tqp6eVWdOi17RJL9c7vtz91BFQAAgE1mYcFz6mb735P82NTy+ZIkj0py\nVpJbklx2lN31qwUAANikTlnESarqXkmuTPI73f37SdLdH5hb/7Ik10yz701yxtzuj5yWfYY9e/bc\nNb20tJSlpaWTXTYAAMC2tLKykpWVlZN2vEUMLlRJ9ib5cHc/d275ad19yzT93CSP7+6nzw0udHbu\nHlzo0fOjCRlcCAAAYHHWOrjQIlo8vz7Jdyf5i6q6flr2k0m+q6rOyqwb7buTPDNJuvuGqroiyQ1J\n7kjyLCkTAABg8xre4jmCFk8AAIDF2fCvUwEAAGB7EzwBAAAYSvAEAABgKMETAACAoQRPAAAAhhI8\nAQAAGErwBAAAYCjBEwAAgKEETwAAAIYSPAEAABhK8AQAAGAowRMAAIChBE8AAACGEjwBAAAYSvAE\nAABgKMETAACAoQRPAAAAhhI8AQAAGErwBAAAYCjBEwAAgKEETwAAAIYSPAEAABhK8AQAAGAowRMA\nAIChBE8AAACGEjwBAAAYSvAEAABgKMETAACAoQRPAAAAhhI8AQAAGErwBAAAYCjBEwAAgKEETwAA\nAIYSPAEAABhK8AQAAGAowRMAAIChBE8AAACGEjwBAAAYSvAEAABgKMETAACAoQRPAAAAhhI8AQAA\nGErwBAAAYCjBEwAAgKEETwAAAIYSPAEAABhK8AQAAGAowRMAAIChBE8AAACGEjwBAAAYSvAEAABg\nKMETAACAoQRPAAAAhhI8AQAAGErwBAAAYCjBEwAAgKEETwAAAIYaHjyr6oyqen1VvaOq/rKqnjMt\nf0hVXVtVf11V+6rq1Ll9Lqmqd1XVjVW1c3SNAAAAjFPdPfYEVQ9P8vDufmtV3T/JW5I8Jcn3J/lQ\nd7+oqi5K8uDuvriqzkzyqiSPT3J6ktcmeUx33zl3zB5dNwAAADNVle6uE91/eItnd7+/u986TX8y\nyTszC5TnJtk7bbY3szCaJOcluby7b+/um5PclOTs0XUCAAAwxkKf8ayqL0zyuCR/muRh3X3rtOrW\nJA+bph+RZP/cbvszC6oAAABsQqcs6kRTN9srk/xYd99WdXcrbXd3VR2t7+xnrduzZ89d00tLS1la\nWjpptQIAAGxnKysrWVlZOWnHG/6MZ5JU1b2S/EGSP+ruX5yW3ZhkqbvfX1WnJXl9d39ZVV2cJN39\nwmm71yR5Xnf/6dzxPOMJAACwIAt9xnMaifYrj3OfSvLyJDccDJ2Tq5PsnqZ3J/n9ueXfWVX3rqpH\nJfmSJG8+nnMCAACwcRyzxbOq3pDk2zPrlvuWJB9M8j+7+7mrOkHVNyT5kyR/kbu7zF6SWZi8Isnn\nJ7k5yVO7+2PTPj+Z5AeS3JFZ19zlQ46pxRMAAGBB1triuZrg+dbuPquqfijJGd39vKp6e3c/9kRP\nulaCJwAAwOIsoqvtPadnMJ+a5A+nZVIfAAAAq7Ka4PnTSZaT/E13v7mqvjjJu8aWBQAAwFaxkFFt\nTzZdbQEAABZnrV1tj/gez6r6laPs1939nBM9KQAAANvHEYNnZiPYdpLDpVrNjQAAAKyKrrYAAAAc\n1ciutr/U3T9WVdccZnV397knelIAAAC2j6N1tf3t6c/LFlEIAAAAW5OutgAAABzVsK62cyd4TJKf\nS/IVSe4zLe7u/qITPSkAAADbxz1Wsc1vJfm1JLcnWUqyN8krB9YEAADAFrKa4Lmju1+bWbfcv+vu\nPUm+dWxZAAAAbBVHDJ5V9TXT5D9U1T2T3FRV/76q/k2S+y2kOgAAADa9Iw4uVFXXd/fjqursJO9M\ncmqSn0nywCQv6u43La7Mz6rN4EIAAAALstbBhY4ZPE+4soEETwAAgMUZGTw/luSNR9ivu/vcEz3p\nWgmeAAAAizPydSofTPLzSQ53cKkPAACAVTla8Pxkd79hYZUAAACwJR3tdSrvXlgVAAAAbFlHfMZz\nI/OMJwAAwOKs9RnPo7V4AgAAwJoJngAAAAx1XMGzqvYMqgMAAIAt6nhbPM8bUgUAAABblq62AAAA\nDHVco9pW1T27+9MD61ltHUa1BQAAWJCFjmq7EUInAAAAm4uutgAAAAwleAIAADDUMYNnVf2HqnpQ\nzby8qq6vql2LKA4AAIDNbzUtnj/Q3R9PsjPJQ5J8T5IXDq0KAACALWM1wfPgyEXfmuQV3f2XA+sB\nAABgi1lN8HxLVe1L8i1JlqvqgUnuHFsWAAAAW8Ux3+NZVfdI8rgkf9PdH6uqz01yenf/xSIKPEJN\n3uMJAACwIGt9j+cpRznwVyU5mO46yRdVnfB5AAAA2KaO2OJZVSuZBc4dSb4qycEWzq9M8ufd/bWL\nKPBwtHgCAAAszlpbPI/4jGd3L3X3Nyd5X5J/2d1f1d1flVm32/ed6AkBAADYXlYzuNCXdffbD85M\no9p++biSAAAA2EqO+IznnL+oqpcl+Z3MXq3y9CRvG1oVAAAAW8ZqRrXdkeRHknzjtOhPkryku/9h\ncG1Hq8kzngAAAAuy1mc8jxk8NyLBEwAAYHGGvU5l7gSPSfJzSc7MbITbJOnu/qITPSkAAADbx2oG\nF/qtJL+W5I4k35xkb5JXjiwKAACArWM1wXNHd782s265N3f3niTfOrYsAAAAtorVjGr7D1V1zyQ3\nVdW/z+wdnvcbWxYAAABbxWpGtT07yTuTnJrkZ5I8MMmLuvtN48s7Yk0GFwIAAFiQhY1qW1X37e5P\nneiJTibBEwAAYHHWGjyP+YxnVX1dVd2Q5K+m+X9RVb96oicEAABge1nN4EK/mORJST6UJN39tiRP\nGFkUAAAAW8dqgme6+z2HLLpjQC0AAABsQasZ1fY9VfX1SVJV907ynMwGGwIAAIBjWk2L548k+dEk\npyd5b5LHTfMAAABwTKse1XYjMaotAADA4qx1VNsjdrWtql+Zm+0k8yfp7n7OiZ4UAACA7eNoz3i+\nJXcHzucn+ancHT41NwIAALAqq+pqW1XXd/fjFlDPquhqCwAAsDhr7Wq7qteprEVV/WZV3VpVb59b\ntqeq9lfV9dPPk+fWXVJV76qqG6tq5+j6AAAAGGt48EzyW0medMiyTvLi7n7c9PNHSVJVZyZ5WpIz\np31+taoWUSMAAACDHG1woU/m7mc5d1TVbXOru7sfuJoTdPcbq+oLD3eKwyw7L8nl3X17kpur6qYk\nZyd502rOBQAAwMZzxNbE7r5/dz9g+jllbvoBqw2dx/DsqnpbVb28qk6dlj0iyf65bfZn9v5QAAAA\nNqn16sb6kiSPSnJWkluSXHaUbY0iBAAAsIkd7XUqw3T3Bw5OV9XLklwzzb43yRlzmz5yWvZZ9uzZ\nc9f00tJSlpaWTnaZAAAA29LKykpWVlZO2vFW9TqVNZ9k9oznNd392Gn+tO6+ZZp+bpLHd/fTp8GF\nXpXZc52nJ3ltkkcf+u4Ur1MBAABYnLW+TmV4i2dVXZ7kCUkeWlV/n+R5SZaq6qzMutG+O8kzk6S7\nb6iqK5LckOSOJM+SMAEAADa3hbR4nmxaPAEAABZnrS2e3pEJAADAUIInAAAAQwmeAAAADCV4AgAA\nMJTgCQAAwFCCJwAAAEMJngAAAAwleAIAADCU4AkAAMBQgicAAABDCZ4AAAAMJXgCAAAwlOAJAADA\nUIInAAAAQwmeAAAADCV4AgAAMJTgCQAAwFCCJwAAAEMJngAAAAwleAIAADCU4AkAAMBQgicAAABD\nCZ4AAAAMJXgCAAAwlOAJAADAUIInAAAAQwmeAAAADCV4AgAAMJTgCQAAwFCCJwAAAEMJngAAAAwl\neAIAADCU4AkAAMBQgicAAABDCZ4AAAAMJXgCAAAwlOAJAADAUIInAAAAQwmeAAAADCV4AgAAMJTg\nCQAAwFD26wo8AAAUqklEQVSCJwAAAEMJngAAAAwleAIAADCU4AkAAMBQgicAAABDCZ4AAAAMJXgC\nAAAwlOAJAADAUIInAAAAQwmeAAAADCV4AgAAMJTgCQAAwFCCJwAAAEMJngAAAAwleAIAADDU8OBZ\nVb9ZVbdW1dvnlj2kqq6tqr+uqn1Vdercukuq6l1VdWNV7RxdHwAAAGMtosXzt5I86ZBlFye5trsf\nk+R103yq6swkT0ty5rTPr1aVVlkAAIBNbHio6+43JvnoIYvPTbJ3mt6b5CnT9HlJLu/u27v75iQ3\nJTl7dI0AAACMs16tiQ/r7lun6VuTPGyafkSS/XPb7U9y+iILAwAA4ORa926s3d1J+mibLKoWAAAA\nTr5T1um8t1bVw7v7/VV1WpIPTMvfm+SMue0eOS37LHv27LlremlpKUtLS2MqBQAA2GZWVlaysrJy\n0o5XswbHsarqC5Nc092PneZflOTD3X1pVV2c5NTuvngaXOhVmT3XeXqS1yZ5dB9SZFUduggAAIBB\nqirdXSe6//AWz6q6PMkTkjy0qv4+yU8leWGSK6rqB5PcnOSpSdLdN1TVFUluSHJHkmdJmAAAAJvb\nQlo8TzYtngAAAIuz1hbPdR9cCAAAgK1N8AQAAGAowRMAAIChBE8AAACGEjwBAAAYSvAEAABgKMET\nAACAoQRPAAAAhhI8AQAAGErwBAAAYCjBEwAAgKEETwAAAIYSPAEAABhK8AQAAGAowRMAAIChBE8A\nAFij5eXl7Nx5QXbuvCDLy8vrXU6SjVkT21d193rXcNyqqjdj3QAAbD3Ly8s5//zdOXDg0iTJjh0X\n5aqr9mbXrl1qYsuoqnR3nfD+mzHACZ4AAGwUO3dekGuvPTfJ7mnJ3pxzztXZt+9KNbFlrDV46moL\nAADAUKesdwEAALCZXXjhM3Lddbtz4MBsfseOi3LhhXvVBHN0tQUA4IiWl5dz2WUvTTILM54RPLyN\neJ02Yk1sXp7xBABgCAPUAAcJngAADGGAGuAggwsBAACwoRlcCACAwzJADXCy6GoLAMARGaAGSDzj\nCQAAwGCe8QQAAGBDEzwBAAAYSvAEAABgKMETAACAoQRPAAAAhhI8AQAAGErwBAAAYCjBEwAAgKEE\nTwAAAIYSPAEAABhK8AQAAGAowRMAAIChBE8AAACGEjwBAAAYSvAEAABgKMETAACAoQRPAAAAhhI8\nAQAAGErwBAAAYCjBEwAAgKEETwAAAIYSPAEAABhK8AQAAGAowRMAAIChBE8AAACGEjwBAAAYSvAE\nAABgKMETAIBNZXl5OTt3XpCdOy/I8vLyepcDrEJ193rXcNyqqjdj3QAArM3y8nLOP393Dhy4NEmy\nY8dFueqqvdm1a9c6VwZbW1Wlu+uE91/PAFdVNyf5RJJPJ7m9u8+uqock+d0kX5Dk5iRP7e6PHbKf\n4AkAsA3t3HlBrr323CS7pyV7c845V2ffvivXsyzY8tYaPNe7q20nWerux3X32dOyi5Nc292PSfK6\naR4AAIBN6pT1LiDJoan53CRPmKb3JlmJ8AkAQJILL3xGrrtudw4cmM3v2HFRLrxw7/oWBRzTene1\n/dskH8+sq+2vd/dvVNVHu/vB0/pK8pGD83P76WoLALBNLS8v57LLXppkFkQ93wnjbfZnPE/r7luq\n6vOSXJvk2Umung+aVfWR7n7IIfsJngAAAAuy1uC5rl1tu/uW6c8PVtVVSc5OcmtVPby7319VpyX5\nwOH23bNnz13TS0tLWVpaGl8wAADANrCyspKVlZWTdrx1a/GsqvsmuWd331ZV90uyL8nzk/xfST7c\n3ZdW1cVJTu3uiw/ZV4snAADAgmzarrZV9agkV02zpyR5ZXe/YHqdyhVJPj9epwIAALDuNm3wXAvB\nEwAAYHE2+3s8AQAA2OIETwAAAIYSPAEAABhK8AQAAGAowRMAAIChBE8AAACGEjwBAAAYSvAEAABg\nKMETAACAoQRPAAAAhhI8AQAAGErwBAAAYCjBEwAAgKEETwAAAIYSPAEAABhK8AQAAGAowRMAAICh\nBE8AAACGEjwBAAAYSvAEAABgKMETAACAoQRPAAAAhhI8AQAAGErwBADYAJaXl7Nz5wXZufOCLC8v\nr3c5ACdVdfd613Dcqqo3Y90AAIezvLyc88/fnQMHLk2S7NhxUa66am927dq1zpUBzFRVurtOeP/N\nGOAETwBgK9m584Jce+25SXZPS/bmnHOuzr59V65nWQB3WWvw1NUWAACAoU5Z7wIAALa7Cy98Rq67\nbncOHJjN79hxUS68cO/6FgVwEulqCwCwASwvL+eyy16aZBZEPd8JbCSe8QQAAGAoz3gCAACwoQme\nAAAADCV4AgAAMJTgCQAAwFCCJwAAAEMJngAAAAwleAIAADCU4AkAAMBQgicAAABDCZ4AAAAMJXgC\nAAAwlOAJAADAUIInAAAAQwmeAAAADCV4Aqyj5eXl7Nx5QXbuvCDLy8vrXQ5bgN8pADai6u71ruG4\nVVVvxroB5i0vL+f883fnwIFLkyQ7dlyUq67am127dq1zZWxWfqcAGKWq0t11wvtvxgAneAJbwc6d\nF+Taa89NsntasjfnnHN19u27cj3LYhPzOwXAKGsNnrraAgAAMNQp610AwHZ14YXPyHXX7c6BA7P5\nHTsuyoUX7l3fotjU/E4BsFHpagtsG8vLy7nsspcmmf0FfSM897YRa2Jz8zsFwAie8QRYBYOuAACc\nOM94wjbn1Qmrc9llL51C5+4kswB6sFWIz+R3CgA42TzjCZvYoa141123Wysea+J3CgAYQfCETewz\nW/GSAwdmy4SEz2bQldXxOwUAjKCrLRwHXRBXb6Ndq127duWqq2bvNDznnKu14gEALJDBhdiwNtrI\njBtxcJqNWNNGrotjc+8AgMPZkqPaVtWTkvxiknsmeVl3X3rIesFzi9uIf/ndufOCXHvtuTnYBTGZ\ntZ7t23flutWUbLyAnmzca8XqbMTfKQBgfW25UW2r6p5J/kuSJyU5M8l3VdWXr29VLJoRSFdv165d\n2bfvyuzbd6WAwEmxEX+nNlrX7YM2al0bzUa8ThuxJoCtbCMOLnR2kpu6++YkqapXJzkvyTvXsygw\nOM3quVacTBt1pN2NWtdGsxGv00asCWCr23Bdbavq3ybZ1d3/bpr/7iT/qrufPbeNrrZb3Ebsanuw\nLl0QV8e14mTZqF23N2pdG81GvE4bsSaAjW6tXW03YounRMldI5DeHVzWP3Qms7o2Qh2bgWsFAMBB\nGzF4vjfJGXPzZyTZf+hGe/bsuWt6aWkpS0tLo+tiwQQXINm4Xbc3al0bzUa8ThuxJoCNZmVlJSsr\nKyfteBuxq+0pSf4qyROTvC/Jm5N8V3e/c24bXW0BtpGN2nV7o9a10WzE67QRawLYyLbq61SenLtf\np/Ly7n7BIesFTwAAgAXZksHzWARPAACAxdly7/EEAABgaxE8AQAAGErwBAAAYCjBEwAAgKEETwAA\nAIYSPAEAABhK8AQAAGAowRMAAIChBE8AAACGEjwBAAAYSvAEAABgKMETAACAoQRPAAAAhhI8AQAA\nGErwBAAAYCjBEwAAgKEETwA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+ "text": [ + "" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\"\"\"Set up and show a scatter plot with log scale x-axis for ratio\"\"\"\n", + "x2 = [2**n for n in range(len(data))]\n", + "fig = plt.gcf()\n", + "fig.set_size_inches(15.5,10.5)\n", + "plt.xscale(\"log\")\n", + "plt.xlabel(\"Number of Flips\")\n", + "plt.ylabel(\"Heads / Tails\")\n", + "plt.title(\"Ratio of Heads to Tails\")\n", + "plt.scatter(x2, ratio)\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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YsSuTJEtL+3Po0MHs2bNnwZUBsB1UVbq71n3+VghwgiYA3NHy8t4cOXJpkn2zZw7m4ouv\ny+HD1y6yLAC2iXMNmqbOAgAAMNSuRRcAAJy9lZXLc/31+3Ls2HR7aWl/VlYOLrYoAJgxdRYAtqjJ\nZJKrrro6yTR4Wp8JwCjWaAIAADCUNZoAAABsKoImAAAAQwmaAAAADCVoAgAAMJSgCQAAwFCCJgAA\nAEMJmgAAAAwlaAIAADCUoAkAAMBQgiYAAABDCZoAAAAMJWgCAAAwlKAJAADAUIImAAAAQwmaAAAA\nDCVoAgAAMJSgCQAAwFCCJgAAAEMJmgAAAAwlaAIAADCUoAkAAMBQgiYAAABDCZoAAAAMJWgCAAAw\nlKAJAADAUIImAAAAQwmaAAAADCVoAgAAMJSgCQAAwFCCJgAAAEMJmgAAAAwlaAIAADCUoAkAAMBQ\ngiYAAABDCZoAAAAMJWgCAAAwlKAJAADAUIImAAAAQwmaAAAADCVoAgAAMJSgCQAAwFCCJsAON5lM\nsry8N8vLezOZTBZdDgCwDVR3L7qGM6qq3gp1Amw1k8kkl122L8eOXZkkWVran0OHDmbPnj0LrgwA\nWKSqSnfXus/fCgFO0ASYj+XlvTly5NIk+2bPHMzFF1+Xw4evXWRZAMCCnWvQNHUWAACAoXYtugAA\nFmdl5fJcf/2+HDs23V5a2p+VlYOLLQoA2PJMnQXY4SaTSa666uok0+BpfSYAYI0mAAAAQ1mjCQAA\nwKYiaAIAADCUoAkAAMBQgiYAAABDCZoAAAAMJWgCAAAwlKAJAADAUIImAAAAQwmaAAAADCVoAgAA\nMJSgCQAAwFCCJgAAAEMJmgAAAAwlaAIAADCUoAkAAMBQgiYAAABDCZoAAAAMJWgCAAAwlKAJAADA\nUIImAAAAQ801aFbVJVV1U1W9s6r2n2T/farqt6vqLVX19qp6+jzrAQAAYP6qu+fTcNV5Sd6R5OuS\nvDfJG5M8tbtvXHXMgSSf3d0/WFX3mR1/3+6+9YS2el51AgAAcEdVle6u9Z4/zxHNi5Lc3N3v7u5P\nJbkmyVNOOOYvk5w/e3x+kg+dGDIBAADYWnbNse0Lktyyavs9SR59wjEvS/I7VfW+JHdP8q/nWA8A\nAAAbYJ4jmmuZ6/p/JHlLd39hki9P8p+r6u5zrAkAAIA5m+eI5nuT3H/V9v0zHdVc7auT/GiSdPe7\nqurPknxJkjed2NiBAwdue7x79+7s3r17bLUAAAA71NGjR3P06NFh7c3zZkC7Mr25zxOSvC/JG3Ln\nmwH9RJKPdvfzquq+Sf4oySO7+29OaMvNgAAAADbIud4MaG4jmt19a1VdkWSS5LwkL+/uG6vqWbP9\nL03y/CSvqKq3ZjqN9/tPDJkAAABsLXMb0RzJiCYAAMDG2cwfbwIAAMAOJGgCAAAwlKAJAADAUIIm\nAAAAQwmaAAAADCVoAgAAMJSgCQAAwFCCJgAAAEMJmgAAAAwlaAIAADCUoAkAAMBQgiYAAABDCZoA\nAAAMJWgCAAAwlKAJAADAUIImAAAAQwmaAAAADCVoAgAAMJSgCQAAwFCCJgAAAEMJmgAAAAwlaAIA\nADCUoAkAAMBQgiYAAABDCZoAAAAMJWgCAAAwlKAJAADAUIImAAAAQwmaAAAADCVoAgAAMJSgCQAA\nwFCCJgAAAEMJmgAAAAwlaAIAADCUoAkAAMBQgiYAAABDCZoAAAAMJWgCAAAwlKAJAADAUIImAAAA\nQwmaAAAADCVoAgAAMJSgCQAAwFCCJgAAAEMJmgAAAAwlaAIAADCUoAkAAMBQgiYAAABDCZoAAAAM\nJWgCAAAwlKAJAADAUIImAAAAQwmaAAAADCVoAgAAMJSgCQAAwFCCJgAAAEMJmgAAAAwlaAIAADCU\noAkAAMBQgiYAAABDCZoAAAAMJWgCAAAwlKAJAADAUIImAAAAQ50xaFbVj1fV+VV116p6dVV9sKqe\nthHFAQAAsPWsZURzubs/luTrk7w7yYOT/Id5FgUAAMDWtZaguWv299cn+bXu/miSnl9JAAAAbGW7\nznxIXlVVNyX5+yTPrqovmD0GAACAO6nuMw9OVtW9k3ykuz9dVXdLcvfu/qu5V3f79XstdQIAAHDu\nqirdXes9/5QjmlW1NydMka2q4xfqJL++3osCAACwfZ1u6uw35PRrMQVNAAAA7mRNU2cXzdRZAACA\njTPPqbPf3t2/WFUrmY5s1uq/u/sn1ntRAAAAtq/TTZ292+zvu+eOU2grPt4EAACAUzB1FgAAgDuY\n29TZVRdYSvLMJF+aZCmz0czu/s71XhQAAIDt6y5rOOYXktw3ySVJjia5f5JPzLEmAAAAtrAzTp2t\nqrd095dX1du6+5FVddck13f3ozemRFNnAQAANtK5Tp095YhmVR2fVvvJ2d8frapHJLlnks9f7wUB\nAADY3k43dfYNs79fVlX3SvJDSa5LckOSH5t3YQAAAGxNp5w6W1Vv7u4LN7iekzJ1FgAAYOPM866z\nn19V/z7Tz808rmfb3d0/sd6LAgAAsH2dLmiel+TuG1UIAAAA24OpswAAANzB3O46CwAAAOtxuhHN\ne3f3hza4npMyogkAALBxznVE85RBczMRNAEAADaOqbMAAABsKqcMmlU1qarvraqHbWRBAAAAbG2n\nG9F8epKPJDlQVW+uqp+pqqdU1d3W2nhVXVJVN1XVO6tq/ymO2T1r/+1VdfSsqgcAAGDTWdMazao6\nL8mjkzwxydcm+fskk+7+sTOc844kX5fkvUnemOSp3X3jqmPumeS1SfZ093uq6j7d/cGTtGWNJgAA\nwAbZkDWa3f3p7v6D7v6P3f01Sb4l0/B4Ohclubm7393dn0pyTZKnnHDMtya5trvfM7vOnUImAAAA\nW8u6bgbU3R/o7l86w2EXJLll1fZ7Zs+t9sVJ7lVVv1tVb6qqp62nHgAAADaPXXNsey1zXe+a5CuS\nPCHJ5yR5XVX9YXe/c451AQAAMEfzDJrvTXL/Vdv3z3RUc7Vbknywu48lOVZVv5/ky5LcKWgeOHDg\ntse7d+/O7t27B5cLAACwMx09ejRHjx4d1t4ZbwZUVf97klck+ViSn810BPIHuntyhvN2ZXozoCck\neV+SN+TONwN6WJIXJ9mT5LOTvD7JN3f3DSe05WZAAAAAG2Qjbgb0nd390STLSe6V5GlJXnCmk7r7\n1iRXJJkkuSHJr3T3jVX1rKp61uyYm5L8dpK3ZRoyX3ZiyAQAAGBrWcuI5p909yOq6kVJjnb3r1fV\nm7v7wo0p0YgmAADARtqIEc0/qqrDSZ6UZFJV5yf5zHovCAAAwPa2lhHNuyS5MMm7uvsjVXXvJBd0\n99s2osBZDUY0AQAANsi5jmie8q6zVfWo3P4RJZ3kQVXrvg4AAAA7xClHNKvqaKYBcynJozK9YU+S\nPDLJm7r7qzaiwFktRjQBAAA2yNzWaHb37u5+fKYfTfIV3f2o7n5UptNo37feCwIAALC9reVmQA/r\n7j85vtHdb0/y8PmVBAAAwFZ2yjWaq7ytqn42yS8mqSTfmuStc60KAACALWstI5rPSHJDkv8tyXNm\nj58xz6KArWUymWR5eW+Wl/dmMpksuhwAABbsjB9vshm4GRBsXpPJJJddti/Hjl2ZJFla2p9Dhw5m\nz549C64MAID1OtebAa3lczQfmuT5Sb400zvQJkl394PWe9GzJWjC5rW8vDdHjlyaZN/smYO5+OLr\ncvjwtYssCwCAczC3u86u8ookP5Pk1iSPT3IwyS+t94IAAABsb2sJmkvd/d8zHf18d3cfSPLk+ZYF\nbBUrK5dnaWl/pr+DOpilpf1ZWbl80WUBALBAa7nr7N9X1XlJbq6qKzL9DM27zbcsYKvYs2dPDh06\nmKuuujpJsrJifSYAwE63ljWaFyW5Mck9k/xIkvOT/Fh3/+H8y7utBms0AQAANsjcbwa06kKf091/\nt94LnQtBEwAAYOPM/WZAVfXVVXVDknfMtr+sqv7Lei8IAADA9raWmwG9MMklST6YJN391iSPm2dR\nAAAAbF1rCZrp7r844alb51ALAAAA28Ba7jr7F1X1NUlSVZ+V5DmZ3hwIAAAA7mQtI5rPTvLdSS5I\n8t4kF862AQAA4E7WfNfZRXLXWQAAgI1zrnedPeXU2ar66VWbnWT1Rbq7n7PeiwIAALB9nW6N5h/l\n9oD5vCQ/nNvDpuFFAAAATmpNU2er6s3dfeEG1HOq65s6CwAAsEHOdersmj7eBAAAANZK0AQAAGCo\n090M6BO5fS3mUlV9fNXu7u7z51oZAAAAW9Ipg2Z3f+5GFgIAAMD2YOosAAAAQwmaAAAADCVoAgAA\nMJSgCbBBJpNJlpf3Znl5byaTyaLLAQCYm+ruMx+1YFXVW6FOgFOZTCa57LJ9OXbsyiTJ0tL+HDp0\nMHv27FlwZQAAd1ZV6e5a9/lbIcAJmsBWt7y8N0eOXJpk3+yZg7n44uty+PC1iywLAOCkzjVomjoL\nAADAUKf8HE0AxllZuTzXX78vx45Nt5eW9mdl5eBiiwIAmBNTZwE2yGQyyVVXXZ1kGjytzwQANitr\nNAEAABjKGk0AAAA2FUETAACAoQRNAAAAhhI0AQAAGErQBAAAYChBEwAAgKEETQAAAIYSNAEAABhK\n0AQAAGAoQRMAAIChBE0AAACGEjQBAAAYStAEAABgKEETAACAoQRNAAAAhhI0AQAAGErQBAAAYChB\nEwAAgKEETQAAAIYSNAEAABhK0AQAAGAoQRMAAIChBE0AAACGEjSBbWkymWR5eW+Wl/dmMpksuhwA\ngB2lunvRNZxRVfVWqBPYHCaTSS67bF+OHbsySbK0tD+HDh3Mnj17FlwZAMDWUFXp7lr3+VshwAma\nwNlYXt6bI0cuTbJv9szBXHzxdTl8+NpFlgUAsGWca9A0dRYAAIChdi26AIDRVlYuz/XX78uxY9Pt\npaX9WVk5uNiiAAB2EFNngW1pMpnkqquuTjINntZnAgCsnTWaAAAADGWNJgAAAJuKoAkAAMBQgiYA\nAABDCZoAAAAMJWgCAAAwlKAJAADAUIImAAAAQwmaAAAADCVoAgAAMJSgCQAAwFCCJgAAAEMJmgAA\nAAwlaAIAADCUoAkAAMBQgiYAAABDCZoAAAAMJWgCAAAwlKAJAADAUIImAAAAQwmaAAAADCVoAgAA\nMNRcg2ZVXVJVN1XVO6tq/2mO+8qqurWqvnGe9QAAADB/cwuaVXVekhcnuSTJlyZ5alU9/BTHXZnk\nt5PUvOoBAABgY8xzRPOiJDd397u7+1NJrknylJMc9z1Jfi3JB+ZYCwAAABtknkHzgiS3rNp+z+y5\n21TVBZmGz5fMnuo51gMAAMAGmGfQXEtofGGSH+juznTarKmzAAAAW9yuObb93iT3X7V9/0xHNVd7\nVJJrqipJ7pPkiVX1qe6+7sTGDhw4cNvj3bt3Z/fu3YPLBQAA2JmOHj2ao0ePDmuvpoOJ41XVriTv\nSPKEJO9L8oYkT+3uG09x/CuSvKq7f/0k+3pedQIAAHBHVZXuXveM07mNaHb3rVV1RZJJkvOSvLy7\nb6yqZ832v3Re1wYAAGBx5jaiOZIRTQAAgI1zriOa87wZEAAAADuQoAkAAMBQgiYAAABDCZoAAAAM\nJWgCAAAwlKAJAADAUIImAAAAQwmaAAAADCVoAgAAMJSgCQAAwFCCJgAAAEMJmgAAAAwlaAIAADCU\noAkAAMBQgiYAAABDCZoAAAAMJWgCAAAwlKAJAADAUIImAAAAQwmaAAAADCVoAgAAMJSgCQAAwFCC\nJgAAAEMJmgAAAAwlaAIAADCUoMmmMZlMsry8N8vLezOZTBZdDgAAsE7V3Yuu4YyqqrdCnazfZDLJ\nZZfty7FjVyZJlpb259Chg9mzZ8+CKwMAgJ2nqtLdte7zt0KAEzS3v+XlvTly5NIk+2bPHMzFF1+X\nw4evXWRZAACwI51r0DR1FgAAgKF2LboASJKVlctz/fX7cuzYdHtpaX9WVg4utigAAGBdTJ1l05hM\nJrnqqquTTIOn9ZkAALAY1mgCAAAwlDWaAAAAbCqCJgAAAEMJmgAAAAwlaAIAADCUoAkAAMBQgiYA\nAABDCZoAAAAMJWgCAAAwlKAJAADAUIImAAAAQwmaAAAADCVoAgAAMJSgCQAAwFCCJgAAAEMJmgAA\nAAwlaAI9fHx8AAAO4ElEQVQAADCUoAkAAMBQgiYAAABDCZoAAAAMJWgCAAAwlKAJAADAUIImAAAA\nQwmaAAAADCVoAgAAMJSgCQAAwFCCJgAAAEMJmgAAAAwlaAIAADCUoAkAAMBQgiYAAABDCZoAAAAM\nJWgCAAAwlKAJAADAUIImAAAAQwmacBqTySTLy3uzvLw3k8lk0eUAAMCWUN296BrOqKp6K9TJ9jKZ\nTHLZZfty7NiVSZKlpf05dOhg9uzZs+DKAABgvqoq3V3rPn8rBDhBk0VYXt6bI0cuTbJv9szBXHzx\ndTl8+NpFlgUAAHN3rkHT1FkAAACG2rXoAmCzWlm5PNdfvy/Hjk23l5b2Z2Xl4GKLAgCALcDUWTiN\nyWSSq666Osk0eFqfCQDATmCNJgAAAENZowkAAMCmImgCAAAwlKAJAADAUIImAAAAQwmaAAAADCVo\nAgAAMJSgCQAAwFCCJgAAAEMJmgAAAAwlaAIAADCUoAkAAMBQgiYAAABDCZoAAAAMJWgCAAAwlKAJ\nAADAUHMPmlV1SVXdVFXvrKr9J9n/bVX11qp6W1W9tqoeOe+aAAAAmJ/q7vk1XnVeknck+bok703y\nxiRP7e4bVx3zVUlu6O6PVtUlSQ5092NOaKfnWScAAAC3q6p0d633/HmPaF6U5Obufnd3fyrJNUme\nsvqA7n5dd390tvn6JPebc00AAADM0byD5gVJblm1/Z7Zc6fyzCS/NdeKAAAAmKtdc25/zfNdq+rx\nSb4zydfMrxwAAADmbd5B871J7r9q+/6ZjmrewewGQC9Lckl3f/hkDR04cOC2x7t3787u3btH1gkA\nALBjHT16NEePHh3W3rxvBrQr05sBPSHJ+5K8IXe+GdAXJfmdJN/e3X94inbcDAgAAGCDnOvNgOY6\notndt1bVFUkmSc5L8vLuvrGqnjXb/9IkP5zk85K8pKqS5FPdfdE86wIAAGB+5jqiOYoRTQAAgI2z\n2T/eBAAAgB1G0AQAAGAoQRMAAIChBE0AAACGEjQBAAAYStAEAABgKEETAACAoQRNAAAAhhI0AQAA\nGErQBAAAYChBE7aYyWSS5eW9WV7em8lksuhyAADgTqq7F13DGVVVb4U6Yd4mk0kuu2xfjh27Mkmy\ntLQ/hw4dzJ49exZcGQAA20lVpbtr3edvhQAnaMLU8vLeHDlyaZJ9s2cO5uKLr8vhw9cusiwAALaZ\ncw2aps4CAAAw1K5FFwCs3crK5bn++n05dmy6vbS0PysrBxdbFAAAnMDUWdhiJpNJrrrq6iTT4Gl9\nJgAAo1mjCQAAwFDWaAIAALCpCJoAAAAMJWgCAAAwlKAJAADAUIImAAAAQwmaAAAADCVoAgAAMJSg\nCQAAwFCCJgAAAEMJmgAAAAwlaAIAADCUoAkAAMBQgiYAAABDCZoAAAAMJWgCAAAwlKAJAADAUIIm\nAAAAQwmaAAAADCVoAgAAMJSgCQAAwFCCJgAAAEMJmgAAAAwlaAIAADCUoAkAAMBQgiYAAABDCZoA\nAAAMJWgCAAAwlKAJAADAUIImAAAAQwmaAAAADCVoAgAAMJSgCQAAwFCCJgAAAEMJmgAAAAwlaAIA\nADCUoAkAAMBQgiYAAABDCZoAAAAMJWgCAAAwlKAJAADAUIImAAAAQwmaAAAADCVoAgAAMJSgCQAA\nwFCCJgAAAEMJmgAAAAwlaAIAADCUoAkAAMBQgiYAAABDCZoAAAAMJWgCAAAwlKAJAADAUIImAAAA\nQwmaAAAADCVoAgAAMJSgCQAAwFCCJgAAAEMJmgAAAAwlaAIAADCUoAkAAMBQgiYAAABDCZoAAAAM\nJWgCAAAwlKAJAADAUIImAAAAQwmaAAAADCVoAgAAMJSgCQAAwFCCJgAAAEMJmgAAAAwlaAIAADCU\noAkAAMBQcw2aVXVJVd1UVe+sqv2nOOZFs/1vraoL51kPAAAA8ze3oFlV5yV5cZJLknxpkqdW1cNP\nOOZJSR7S3V+c5PIkL5lXPWwdR48eXXQJbBB9vbPo751DX+8s+nvn0NecjXmOaF6U5Obufnd3fyrJ\nNUmecsIxlyY5mCTd/fok96yq+86xJrYA38R2Dn29s+jvnUNf7yz6e+fQ15yNeQbNC5Lcsmr7PbPn\nznTM/eZY0zDzeqOdS7tne+5ajz/Tcevdv5W+Wc2j1nNtczP2t76eT7ubsa9Pt19/b7/+Xu++zWQz\n9vV6zl/L8ed6jPf2fNr13p6PzdjX6zl/O7635xk0e43H1TrPW6jN+I96M34DO93+rfINLBE017pf\nX8+n3c3Y16fbr7+3X3/7YXR+7fphdD42Y397b8/HZuzr9Zy/Hd/b1T2fXFdVj0lyoLsvmW3/YJLP\ndPeVq475mSRHu/ua2fZNSR7X3e8/oa0tET4BAAC2i+4+cVBwzXaNLOQEb0ryxVX1wCTvS/LNSZ56\nwjHXJbkiyTWzYPqRE0Nmcm4vEAAAgI01t6DZ3bdW1RVJJknOS/Ly7r6xqp412//S7v6tqnpSVd2c\n5G+TPGNe9QAAALAx5jZ1FgAAgJ1pnjcDAgAAYAcSNAEAABhqywbNqvonVfWzVfWri66F+amqu1XV\nwaq6uqq+ddH1MF/e1ztHVT1l9r6+pqouXnQ9zFdVPayqXlJVr6yqZy66HuZr9n/3G6vqyYuuhfmq\nqt1V9ZrZ+/txi66H+ampH62qF1XVd6zlnC0bNLv7z7r7uxZdB3P3jUle2d2XJ7l00cUwX97XO0d3\n/+bsff1vM70rOdtYd9/U3c9O8i1J9iy6Hubu+5P8yqKLYEN8JsnHk3x2kvcsuBbm618muSDJJ7PG\nvl540Kyqn6uq91fVn5zw/CVVdVNVvbOq9i+qPsY7yz6/IMkts8ef3tBCGcJ7fOdYZ1//UJIXb1yV\njHK2/V1V35Dk/01yzUbXyrk5m76ezVC4IckHFlEr5+4s39uv6e4nJfmBJM/b8GI5J2fZ1w9N8tru\n/r4kz15L+wsPmklekeSS1U9U1XmZ/uBxSZIvTfLUqnp4VT2tqn6yqr5wAXUyzpr7PNPfmNx/dthm\n+PfK2Tub/mZrO5vv51VVVyb5/7r7LRtfKgOc1Xu7u1/V3U9Msm+jC+WcnU1fPy7JY5J8a5J/U1U+\nC33rWXN/9+0fX/GRTEc12VrO9mfyj8wO+8xaGp/b52iuVXe/pqoeeMLTFyW5ubvfnSRVdU2Sp3T3\nC5L8wuy5eyV5fpIvr6r93X3lhhXNOTmbPk/yoiQvnq3zuG4Dy2SQs+nvqnp/vK+3rLN8b39dkick\nOb+qHtLdL93AUhngLN/bX5DpUoh/lOR3N7BMBjjLn9V+aLa9L8kHVgURtoizfG8/LNPp8PdM8tMb\nWCYDnOX/2z+V5Ker6rFJjq6l/YUHzVNYPV0ymSboR68+oLv/JtO1PWwPJ+3z7v67JN+5mJKYo1P1\nt/f19nOqvv6e+KFkOzpVf/9ekt9bTEnMyWl/VuvugxteEfN0qvf2C5IcWkxJzMmp+vpYkrO6j8Zm\nnYrot187jz7fWfT3zqGvdxb9vXPo651Ff+8cw/p6swbN9+b2dXmZPXYnq+1Nn+8s+nvn0Nc7i/7e\nOfT1zqK/d45hfb1Zg+abknx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+ "text": [ + "" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\"\"\"Run 20 simulations of 100000 iterations, rotate the 2d-array and find the mean of each row. Store data in a list\n", + "of means\"\"\"\n", + "\n", + "data_list = []\n", + "ratio_list = []\n", + "mean_list = []\n", + "\n", + "for count in range(20):\n", + " data = flip_coin_n_times(100000)\n", + " data_list.append(data)\n", + " \n", + "data_list = list(zip(*data_list[::-1]))\n", + "\n", + "for row in data_list:\n", + " ratio_list.append([item[0]/item[1] for item in row])\n", + "\n", + "for row in ratio_list:\n", + " mean_list.append(st.mean(row))\n" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 11 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\"\"\"Set up and show the scatter plot for the mean data using a log scale for the x-axis\"\"\"\n", + "x2 = [2**n for n in range(len(data))]\n", + "fig = plt.gcf()\n", + "fig.set_size_inches(15.5,10.5)\n", + "plt.xscale(\"log\")\n", + "plt.xlabel(\"Number of Flips\")\n", + "plt.ylabel(\"Mean of Ratios of Heads / Tails\")\n", + "plt.title(\"Means of Ratios of Heads to Tails\")\n", + "plt.scatter(x2, mean_list)\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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zLAsAgC1mvQFUF1wAAAC6OHfWBQDrt7CwPydO7Mvi4nh5bu5AFhYOz7YoAAA4hS64sEWM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\nJElSJyxAJUmSJEmdsACVJEmSJHXifxByVEzdAvCNAAAAAElFTkSuQmCC\n", + "text": [ + "" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\"\"\"Calculate the standard deviation of the ratio of heads to tails for each of the 20 simulations run in the previous section\"\"\"\n", + "std_dev_list = []\n", + "for row in ratio_list:\n", + " std_dev_list.append(st.stdev(row))" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 13 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\"\"\"Set up and display the scatter plot for the standard deviation data\"\"\"\n", + "x2 = [2**n for n in range(len(data))]\n", + "fig = plt.gcf()\n", + "fig.set_size_inches(15.5,10.5)\n", + "plt.xscale(\"log\")\n", + "plt.yscale(\"log\")\n", + "plt.xlabel(\"Number of Flips\")\n", + "plt.ylabel(\"Standard Deviation of Ratio of Heads / Tails\")\n", + "plt.title(\"Standard Deviations of Ratios of Heads to Tails\")\n", + "plt.scatter(x2, std_dev_list)\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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P1/ry4npfPqoqvSpDcKvq2Ul+O8knV9Wrq+oJ3f2eJF+bZJzklUl+fp7wyeVnlf7Hjb1x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\nbW/Ztv6itre2/UTbl6yrPvbfLnt+3yS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+ "text": [ + "" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The scatter plots show that at low sample size the mean of the data may seem to swing wildly, but at higher sample sizes the data equalizes an the mean settles almost exactly around one. The standard deviation graph shows that as sample size increases the standard deviation decreases linearly." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\"\"\"Run 100000 simulations of 100 coin flips. Calculate the ratio of heads to total flips\"\"\"\n", + "data_list = []\n", + "head_ratio = []\n", + "\n", + "for count in range(100000):\n", + " data = flip_coin_n_times(100)\n", + " data_list.append(data)\n", + "\n", + "for trial in data_list:\n", + " head_ratio.append(trial[len(trial)-1][0]/100)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 15 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\"\"\"Calculate the mean and standard deviation of the previous simulations\"\"\"\n", + "mean = st.mean(head_ratio)\n", + "std_dev = st.stdev(head_ratio)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 16 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\"\"\"Set up and display the histogram of the ratio of Heads results to total flips for the previous simulation.\"\"\"\n", + "plt.hist(head_ratio, bins=40)\n", + "fig = plt.gcf()\n", + "fig.set_size_inches(15.5,10.5)\n", + "plt.yscale(\"log\")\n", + "plt.xlabel(\"Trial\")\n", + "plt.ylabel(\"Head/Total Ratio\")\n", + "plt.title(\"Head/Total Ratio Histogram\\n\"\n", + " \"Mean = {}, Sandard Deviation = {}\".format(mean, std_dev))\n", + "\n", + "ymin, ymax = plt.ylim()\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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AwCQETgAAACaxsoFzNptlPp8fdDcAAACOrPl8ntlstuv2tYoHrVdVr2K/AVbF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\nwAkAAMAQAicAAABD/B8hBA254fk+IwAAAABJRU5ErkJggg==\n", + "text": [ + "" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\"\"\"Run 100000 simulations of 1000 coin flips. Calculate the ratio of heads to total flips for each simulation.\"\"\"\n", + "data_list = []\n", + "head_ratio2 = []\n", + "\n", + "for count in range(100000):\n", + " data = flip_coin_n_times(1000)\n", + " data_list.append(data)\n", + "\n", + "for trial in data_list:\n", + " head_ratio2.append(trial[len(trial)-1][0]/1000)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 18 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\"\"\"Calculate the mean and standard deviation of the previous simulations.\"\"\"\n", + "mean = st.mean(head_ratio2)\n", + "std_dev = st.stdev(head_ratio2)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 19 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\"\"\"Set up and display the histgram for the previous simulations.\"\"\"\n", + "plt.hist(head_ratio2, bins=40)\n", + "fig = plt.gcf()\n", + "fig.set_size_inches(15.5,10.5)\n", + "plt.yscale(\"log\")\n", + "plt.xlabel(\"Trial\")\n", + "plt.ylabel(\"Head/Total Ratio\")\n", + "plt.title(\"Head/Total Ratio Histogram\\n\"\n", + " \"Mean = {}, Sandard Deviation = {}\".format(mean, std_dev))\n", + "\n", + "ymin, ymax = plt.ylim()\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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AwOgUnwAAAIxO8QkAAMDoFJ8AAACMTvEJAADA6BSfAAAAjE7xCQAAwOgUnwAA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\n", + "text": [ + "" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\"\"\"Set up and display the box plot comparing the last two simulations.\"\"\"\n", + "fig = plt.gcf()\n", + "fig.set_size_inches(15.5,10.5)\n", + "plt.boxplot([head_ratio, head_ratio2])\n", + "ymin, ymax = plt.ylim()\n", + "plt.ylim(ymin - .1, ymax + .1)\n", + "plt.title(\"Proportion of Heads in Simulations\")\n", + "plt.ylabel(\"Proportion of Heads\")\n", + "plt.xticks(range(1,3), [\"100/100000\", \"1000/100000\"])\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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AABgmRAIAADBMiIQlt7a26AoAANhLhEhYckIkAADHQ4gEAABg2MFFFwDsvrW1Iy2QF110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\nw4RIAAAAhgmRAAAADBMiAQA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+ "text": [ + "" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The histograms show that the results of coin flips have a normal distribution. Most of the runs of coin flips fall very close to a 50% ratio of heads. Again, a tenfold increase in sample size shows a dramatic decrease in the variability of the simulation. " + ] + } + ], + "metadata": {} + } + ] +} \ No newline at end of file