{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Cookie Problem"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Imports"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import scipy as sp\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns\n",
"import empiricaldist\n",
"from empiricaldist import Pmf, Distribution\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Basics Pmf"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"
\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" probs | \n",
"
\n",
" \n",
" \n",
" \n",
"
\n",
"
"
],
"text/plain": [
"Pmf([], dtype: float64)"
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"d6 = Pmf(); d6"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" probs | \n",
"
\n",
" \n",
" \n",
" \n",
" 1 | \n",
" 1 | \n",
"
\n",
" \n",
" 2 | \n",
" 1 | \n",
"
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" \n",
" 3 | \n",
" 1 | \n",
"
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" \n",
" 4 | \n",
" 1 | \n",
"
\n",
" \n",
" 5 | \n",
" 1 | \n",
"
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" \n",
" 6 | \n",
" 1 | \n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
"1 1\n",
"2 1\n",
"3 1\n",
"4 1\n",
"5 1\n",
"6 1\n",
"dtype: int64"
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"for i in range(6):\n",
"# print(i+1)\n",
" d6[i+1] = 1\n",
" \n",
"d6"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# Pmf??"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# Distribution??"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" probs | \n",
"
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" \n",
" \n",
" \n",
" 1 | \n",
" 0.166667 | \n",
"
\n",
" \n",
" 2 | \n",
" 0.166667 | \n",
"
\n",
" \n",
" 3 | \n",
" 0.166667 | \n",
"
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" \n",
" 4 | \n",
" 0.166667 | \n",
"
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" \n",
" 5 | \n",
" 0.166667 | \n",
"
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" \n",
" 6 | \n",
" 0.166667 | \n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
"1 0.166667\n",
"2 0.166667\n",
"3 0.166667\n",
"4 0.166667\n",
"5 0.166667\n",
"6 0.166667\n",
"dtype: float64"
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"d6.normalize(); d6"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# d6"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"3.5"
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"d6.mean()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([5, 5, 5, 1, 6, 2, 6, 1, 6, 2])"
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"d6.choice(size=10)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"def decorate_dice(title):\n",
" \"\"\"Labels the axes\n",
" title: string\n",
" \"\"\"\n",
" \n",
" plt.xlabel('Outcome')\n",
" plt.ylabel('PMF')\n",
" plt.title(title)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# d6.bar(xlabel='Outcome')\n",
"d6.bar()\n",
"decorate_dice('One die')"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" probs | \n",
"
\n",
" \n",
" \n",
" \n",
" 2 | \n",
" 0.027778 | \n",
"
\n",
" \n",
" 3 | \n",
" 0.055556 | \n",
"
\n",
" \n",
" 4 | \n",
" 0.083333 | \n",
"
\n",
" \n",
" 5 | \n",
" 0.111111 | \n",
"
\n",
" \n",
" 6 | \n",
" 0.138889 | \n",
"
\n",
" \n",
" 7 | \n",
" 0.166667 | \n",
"
\n",
" \n",
" 8 | \n",
" 0.138889 | \n",
"
\n",
" \n",
" 9 | \n",
" 0.111111 | \n",
"
\n",
" \n",
" 10 | \n",
" 0.083333 | \n",
"
\n",
" \n",
" 11 | \n",
" 0.055556 | \n",
"
\n",
" \n",
" 12 | \n",
" 0.027778 | \n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
"2 0.027778\n",
"3 0.055556\n",
"4 0.083333\n",
"5 0.111111\n",
"6 0.138889\n",
"7 0.166667\n",
"8 0.138889\n",
"9 0.111111\n",
"10 0.083333\n",
"11 0.055556\n",
"12 0.027778\n",
"dtype: float64"
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"twice = d6.add_dist(d6)\n",
"twice"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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AyoE+K4GTm+nFwDVVVcBVwPOTPKkJjlcCt3RYqyRpwPSuNlxVm5MspffLfhpwflWtTXIGsKaqVgLnARclGQHuphciVNU9ST5CL2QKWFVVV3ZVqyRpvM4CAqCqVtG7PNTfdnrf9APA8VtZ92J6j7pKkoag04DQ1s1Z1s0J0cYzj+1ku9Kepqt/g7Dn/DvcVZ9ikiQNmQEhSWplQEiSWhkQkqRWBoQkqZUBIUlqZUBIkloZEJKkVgaEJKmVASFJamVASJJaGRCSpFYGhCSplQEhSWplQEiSWnUaEEkWJlmfZCTJspbleye5rFl+fZI5A8sPTnJ/kvd1WackabzOAiLJNOBc4BhgHnBiknkD3U4F7qmqQ4CzgbMGln8E+EJXNUqStq7LM4gFwEhVbaiqB4EVwKKBPouAC5vpK4CjkwQgye8APwTWdlijJGkrugyImcBtffObmrbWPlW1GbgPODDJvsB/A/58WztIsiTJmiRrRkdHJ61wSdKue5P6A8DZVXX/tjpV1fKqml9V82fMmDE1lUnSY8T0Drd9OzC7b35W09bWZ1OS6cD+wF3AS4DFSf4GOAB4JMkDVXVOh/VKkvp0GRCrgUOTzKUXBCcAbxzosxI4GbgOWAxcU1UFvGKsQ5IPAPcbDpI0tToLiKranGQpcBUwDTi/qtYmOQNYU1UrgfOAi5KMAHfTCxFJ0i6gyzMIqmoVsGqg7fS+6QeA4yfYxgc6KU6StE276k1qSdKQGRCSpFYGhCSplQEhSWplQEiSWhkQkqRWBoQkqZUBIUlqZUBIklp1+knq3cmcZVd2st2NZx7byXYl7V66+h0D3f2e8QxCktTKgJAktTIgJEmtDAhJUisDQpLUyoCQJLXqNCCSLEyyPslIkmUty/dOclmz/Pokc5r2Vye5IcnNzfejuqxTkjReZwGRZBpwLnAMMA84Mcm8gW6nAvdU1SHA2cBZTfudwOuq6vn03ll9UVd1SpLadXkGsQAYqaoNVfUgsAJYNNBnEXBhM30FcHSSVNW3qurHTfta4IlJ9u6wVknSgC4DYiZwW9/8pqattU9VbQbuAw4c6POfgRur6peDO0iyJMmaJGtGR0cnrXBJ0i5+kzrJYfQuO72tbXlVLa+q+VU1f8aMGVNbnCTt4boMiNuB2X3zs5q21j5JpgP7A3c187OAzwJvrqofdFinJKlFlwGxGjg0ydwkewEnACsH+qykdxMaYDFwTVVVkgOAK4FlVfW1DmuUJG1FZwHR3FNYClwFrAMur6q1Sc5IclzT7TzgwCQjwHuAsUdhlwKHAKcn+Xbz9R+6qlWSNF6nw31X1Spg1UDb6X3TDwDHt6z3F8BfdFmbJGnbdumb1JKk4TEgJEmtDAhJUisDQpLUyoCQJLUyICRJrQwISVIrA0KS1MqAkCS1MiAkSa0MCElSKwNCktTKgJAktTIgJEmtDAhJUisDQpLUqtOASLIwyfokI0mWtSzfO8llzfLrk8zpW3Za074+yW91WackabzOAiLJNOBc4BhgHnBiknkD3U4F7qmqQ4CzgbOadefRe4f1YcBC4H8025MkTZEuzyAWACNVtaGqHgRWAIsG+iwCLmymrwCOTpKmfUVV/bKqfgiMNNuTJE2RVFU3G04WAwur6r82828CXlJVS/v6fLfps6mZ/wHwEuADwDeq6uKm/TzgC1V1xcA+lgBLmtnnAus7OZjxDgLunKJ9DcOefnyw5x+jx7f7m6pjfFZVzWhbMH0Kdt6ZqloOLJ/q/SZZU1Xzp3q/U2VPPz7Y84/R49v97QrH2OUlptuB2X3zs5q21j5JpgP7A3dt57qSpA51GRCrgUOTzE2yF72bzisH+qwETm6mFwPXVO+a10rghOYpp7nAocA3O6xVkjSgs0tMVbU5yVLgKmAacH5VrU1yBrCmqlYC5wEXJRkB7qYXIjT9LgduATYD76iqh7uqdSdM+WWtKbanHx/s+cfo8e3+hn6Mnd2kliTt3vwktSSplQEhSWplQOyAJLOT/J8ktyRZm+Rdw66pC0mmJflWks8Pu5bJluSAJFck+Zck65K8bNg1TbYk725+Pr+b5NIkTxh2TY9GkvOT3NF8bmqs7alJrk7y/eb7U4ZZ46O1lWP8UPNzelOSzyY5YKrrMiB2zGbgvVU1D3gp8I6W4UP2BO8C1g27iI58DPhiVf0a8EL2sONMMhP4A2B+VT2P3gMiJwy3qkftAnpD7vRbBny5qg4FvtzM784uYPwxXg08r6peAHwPOG2qizIgdkBV/aSqbmymf0bvl8vM4VY1uZLMAo4F/mHYtUy2JPsDR9J7eo6qerCq7h1qUd2YDjyx+WzRk4AfD7meR6WqvkLvKcd+/cP0XAj8zlTWNNnajrGqvlRVm5vZb9D7PNiUMiB2UjPy7G8A1w+5lMn2UeCPgUeGXEcX5gKjwCebS2j/kGSfYRc1marqduC/A7cCPwHuq6ovDbeqTjytqn7STP8r8LRhFjMF3gp8Yap3akDshCT7Av8L+MOq+umw65ksSX4buKOqbhh2LR2ZDrwI+Luq+g3g5+z+lya20FyLX0QvDJ8J7JPk94ZbVbeaD9fusc/rJ3k/vcvbl0z1vg2IHZTk8fTC4ZKq+syw65lkLweOS7KR3ui7RyW5eLglTapNwKaqGjvru4JeYOxJfhP4YVWNVtVDwGeA/zjkmrrwb0meAdB8v2PI9XQiySnAbwMn1RA+tGZA7IBmKPLzgHVV9ZFh1zPZquq0qppVVXPo3di8pqr2mL8+q+pfgduSPLdpOprep/X3JLcCL03ypObn9Wj2sBvxjf5hek4GPjfEWjqRZCG9y73HVdUvhlGDAbFjXg68id5f1t9uvl477KK0Q94JXJLkJuBw4K+GW87kas6OrgBuBG6m92986EM2PBpJLgWuA56bZFOSU4EzgVcn+T69s6Yzh1njo7WVYzwH2A+4uvld8/dTXpdDbUiS2ngGIUlqZUBIkloZEJKkVgaEJKmVASFJamVASAOSzEryuWak0B8k+Vjz2txtrfMnU1WfNFUMCKlP8+GyzwD/1IwU+hxgX+AvJ1jVgNAex4CQtnQU8EBVfRKgeRf6u4G3Jnl7knPGOib5fJJXJTmT3uip305ySbPszc04/t9JclHTNifJNU37l5Mc3LRfkOTvknwjyYZmm+c376u4oG9/r0lyXZIbk/xjMyaY1BkDQtrSYcAWgxU2AzLeSm+wv3Gqahnw71V1eFWdlOQw4E+Bo6rqhfTerwHwt8CFzfj+lwAf79vMU4CX0QujlcDZTS3PT3J4koOabf5mVb0IWAO8ZzIOWNqa1h94SY/KUcA/VtWdAFU1Ns7/y4DfbaYvAv6mb53/XVWV5Gbg36rqZoAka4E59N4FMA/4Wu8qGHvRG5pB6owBIW3pFmBxf0OSJwMHA/ey5Vn3ZL7K85fN90f6psfmpwMPA1dX1YmTuE9pm7zEJG3py8CTkrwZeu/nBj5M75WQG4DDkzwuyWxgQd96DzVDwQNcAxyf5MBmG09t2r/Or17/eRLw1R2o6xvAy5Mc0mxznyTP2dGDk3aEASH1acbcfz29X/Dfp/cu4AfoPaX0NeCH9M4yPk5vxNQxy4GbklxSVWvpPfV0bZLvAGNDw78TeEszkuyb+NW9ie2paxQ4Bbi0Wf864Nd29jil7eForpKkVp5BSJJaGRCSpFYGhCSplQEhSWplQEiSWhkQkqRWBoQkqdX/A9H9SHHstTG2AAAAAElFTkSuQmCC\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"twice.bar()\n",
"decorate_dice('Two Dice')"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"d6.add_dist??"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(array([0.16666667, 0.16666667, 0.16666667, 0.16666667, 0.16666667,\n",
" 0.16666667]),\n",
" array([1, 2, 3, 4, 5, 6]))"
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"d6.ps, d6.qs"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" probs | \n",
"
\n",
" \n",
" \n",
" \n",
" 1 | \n",
" 0.166667 | \n",
"
\n",
" \n",
" 2 | \n",
" 0.166667 | \n",
"
\n",
" \n",
" 3 | \n",
" 0.166667 | \n",
"
\n",
" \n",
" 4 | \n",
" 0.166667 | \n",
"
\n",
" \n",
" 5 | \n",
" 0.166667 | \n",
"
\n",
" \n",
" 6 | \n",
" 0.166667 | \n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
"1 0.166667\n",
"2 0.166667\n",
"3 0.166667\n",
"4 0.166667\n",
"5 0.166667\n",
"6 0.166667\n",
"dtype: float64"
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"d6"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"7.000000000000002"
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"twice.mean()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.10185185185185187"
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"twice[twice.qs >3].mean()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"twice[twice.qs >3].plot.bar()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.10185185185185187"
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"twice[twice.qs >3].mean()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"7.142857142857141"
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"twice[1] = 0 \n",
"twice[2] = 0\n",
"twice.normalize()\n",
"twice.mean()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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CYvgot+5lwGVDeT8zM6ufgY4gXl+aPrPKQszMrLkMFBAxLFWYmVnT6XeICRgn6UJApen/ERH/UFllZmbWUAMFxKdK0+1VFmJmZs2l34AY6klpMzMbOQa6iqnf+xYi4qT6lmNmZs1ioCGmoyieiXQtcCfFuQgzM3sRGCgg/gx4OzATeD9wI3BtRHRUXZiZmTVWv5e5RsQLEfHDiDgdeBPQCfxY0pxhqc7MzBpmoCMIJO0CnEhxFDERuBC4odqyzMys0QY6SX0l8FqKx2V8PiJ+OSxVmZlZww10BHEq8HuKx2ycKannzmoBERF7V1mcNbeJc2+s+zbXzj+x7tu0HV+9f9f8ezY4A90HsUN/oZCZmW27gYaYdgU+DBwI3Adclh7jbWZmI9xARwhXAG3ASuCdwJcrr8jMzJrCQAHRGhGnRsQlwHTg6KFsXNJUSasldUqam1m+i6Tr0vI7JU1M7TtLukLSSkmrJJ09lPc1M7PtN1BAPN8zMdShJUmjgIuBE4BWYKak1ppuZwCbIuJA4HzgvNR+MrBLRBwKvBH4+57wMDOz4THgFwZJejK9ngJe1zMt6ckB1p0CdEbEmoh4DlgITKvpM41iGAtgMXCcJFF8D8UekkYDuwHPAQO9n5mZ1dFAVzGN2o5tj6V4jlOPLuDIvvpExGZJTwAHUITFNOC3wO7Ax3PfSS1pNjAbYMKECdtRqpmZ1WrWy1inAC8ALwcmAZ+U9MraThGxICLaIqKtpaVluGs0MxvRqgyIDcD40vy41Jbtk4aT9gEepXgw4A8j4vmIeAS4jeJqKjMzGyZVBsQKYLKkSZLGADOA2u+XWAKcnqanA7dERADrgGMBJO1B8aDA/66wVjMzq1FZQKSrnuYAy4BVwKKI6JA0T1LPFw1dChwgqRP4BNBzKezFwJ6SOiiC5psRcV9VtZqZWW8DPs11e0TEUooH/ZXbzilNP0txSWvtek/n2s3MbPg060lqMzNrMAeEmZllOSDMzCzLAWFmZlkOCDMzy3JAmJlZlgPCzMyyHBBmZpblgDAzsywHhJmZZTkgzMwsywFhZmZZDggzM8tyQJiZWZYDwszMsioNCElTJa2W1Clpbmb5LpKuS8vvlDSxtOx1km6X1CFppaRdq6zVzMy2VllASBpF8c1wJwCtwExJrTXdzgA2RcSBwPnAeWnd0cDVwIcj4hDgrcDzVdVqZma9VXkEMQXojIg1EfEcsBCYVtNnGnBFml4MHCdJwPHAfRFxL0BEPBoRL1RYq5mZ1agyIMYC60vzXakt2yd9h/UTwAHAQUBIWibpbkn/mHsDSbMltUtq7+7urvsOmJm9mDXrSerRwF8Cp6R/3yPpuNpOEbEgItoioq2lpWW4azQzG9GqDIgNwPjS/LjUlu2TzjvsAzxKcbTxk4jYGBHPAEuBwyus1czMalQZECuAyZImSRoDzACW1PRZApyepqcDt0REAMuAQyXtnoLjLcD9FdZqZmY1Rle14YjYLGkOxYf9KOCyiOiQNA9oj4glwKXAVZI6gccoQoSI2CTpKxQhE8DSiLixqlpHmolz6/+jWjv/xLpv06zZ1Pv/nR39/5vKAgIgIpZSDA+V284pTT8LnNzHuldTXOpqZmYN0Kwnqc3MrMEcEGZmluWAMDOzLAeEmZllOSDMzCzLAWFmZlkOCDMzy3JAmJlZlgPCzMyyHBBmZpblgDAzsywHhJmZZTkgzMwsywFhZmZZDggzM8uqNCAkTZW0WlKnpLmZ5btIui4tv1PSxJrlEyQ9LemsKus0M7PeKgsISaOAi4ETgFZgpqTWmm5nAJsi4kDgfOC8muVfAX5QVY1mZta3Ko8gpgCdEbEmIp4DFgLTavpMA65I04uB4yQJQNK7gYeAjgprNDOzPlQZEGOB9aX5rtSW7RMRm4EngAMk7Ql8Gvh8f28gabakdknt3d3ddSvczMya9yT154DzI+Lp/jpFxIKIaIuItpaWluGpzMzsRWJ0hdveAIwvzY9Lbbk+XZJGA/sAjwJHAtMlfRHYF9gi6dmIuKjCes3MrKTKgFgBTJY0iSIIZgDvr+mzBDgduB2YDtwSEQEc3dNB0ueApx0OZmbDq7KAiIjNkuYAy4BRwGUR0SFpHtAeEUuAS4GrJHUCj1GEiJmZNYEqjyCIiKXA0pq2c0rTzwInD7CNz1VSnJmZ9atZT1KbmVmDOSDMzCzLAWFmZlkOCDMzy3JAmJlZlgPCzMyyHBBmZpblgDAzs6xKb5QzM7OtTZx7Y923uXb+iXXfJvgIwszM+uCAMDOzLAeEmZllOSDMzCzLAWFmZlkOCDMzy6o0ICRNlbRaUqekuZnlu0i6Li2/U9LE1P52SXdJWpn+PbbKOs3MrLfKAkLSKOBi4ASgFZgpqbWm2xnApog4EDgfOC+1bwTeFRGHUnwl6VVV1WlmZnlVHkFMATojYk1EPAcsBKbV9JkGXJGmFwPHSVJE/CIifpPaO4DdJO1SYa1mZlajyoAYC6wvzXeltmyfiNgMPAEcUNPnfcDdEfHHiuo0M7OMpn7UhqRDKIadju9j+WxgNsCECROGsTIzs5GvyiOIDcD40vy41JbtI2k0sA/waJofB9wAnBYRD+beICIWRERbRLS1tLTUuXwzsxe3KgNiBTBZ0iRJY4AZwJKaPksoTkIDTAduiYiQtC9wIzA3Im6rsEYzM+tDZQGRzinMAZYBq4BFEdEhaZ6kk1K3S4EDJHUCnwB6LoWdAxwInCPpnvR6aVW1mplZb5Weg4iIpcDSmrZzStPPAidn1vsX4F+qrM3MzPrnO6nNzCzLAWFmZlkOCDMzy3JAmJlZlgPCzMyyHBBmZpblgDAzsywHhJmZZTkgzMwsywFhZmZZDggzM8tyQJiZWZYDwszMshwQZmaW5YAwM7MsB4SZmWVVGhCSpkpaLalT0tzM8l0kXZeW3ylpYmnZ2al9taR3VFmnmZn1VllASBoFXAycALQCMyW11nQ7A9gUEQcC5wPnpXVbKb7D+hBgKvAfaXtmZjZMqjyCmAJ0RsSaiHgOWAhMq+kzDbgiTS8GjpOk1L4wIv4YEQ8BnWl7ZmY2TBQR1WxYmg5MjYgPpfkPAEdGxJxSn1+mPl1p/kHgSOBzwB0RcXVqvxT4QUQsrnmP2cDsNPtqYHUlO9MYLwE2NrqIOhlJ+wLen2Y2kvYFhmd/XhERLbkFoyt+40pFxAJgQaPrqIKk9ohoa3Qd9TCS9gW8P81sJO0LNH5/qhxi2gCML82PS23ZPpJGA/sAjw5yXTMzq1CVAbECmCxpkqQxFCedl9T0WQKcnqanA7dEMea1BJiRrnKaBEwGfl5hrWZmVqOyIaaI2CxpDrAMGAVcFhEdkuYB7RGxBLgUuEpSJ/AYRYiQ+i0C7gc2Ax+NiBeqqrVJjaShs5G0L+D9aWYjaV+gwftT2UlqMzPbsflOajMzy3JAmJlZlgOiiUgaL+lHku6X1CHpzEbXVA+SRkn6haTvN7qW7SVpX0mLJf23pFWSjmp0TdtK0sfT79kvJV0raddG1zQUki6T9Ei6n6qnbX9JyyU9kP7dr5E1DlYf+/Kl9Ht2n6QbJO073HU5IJrLZuCTEdEKvAn4aObxJDuiM4FVjS6iTr4K/DAiDgZezw66X5LGAv8AtEXEaykuJJnR2KqG7HKKR/GUzQVujojJwM1pfkdwOb33ZTnw2oh4HfAr4OzhLsoB0UQi4rcRcXeaforiw2dsY6vaPpLGAScC32h0LdtL0j7AMRRX3xERz0XE4w0tavuMBnZL9yDtDvymwfUMSUT8hOLqx7Ly43uuAN49nDVtq9y+RMRNEbE5zd5BcT/YsHJANKn0ZNs3AHc2uJTtdQHwj8CWBtdRD5OAbuCbacjsG5L2aHRR2yIiNgD/DqwDfgs8ERE3NbaqunhZRPw2Tf8OeFkji6mjvwN+MNxv6oBoQpL2BP4v8L8j4slG17OtJP018EhE3NXoWupkNHA48LWIeAPwe3acIYytpLH5aRSh93JgD0mnNraq+ko33e7w1/FL+gzF8PM1w/3eDogmI2lninC4JiKub3Q92+nNwEmS1lI8zfdYSVc3tqTt0gV0RUTPUd1iisDYEb0NeCgiuiPieeB64C8aXFM9PCzpzwHSv480uJ7tImkW8NfAKdGAm9YcEE0kPer8UmBVRHyl0fVsr4g4OyLGRcREihOgt0TEDvtXakT8Dlgv6dWp6TiKu/13ROuAN0naPf3eHccOesK9RvnxPacD321gLdtF0lSK4dmTIuKZRtTggGgubwY+QPGX9j3p9c5GF2Vb+RhwjaT7gMOAf21sOdsmHQUtBu4GVlJ8FuxQj6mQdC1wO/BqSV2SzgDmA2+X9ADFUdL8RtY4WH3sy0XAXsDy9Fnw9WGvy4/aMDOzHB9BmJlZlgPCzMyyHBBmZpblgDAzsywHhJmZZTkgzGpIGifpu+mJoA9K+mr62tz+1vmn4arPbLg4IMxK0k1j1wPfSU8EPQjYE/jCAKs6IGzEcUCYbe1Y4NmI+CZA+i70jwN/J+kjki7q6Sjp+5LeKmk+xVNR75F0TVp2WnqO/72SrkptEyXdktpvljQhtV8u6WuS7pC0Jm3zsvR9E5eX3u94SbdLulvSt9Mzu8wq44Aw29ohwFYPF0wPTFxH8bC+XiJiLvCHiDgsIk6RdAjwz8CxEfF6iu/DAPg/wBXp+f7XABeWNrMfcBRFGC0Bzk+1HCrpMEkvSdt8W0QcDrQDn6jHDpv1JfsLb2bb5Vjg2xGxESAiep7zfxTw3jR9FfDF0jrfi4iQtBJ4OCJWAkjqACZSfBdAK3BbMQrGGIpHM5hVxgFhtrX7genlBkl7AxOAx9n6qLueX9H5x/TvltJ0z/xo4AVgeUTMrON7mvXLQ0xmW7sZ2F3SaVB8nzbwZYqvhFwDHCZpJ0njgSml9Z5Pj2oHuAU4WdIBaRv7p/af8aev9TwF+OkQ6roDeLOkA9M295B00FB3zmwoHBBmJemZ+++h+IB/gOK7gJ+luErpNuAhiqOMCymehNpjAXCfpGsiooPiqqdbJd0L9Dy6/WPAB9OTYD/An85NDKaubmAWcG1a/3bg4G3dT7PB8NNczcwsy0cQZmaW5YAwM7MsB4SZmWU5IMzMLMsBYWZmWQ4IMzPLckCYmVnW/wfmNay+VdlI6QAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"twice.bar()\n",
"decorate_dice('Two dice, greater than 3')"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- Pmf => Prior probability \n",
"- Likelihood => Multiply each prior probability by the likelihood of data \n",
"- Normalize => Add all up and divide by total\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Cookie Problem "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" probs | \n",
"
\n",
" \n",
" \n",
" \n",
" B1 | \n",
" 0.5 | \n",
"
\n",
" \n",
" B2 | \n",
" 0.5 | \n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
"B1 0.5\n",
"B2 0.5\n",
"dtype: float64"
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"cookie = Pmf.from_seq(['B1', 'B2']); priors"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" probs | \n",
"
\n",
" \n",
" \n",
" \n",
" B1 | \n",
" 0.375 | \n",
"
\n",
" \n",
" B2 | \n",
" 0.250 | \n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
"B1 0.375\n",
"B2 0.250\n",
"dtype: float64"
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"cookie['B1']*=0.75\n",
"cookie['B2']*=0.5\n",
"cookie"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.625"
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"cookie.normalize()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" probs | \n",
"
\n",
" \n",
" \n",
" \n",
" B1 | \n",
" 0.6 | \n",
"
\n",
" \n",
" B2 | \n",
" 0.4 | \n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
"B1 0.6\n",
"B2 0.4\n",
"dtype: float64"
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"cookie"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.35"
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"cookie['B1']*=0.25\n",
"cookie['B2']*=0.5\n",
"\n",
"cookie.normalize()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" probs | \n",
"
\n",
" \n",
" \n",
" \n",
" B1 | \n",
" 0.428571 | \n",
"
\n",
" \n",
" B2 | \n",
" 0.571429 | \n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
"B1 0.428571\n",
"B2 0.571429\n",
"dtype: float64"
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"cookie"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.21875"
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"cookie2 = Pmf.from_seq([\"B1\", \"B2\"])\n",
"cookie2['B1']*= (0.75*0.25)\n",
"cookie2['B2']*=(0.5*0.5)\n",
"cookie2.normalize()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" probs | \n",
"
\n",
" \n",
" \n",
" \n",
" B1 | \n",
" 0.428571 | \n",
"
\n",
" \n",
" B2 | \n",
" 0.571429 | \n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
"B1 0.428571\n",
"B2 0.571429\n",
"dtype: float64"
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"cookie2"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# cookie['B1B1']*=0.75\n",
"# cookie['B1B2']*=0."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"d6.normalize??"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
}
},
"nbformat": 4,
"nbformat_minor": 4
}