Empirical joint vs conditional probability for a dataset

joint_vs_conditional_probability.ipynb

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    "Joint vs Conditional Probability\n",
    "-------"
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    "<h1>Table of Contents<span class=\"tocSkip\"></span></h1>\n",
    "<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#Joint-vs-Conditional-Probability\" data-toc-modified-id=\"Joint-vs-Conditional-Probability-1\">Joint vs Conditional Probability</a></span></li><li><span><a href=\"#Learning-Outcomes\" data-toc-modified-id=\"Learning-Outcomes-2\">Learning Outcomes</a></span></li><li><span><a href=\"#Joint-Probability-\" data-toc-modified-id=\"Joint-Probability--3\">Joint Probability </a></span></li><li><span><a href=\"#Conditional-probability-distribution\" data-toc-modified-id=\"Conditional-probability-distribution-4\">Conditional probability distribution</a></span></li><li><span><a href=\"#Empirical-Data--\" data-toc-modified-id=\"Empirical-Data---5\">Empirical Data  </a></span></li><li><span><a href=\"#Joint-probability-distribution-p(x,y)\" data-toc-modified-id=\"Joint-probability-distribution-p(x,y)-6\">Joint probability distribution p(x,y)</a></span></li><li><span><a href=\"#Conditional-probability-distribution-p(y|x)\" data-toc-modified-id=\"Conditional-probability-distribution-p(y|x)-7\">Conditional probability distribution p(y|x)</a></span></li><li><span><a href=\"#Another-Problem\" data-toc-modified-id=\"Another-Problem-8\">Another Problem</a></span></li><li><span><a href=\"#-Outcome-Table\" data-toc-modified-id=\"-Outcome-Table-9\"> Outcome Table</a></span></li><li><span><a href=\"#Joint-probability-distribution\" data-toc-modified-id=\"Joint-probability-distribution-10\">Joint probability distribution</a></span></li><li><span><a href=\"#Conditional-probability-distribution\" data-toc-modified-id=\"Conditional-probability-distribution-11\">Conditional probability distribution</a></span></li></ul></div>"
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    "<center><h2>Learning Outcomes</h2></center>\n",
    "\n",
    "__By the end of this session, you should be able to__:\n",
    "\n",
    "- Calculate the joint and conditional probability distribution for a given dataset.\n",
    "- Describe the difference in your own words."
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    "Joint Probability \n",
    "------\n",
    "\n",
    "How likely will two events both happen?\n",
    "\n",
    "p(x , y)"
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    "Conditional probability distribution\n",
    "---------\n",
    "\n",
    "How likely will one event happen given a different event happened?\n",
    "\n",
    "p(y ❘ x)"
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    "Empirical Data  \n",
    "-------\n",
    "\n",
    "| x | y |  \n",
    "|:-------:|:------:|\n",
    "| 1 | 0 |\n",
    "| 1 | 0 |\n",
    "| 2 | 0 |\n",
    "| 2 | 1 |\n",
    "\n",
    "Create the following tables:\n",
    "\n",
    "- __Joint probability distribution p(x,y)__ \n",
    "- __Conditional probability distribution p(y|x)__"
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    "__Joint probability distribution p(x,y)__:\n",
    "\n",
    "| __p(x,y)__ | y=0 | y=1 |  \n",
    "|:-------:|:------:|:------:|\n",
    "| x=1 | ?  | ?  |\n",
    "| x=2 | ? | ? |\n",
    "\n",
    "\n",
    "__Conditional probability distribution p(y|x)__:\n",
    "\n",
    "| __p(y ❙  x)__ | y=0 | y=1 |  \n",
    "|:-------:|:------:|:------:|\n",
    "| x=1 | ? | ? |\n",
    "| x=2 | ? | ? |"
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    "Joint probability distribution p(x,y)\n",
    "------\n",
    "\n",
    "| __p(x,y)__ | y=0 | y=1 |  \n",
    "|:-------:|:------:|:------:|\n",
    "| x=1 | 1/2 | 0 |\n",
    "| x=2 | 1/4 | 1/4 |\n",
    "\n"
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    "Conditional probability distribution p(y|x)\n",
    "------\n",
    "\n",
    "| __p(y ❙ x)__ | y=0 | y=1 |  \n",
    "|:-------:|:------:|:------:|\n",
    "| x=1 | 1 | 0 |\n",
    "| x=2 | 1/2 | 1/2 |"
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    "Another Problem\n",
    "------\n",
    "\n",
    "X(n) will be True (or 1) when n is even.  \n",
    "Y(n) will be True (or 1) when n is prime.\n",
    "\n",
    "Make the following tables:\n",
    "\n",
    "1. Outcome table\n",
    "1. Joint probability distribution\n",
    "1. Conditional probability distribution"
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    " Outcome Table\n",
    " ----\n",
    "\n",
    "| n | 1 |   2 |  3 |  4 |  5 |  6 |  7 |  8 |\n",
    "|:-------:|:------:|:------:|:------:|:------:|:------:|:------:|:------:|:------:|\n",
    "| X | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 |\n",
    "| Y | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 0 |"
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    "Joint probability distribution\n",
    "------\n",
    "\n",
    "| __p(x,y)__ | x is True (1) | x is Not True (0) |  \n",
    "|:-------:|:------:|:------:|\n",
    "|Y is True (1) | TODO | TODO |\n",
    "| y is Not True (0) | TODO | TODO |  "
   ]
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    "Conditional probability distribution\n",
    "------\n",
    "\n",
    "| __p(x ❙ y)__ | x is True (1) | x is Not True (0) |  \n",
    "|:-------:|:------:|:------:|\n",
    "|Y is True (1) | TODO | TODO |\n",
    "| y is Not True (0) | TODO | TODO |  "
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    "<br>\n",
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