Probability Theory Cheat Sheet

Chain Rule of Probability:

$\begin{displaymath} \Pr(A,S_1\vert S_2) = \Pr(A\vert S_2) \Pr(S_1 \vert A, S_2)\end{displaymath}$

Summation Rule

$\begin{displaymath} \Pr(S_1\vert S_2) = \sum_A \Pr(A,S_1\vert S_2)\end{displaymath}$

Bayes Rule

$\begin{displaymath} \Pr(A\vert B,S_1) = \Pr(B\vert A,S_1) \Pr(A\vert S_1) / \Pr(B\vert S_1)\end{displaymath}$

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