cheat sheet

2022-03-12 · 1 min read

$$ \renewcommand{\Pr}[1]{\text{Pr}\left[ #1 \right]} $$

Law of Total Probability #

$$ \begin{align*} \Pr{A} &= \sum_n \Pr{A,, B_n} \ &= \sum_n \Pr{A ;|; B_n} \cdot \Pr{B_n} \ \ \Pr{A ;|; C} &= \sum_n \Pr{A ;|; C,, B_n} \cdot \Pr{B_n ;|; C} \ &= \sum_n \Pr{A ;|; C,, B_n} \cdot \Pr{B_n} \qquad \text{(if $B_n$ and $C$ indep.)} \end{align*} $$