Probability and Statistics Cheatsheet

Probabilities Arithmetic

P(A^c) = 1 - P(A)

P(A|B) = \frac{P(A \cap B)}{P(B)}

\MathOverLabel{\textbf{Addition Rule}}{% P(A \cup B) = P(A) + P(B) - P(A \cap B) }

If $A_1, \dots, A_n$ partition a sample space and $B$ is an event in the same space, then:

\MathOverLabel{\textbf{Multiplication Rule}}{% P(B) = \sum_{i=1}^n{P(B|A_i) \, P(A_i)} }

\MathOverLabel{\textbf{Bayes' Rule}}{% P\parens{A_j|B} = \frac{ P\parens{B|A_j} \, P\parens{A_j} }{ \displaystyle \sum_{i=1}^n{P\parens{B|A_i} \, P\parens{A_i}} } }