Statistics 1

$P(A \cup B) = P(A) + P(B) - P(A \cap B)$

$P(A \mid B) = \dfrac{P(A \cap B)}{P(B)}$

$P(A \cap B) = P(A)P(B)$

$S_{xy} = \sum xy - \dfrac{\sum x \sum y}{n}$

$r = \dfrac{S_{xy}}{\sqrt{S_{xx}S_{yy}}}$

$y = a + bx, \quad b = \dfrac{S_{xy}}{S_{xx}}, \quad a = \bar{y} - b\bar{x}$

$E(X) = \sum x\,P(X = x)$

$\operatorname{Var}(X) = E(X^2) - [E(X)]^2$

$E(aX + b) = aE(X) + b, \quad \operatorname{Var}(aX + b) = a^2\operatorname{Var}(X)$

$Z = \dfrac{X - \mu}{\sigma}$