# Probability and Statistics

Mean

$\bar{x} = \dfrac{\Sigma x}{n}$ or $\bar{x} = \dfrac{\Sigma xf}{\Sigma f}$

Variance

$\sigma^2 = \sum \dfrac{(x - \bar{x})^2}{n}$ or $\sigma^2 = \dfrac{\Sigma (x - \bar{x})^2 f}{\Sigma f}$

Permutation

$^{n}P_k = \dfrac{n!}{(n - k)!}$

Combination

$\displaystyle ^{n}C_k = \binom{n}{k} = \dfrac{n!}{k! \, (n - k)!}$

Binomial Distribution

$P(x) = {^{n}C}_x \, p^x q^{n - x}$

Poisson Distribution

$P(x) = \dfrac{e^{-\mu} \mu^x}{x!}$