A Distribution Tables

A.1 Discrete Distributions

Distribution of $X$	$f(x)$	Support	$E[X]$	$\text{Var}[X]$
Hypergeometric$(n, N_1, N_0)$	$\displaystyle \frac{\binom{N_1}{x} \binom{N_0}{n-x}}{\binom{N}{n}}$	$x=0, 1, \ldots, n$	$n \frac{N_1}{N}$	$n \frac{N_1}{N} \frac{N_0}{N} \left(1 - \frac{n-1}{N-1}\right)$
Binomial$(n, N_1, N_0)$	$\displaystyle \frac{\binom{n}{x} N_1^x N_0^{n-x}}{N^n}$	$x=0, 1, \ldots, n$	$n \frac{N_1}{N}$	$n \frac{N_1}{N} \frac{N_0}{N}$
Binomial$(n, p)$	$\binom{n}{x} p^x (1-p)^{n-x}$	$x=0, 1, \ldots, n$	$np$	$np(1-p)$
Geometric$(p)$	$(1-p)^{x-1} p$	$x=1, 2, \ldots$	$\frac{1}{p}$	$\frac{1-p}{p^2}$
NegativeBinomial$(r, p)$	$\binom{x-1}{r-1} (1-p)^{x-r} p^r$	$x=r, r+1, \ldots$	$\frac{r}{p}$	$\frac{r(1-p)}{p^2}$
Poisson$(\mu)$	$e^{-\mu} \frac{\mu^x}{x!}$	$x=0, 1, 2, \ldots$	$\mu$	$\mu$

A.2 Continuous Distributions

Distribution of $X$	$f(x)$	Support	$E[X]$	$\text{Var}[X]$
Uniform$(a, b)$	$\frac{1}{b-a}$	$a < x < b$	$\frac{a+b}{2}$	$\frac{(b-a)^2}{12}$
Exponential$(\lambda)$	$\lambda e^{-\lambda x}$	$0 < x < \infty$	$\frac{1}{\lambda}$	$\frac{1}{\lambda^2}$
Gamma$(r, \lambda)$	$\frac{\lambda^r}{(r-1)!}x^{r-1} e^{-\lambda x}$	$0 < x < \infty$	$\frac{r}{\lambda}$	$\frac{r}{\lambda^2}$
Normal$(\mu, \sigma)$	$\frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{(x - \mu)^2}{2\sigma^2}}$	$-\infty < x < \infty$	$\mu$	$\sigma^2$