Binary pmf. ? = {0, 1}; p(0) = 1 ? p, p(1) = p, where p is a parameter in (0, 1).

mean: p

variance: p(1 ? p)

Uniform pmf. ? = _n = {0, 1, , n ? 1} and p( k) = 1/ n; k ? _n .

mean: ( n + 1)/2

variance: (2 n + 1)( n + 1) n/6 ? (( n + 1)/2) ².

Binomial pmf. ? = _{n +1} = {0, 1, , n} and

where

is the binomial coefficient.

mean: np

variance: np(1 ? p)

Geometric pmf. ? = {1, 2, 3, } and p( k) = (1 ? p) ^{k ? 1} p; k = 1, 2, , where p ? (0, 1) is a parameter.

mean: 1/ p

variance: 2 /p ²

Poisson pmf. ? = ₊ = {0, 1, 2, } and p( k) = ( ? ^k e ^{? ?})/ k!, where ? is a parameter in (0, ?). (Keep in mind that 0! 1.)

mean: ?

variance: ?

Uniform pdf. Given b > a, f( r) = 1/( b ? a) for r ? [ a, b].

mean:...