Description

A random variable X possesses a binomial distribution with parameters n,p, where n = 1, 2, ... and 0 < p < 1, if it has the representation

,              (1)

where B_p⁽ⁱ⁾, i=1,2,...,n are independent standard Bernoulli variables with parameter p.

The following picture presents graphs of probability function (bound to the left axis) and CDF (bound to the right axis) for B _{10, 0.3}

Characteristics

The following table contains formulae for calculation of characteristics of binomial distribution B _n,p

Probability function	,
CDF	,
Expectation	np
Variance	np(1-p)

Simulation of a binomial variable B_n,p is attained by formula (1), where standard Bernoulli variables are generated by method presented here.