BinomialDistribution

BinomialDistribution(n, p)

returns the binomial distribution.

See:

The probability density function of the binomial distribution is

>> PDF(BinomialDistribution(n, p), x)
Piecewise({{(1-p)^(n-x)*p^x*Binomial(n,x),0<=x<=n}},0)

The cumulative distribution function of the binomial distribution is

>> CDF(BinomialDistribution(n, p), x)
Piecewise({{BetaRegularized(1-p,n-Floor(x),1+Floor(x)),0<=x&&x<n},{1,x>=n}},0)

The mean of the binomial distribution is

>> Mean(BinomialDistribution(n, p))
n*p

The standard deviation of the binomial distribution is

>> StandardDeviation(BinomialDistribution(n, p))
Sqrt(n*(1-p)*p)

The variance of the binomial distribution is

>> Variance(BinomialDistribution(n, p))
n*(1-p)*p

The random variates of a binomial distribution can be generated with function RandomVariate

>> RandomVariate(BinomialDistribution(10,0.25), 10^1)
{1,2,1,1,4,1,1,3,2,5}