BernoulliDistribution

BernoulliDistribution(p)

returns the Bernoulli distribution.

See:

The probability density function of the Bernoulli distribution is

>> PDF(BernoulliDistribution(p), x)
Piecewise({{1-p,x==0},{p,x==1}},0)

The cumulative distribution function of the Bernoulli distribution is

>> CDF(BernoulliDistribution(p), x)
Piecewise({{0,x<0},{1-p,0<=x&&x<1}},1)

The mean of the Bernoulli distribution is

>> Mean(BernoulliDistribution(p))
p

The standard deviation of the Bernoulli distribution is

>> StandardDeviation(BernoulliDistribution(p))
Sqrt((1-p)*p)

The variance of the Bernoulli distribution is

>> Variance(BernoulliDistribution(p))
(1-p)*p

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

>> RandomVariate(BernoulliDistribution(0.25), 10^1)
{1,0,0,0,1,1,0,0,0,0}