# Bernoulli distribution

The

**Bernoulli distribution**, named after Swiss scientist

James Bernoulli, is a

discrete probability distribution, which takes value 1 with success probability

*p* and value 0 with failure probability

*q* = 1 −

*p*. The

probability mass function *f* of this distribution is

The

expected value of a Bernoulli random variable is

*p*, and its

variance is

*pq* =

*p*(1 −

*p*).

The Bernoulli distribution is a member of the exponential family.

See also Bernoulli trial, Bernoulli process.