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
(1 − p
The Bernoulli distribution is a member of the exponential family.
See also Bernoulli trial, Bernoulli process.