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.