Bernoulli distribution

A Bernoulli random variable is a discrete random variable which models a Bernoulli trial. Such a random variable follows a Bernoulli distribution, denoted $X\sim \mathrm{Bernoulli}(\alpha )$, where $\alpha \in [0,1]$ is the probability of "success" and $(1-\alpha )$ is the probability of "failure".

Formally,
if $X$ is a Bernoulli random variable, i.e. $X\sim \mathrm{Bernoulli}(\alpha )$, then

completely describes the distribution.

The Bernoulli distribution is a special case of the binomial distribution with $n=1$.