Bernoulli Distribution

Definition: Bernoulli Distribution

Suppose we have some experiment and let $X$ be a discrete random variable with exactly two possible values $\{A,\bar{A}\}$.

We say that $X$ has a Bernoulli distribution if there exist a real number $p\in (0;1)$ such that $P(X=A)=p$ and $P(X=\bar{A})=1-p$.

NOTE

We often say that $p$ is the parameter of the Bernoulli distribution of $X$ or that $X$ is distributed according to the Bernoulli distribution with parameter $p$.

NOTATION

$$X\sim \mathrm{Bern}(p)$$