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Bernoulli Distribution#

Definition: Bernoulli Distribution

Suppose we have some [[Experiments|experiment]] and let \(X\) be a [[Random Variables#Discrete Random Variables|discrete random variable]] with exactly two possible values \(\{A, \bar{A}\}\).

We say that \(X\) has a Bernoulli distribution if there exist a [[The Real Numbers|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

\[ X \sim \mathop{\operatorname{Bern}}(p) \]