Bernoulli Distribution

Definition

$X\sim \text{Bernoulli}(p)$

Models random experiment whose outcomes are “success” or “failure”.

• pmf: $p^x(1-p{)}^{1-x}$, $x\in 0,1$
• Mean: $p$
• Variance: $p(1-p)$
• mgf: $1-p+p{e}^t$