Bernoulli Distribution

• Definition: A discrete distribution with only two outcomes:
  • 1 (success) with probability $p$
  • 0 (failure) with probability $1-p$
• Mean: $E[X]=p$
• Variance: $Var(X)=p(1-p)$
• Use case: models a single trial (coin flip, yes/no event).

Represented as

$\mathrm{Bernoulli}(p)$

Mathematically it is written as

$$P(X=x)=\{\begin{array}{ll}p& x=1\\ 1-p& x=0\end{array}$$

Visually it looks like