Poisson Distribution

Notation:

$X \sim Pois(\lambda)$

Probability Mass Function:

$P(X=x)=\frac{\lambda^xe^{-\lambda}}{x!}$

where:

$\lambda > 0$
$x=0, 1, 2, \ldots$

Mean:

$\mathrm{E}[X]=\lambda$

Variance:

$\mathrm{Var}[X]=\lambda$

References: