Poisson Distribution

For rate $\lambda >0$ and $k\in \{0,1,2,\dots \}$:

$$P(X=k)=\frac{e^{-\lambda }{\lambda }^k}{k!}$$

Expected Value

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

Variance

$$\mathrm{Var}(X)=\lambda$$