Discrete Poisson Distribution

A kind of Discrete Distribution that models the count of events occurring in a fixed interval of time or space, assuming events happen independently at a constant average rate $\lambda$.

• $f(x)=\frac{{\lambda }^x{e}^{-\lambda }}{x!}\text{for }x\in {\mathbb{N}}_0$
• $E(X)=\lambda$
• $\text{Var}(X)=\lambda$
• $X_{\text{Poisson}(n\lambda )}={\sum }_1^n{X}_{i,\text{Poisson}(\lambda )}$