Poisson Distribution

A Discrete Distribution with:

• RV being $\text{\# of succcesses}$ in a continuous space

PMF

$P(X=x)=\frac{{\lambda }^x}{x!}{e}^{-\lambda },x=0,1,2,\dots$

• $\lambda >0$ represents the average $\text{\# of success}$ over a given interval

Expectation

$E(X)=\lambda$

Variance

${\sigma }^2=\lambda$

Concepts

• Poisson Approximation to Binomial