Discrete Probability Distribution

# Poisson Distribution

We use the Poisson Distribution to answer the following question:

- Given a rate $λ$, what is the probability of $x$ successes, i.e. $P(X=x)$?

The Poisson Distribution was invented to predict the probability of a given number of events in a fixed interval of time.

Understand the Poisson Process.

The support of $X$ is ${0,1,2,...}$.

- $E(X)=λ$
- $Var(X)=λ$