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Next: Parameters of Distributions 11/3 Up: Poisson random variable 11/2 Previous: Motivation

   
Definition 11/2

A discrete random variable taking on values 0,1,2,... with the probability mass function:

\begin{displaymath}P(X=k)=\frac{\lambda^k e^{-\lambda}}{k!}\end{displaymath}

is called the Poisson distribution.

We can check it is a probability mass function because

\begin{displaymath}\sum_{k=0}^{\infty} \frac{e^{-\lambda}\lambda^k}{k!}=
e^{-\lambda}e^{\lambda}=1\end{displaymath}



Susan Holmes
1998-12-07