Poisson problem

• Jul 17th 2013, 11:03 PM
downthesun01
Poisson problem
The probability generating function of a discrete non-negative integer valued random variable N is a function of the real variable t: $P(t)=\sum_{k=0}^{\infty}t^{k}*P[N=k]=E[t^N]$.
Which of the following is the correct expression for the probability generating function of the Poisson random variable with mean 2?

I have no idea of how to approach this. Any ideas?
• Jul 17th 2013, 11:13 PM
downthesun01
Re: Poisson problem
Never mind. It was much easier than I thought.

$P(t)=\sum_{k=0}^{\infty}t^{k}*\frac{e^{-2}(2^k)}{k!}$

$P(t)=\sum_{k=0}^{\infty}e^{-2}*\frac{(2t)^k}{k!}$

$P(t)=e^{-2}*e^{2t}=e^{2(t-1)}$