
Poisson problem
The probability generating function of a discrete nonnegative integer valued random variable N is a function of the real variable t: $\displaystyle P(t)=\sum_{k=0}^{\infty}t^{k}*P[N=k]=E[t^N]$.
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?

Re: Poisson problem
Never mind. It was much easier than I thought.
$\displaystyle P(t)=\sum_{k=0}^{\infty}t^{k}*\frac{e^{2}(2^k)}{k!}$
$\displaystyle P(t)=\sum_{k=0}^{\infty}e^{2}*\frac{(2t)^k}{k!}$
$\displaystyle P(t)=e^{2}*e^{2t}=e^{2(t1)}$