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Math Help - Poisson problem

  1. #1
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    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?
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  2. #2
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    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)}
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