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Math Help - Poisson Expectation

  1. #1
    Yan
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    Poisson Expectation

    Suppose X has a Poisson distribution with mean 3. then how to compute E[1/((X+2)(X+1))]?
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  2. #2
    MHF Contributor harish21's Avatar
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    Where are you stuck?

    E\bigg[\dfrac{1}{(x+2)(x+1)}\bigg] =\displaystyle \sum_{x=0}^{\infty}  \dfrac{1}{(x+2)(x+1)} \times \dfrac{e^{-\lambda}{\lambda}^x}{x!}

    =\displaystyle \sum_{x=0}^{\infty} \dfrac{e^{-\lambda}{\lambda}^x}{(x+2)!}

    = \displaystyle \sum_{x=0}^{\infty} \dfrac{e^{-\lambda}{\lambda}^{(x+2)} \; {\lambda}^{-2}}{(x+2)!}\;=\;......
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