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# variance of 1/(X+1)$1/(X+1)$ where X$X$ is Poi(w)Poisson-distributedwithparameter$\lambda$

I cannot compute

What is the variance ! of $1/(X+1)$ where $X$ is Poisson-distributed with parameter $\lambda$! The series for the second moment are is horrible!sum(w^k/kk!) http://mathbin.net/40707

$E({1\over (X+1)^2})=\sum_{k=1}^{\infty}\frac{1}{k^{2}}\frac{\lambda^{k}e^{-\lambda}}{k!}$

Is there an easy way to do it?

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# variance of 1/(X+1) where X is Poi(w)

I cannot compute the variance! The series for the second moment are horrible! sum(w^k/kk!) http://mathbin.net/40707 Is there an easy way to do it?