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**azdang** Let X be Poisson ($\displaystyle \lambda$) with $\displaystyle \lambda$ a positive interger. Show E{|X - $\displaystyle \lambda$|} = $\displaystyle \frac{2 \lambda^\lambda e^{-\lambda}}{(\lambda - 1)!}$ and that $\displaystyle \sigma^2=\lambda$.

We JUST started talking about Expectation Value, and I've never used it in any class before so I am completely confused. I've looked at the whole chapter, but I just cannot figure it out. I do know that for Poisson, EX = $\displaystyle \lambda$, but I don't understand what to do with the absolute value or the subtraction of lambda from X in the expectation.

If it also helps, I know that P(X=k) for Poisson is equal to $\displaystyle \frac{\lambda^k}{k!}e^{-\lambda}$. Can anyone help me out? Thanks so much!