Let X be Poisson (

) with

a positive interger. Show E{|X -

|} =

and that

.

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 =

, 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

. Can anyone help me out? Thanks so much!