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a) If X Pois() and g is any function, show that : E Xg(X)] = E [g(X + 1)] (This is called the Stein-Chen identity
a) If X Pois() and g is any function, show that :
E Xg(X)] = E [g(X + 1)]
(This is called the Stein-Chen identity for the Poisson.)
(b) Find the third moment E [X3] for X Pois() by using the identity from (a) and the fact that X has mean and variance . Simplify your answer.
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