Question: Factorial moments. Let X be a random variable with values in ZC and generating function 'X, and for each k 2 N let X.k/ D

Factorial moments. Let X be a random variable with values in ZC and generating function

'X, and for each k 2 N let X.k/ D X.X 1/ : : : .XkC1/. Show that '.k/

X .1/ D E.X.k// when X 2 Lk.

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