Question: Let X denote a random variable such that K(t) = E(t X ) exists for all real values of t in a certain open interval

Let X denote a random variable such that K(t) = E(t^X) exists for all real values of t in a certain open interval that includes the point t = 1. Show that K(m)(1) is equal to the mth factorial moment E[X(X − 1) · · · (X − m + 1)].

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