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The factorial moment generating function of a discrete random variable X

The factorial moment-generating function of a discrete random variable X is given by

Show that the rth derivative of FX(t) with respect to t at t = 1 is µ'(r), the rth factorial moment defined in Exercise 5.11.

Show that the rth derivative of FX(t) with respect to t at t = 1 is µ'(r), the rth factorial moment defined in Exercise 5.11.

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