Question: Let X be a random variable with the Poisson distribution with parameter ????. Show that the rth factorial moment of X, ????(r) = E[X(X

Let X be a random variable with the Poisson distribution with parameter ????. Show that the rth factorial moment of X,

????(r) = E[X(X − 1) · · · (X − r + 1)], r ≥ 1,

is given by ????(r) = ????r.

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