Question: A random variable X has the geometric distribution g(x; p) = pq for x = 1, 2, 3, . Show that the moment-generating function of

A random variable X has the geometric distribution g(x; p)

= pq for x = 1, 2, 3, …. Show that the moment-generating function of X is and then use M (t) to find the mean and variance of the geometric distribution.

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