Question: A random variable X has the geometric distribution g(x; p) = pqx1 for x = 1, 2, 3,... . Show that the moment-generating function of

A random variable X has the geometric distribution g(x; p) = pqx−1 for x = 1, 2, 3,... . Show that the moment-generating function of X is MX(t) = pet 1 − qet , t< ln q, and then use MX(t) to find the mean and variance of the geometric distribution.

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