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

A random variable X has the geometric distribution g(x; p) = pq^x?1 for x = 1, 2, 3 Show that the moment-generating function of X is and then use Mx(t) to find the mean and variance of the geometric distribution.

t < In q, pe 1- qet Mx(t)

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