Question: 9. Let X be a geometric random variable with parameter p. Show that the momentgenerating function of X is given by MX(t) = pet 1

9. Let X be a geometric random variable with parameter p. Show that the momentgenerating function of X is given by MX(t) = pet 1 − qet , q = 1 − p, t < − ln q. Use MX(t) to find E(X) and Var(X).

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