Use the MGF of the Geometric(p) distribution to give another proof that the mean of this distribution is 1/p and the variance is q/p^2, where q = 1 p. (Note: the B&H textbook uses a different definition of the Geometric, where the RV counts the # of failures rather than the # trials until the first success. The mean # of failures is q/p, whereas the mean # of trials is q/p + 1 = (q + p)/p = 1/p.)