Question: 25. In the Problem 24 above, suppose k = 1. Show that if Y is a random variable denoting the number of trials required to

25. In the Problem 24 above, suppose k = 1. Show that if Y is a random variable denoting the number of trials required to obtain one failure, then the p.f. of Y is p(y) = pqy−1, y= 1, 2, . . .

and that its mean and variance are 1/p and q/p2, respectively. This distribution is called the geometric distribution. Show that

∞

y=1 p(y) = 1.

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