We saw in Exercise 5.159 that the negative binomial random variable Y can be written as
Chapter 6, Problem 6.58(choose chapter or problem)
We saw in Exercise 5.159 that the negative binomial random variable Y can be written as Y = r i=1 Wi , where W1, W2,..., Wr are independent geometric random variables with parameter p.a Use this fact to derive the moment-generating function for Y . b Use the moment-generating function to show that E(Y ) = r/p and V(Y ) = r(1 p)/p2. c Find the conditional probability function for W1, given that Y = W1 + W2 ++ Wr = m
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