Question: 5.23 A random variable X has the negative binomial distribution, pr(X = k) = n + k 1 n 1 p q

5.23 A random variable X has the negative binomial distribution, pr(X = k) = n + k − 1 n − 1

p q

1 − p q

, for k ≥ 0, in which q = 1+ p. Show that the expectation and variance of X are given by E[X] = np, Var(X) = np(1 + p). Use these expressions to derive estimates of n and p using the method of moments.

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