Question: =+28. Consider a negative binomial random variable X with density Pr(X = k) = k 1 n 1 pnqkn for q =

=+28. Consider a negative binomial random variable X with density Pr(X = k) = k − 1 n − 1



pnqk−n for q = 1 − p and k ≥ n. Prove that for any function f(x)

E[qf(X)] = E

(X − n)f(X − 1)

X − 1



.

Use this identity to calculate the mean of X [100].

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