Question: Suppose that the random variables X1, . . . , Xk are independent and that Xi has the negative binomial distribution with parameters ri and

Suppose that the random variables X1, . . . , Xk are independent and that Xi has the negative binomial distribution with parameters ri and p (i = 1 . . . k). Prove that the sum X1 + . . . + Xk has the negative binomial distribution with parameters r = r1 + . . . + rk and p.

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