Question: 2. Let X1, X2, . . . , Xn be independent geometric random variables each with parameter p. Using moment-generating functions, prove that X1 +

2. Let X1, X2, . . . , Xn be independent geometric random variables each with parameter p. Using moment-generating functions, prove that X1 + X2 + · · · + Xn is negative binomial with parameters (n, p).

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