Question: Let X 1 , X 2 , and X 3 be three independent negative binomial random variables with pdfs for i = 1, 2, 3.

Let X1, X2, and X3 be three independent negative binomial random variables with pdfs

5) k=3,4, 5, ,

for i = 1, 2, 3. Define X = X1 + X2 + X3. Find P(10 ≤ X ≤ 12). (Use the moment-generating functions of X1, X2, and X3 to deduce the pdf of X.)

5) k=3,4, 5, ,

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