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Xand Y are independent X~G(p) , Y~G(p) show U=X+Y follow NB(2,p)

Xand Y are independent X~G(p) , Y~G(p)

show U=X+Y follow NB(2,p)

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Answer #1

are IID random variables with Geometric distribution. .

The PMFs are

The PMF of is found as

Clearly, the above PMF is Negative Binomial with parameters .

Thus, . The proof is complete.

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