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1. Let X have a Poisson distribution with parameter 0. Assume that the unknown O is a value of a random variable 0 that has a gamma distribution with parameters IX = r and fJ = (1 -p)/ p, where r is a positive integer and 0 p 1. Show, by the procedure of compounding, that X has a marginal distribution which is negative binomial, a distribution that was introduced earlier (Section 3.1) under very different assumptions.

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