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Consider the following mixtures models: a. If y|0 ~ Poisson(0) and 0 ~ Gamma(a, B), then the marginal distribution for y is a negative binomial

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Consider the following mixtures models: a. If y|0 ~ Poisson(0) and 0 ~ Gamma(a, B), then the marginal distribution for y is a negative binomial with parameters a and B. Use the iterated expectation and variance formulas to derive the mean and variance of the negative binomial distribution

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