17. Let Y be a gamma random variable with parameters (s, ). That is, its density is...
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17. Let Y be a gamma random variable with parameters (s, α). That is, its density is
where C is a constant that does not depend on y. Suppose also that the conditional distribution of X given that Y = y is Poisson with mean y. That is,
Show that the conditional distribution of Y given that X = i is the gamma distribution with parameters (s + i, α + 1).
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