Question: Let Y be a gamma random variable with parameters (s, a). That is, its density is fr(y) Cey, y> 0 where C is a constant

Let Y be a gamma random variable with parameters (s, a). That is, its density is fr(y) Cey, y> 0 where C is a constant that does not depend on y. Suppose also that the conditional distribution of X given that Yy is Poisson with mean y. That is, P(X Y yey'/i!, izo Show that the conditional distribution of Y given that X = i is the gamma distribution with parameters (s + i, a + 1).

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