17. Let Y be a gamma random variable with parameters (s, ). That is, its density is where C is a constant that does not

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).

fy(y) = Cey-1, y >0