17. Let Y be a gamma random variable with parameters (s, ). That is, its density is...

17. Let Y be a gamma random variable with parameters (s, α). That is, its density is fY (y) = Ce−αy ys−1, y > 0 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, P{X = i|Y = y} = e−y yi

/i!, i  0