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

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)=Ceayys-1, y>0