Find the marginal density of X given that (fx|y=y(x)) = e^(-y)*y^x/x!

(i.e., that the conditional density of X, given that Y=y is Poisson(y))

and that fy(y) = lamda^a / gamma(a) * y^(a-1)*e^(-lamda*y) where a(alpha) is a positive integer (i.e., the random variable Y has gamma(a,lamda) density). Hint: fx(x) is a well-known density.

???? ㅡㅡ;;