Calculating Marginal Probability Mass Functions for Discrete Random Variables

[Mathemag1c1an]

I have this question which I cannot seem to solve:
The joint probability mass function p(x, y) of two discrete random variables X and Y is given by.
p(x,y) = ([5^x][7^y][e^-5])/x!(y-x)!
x and y are non-negative integers and x <= y
(i) Find the marginal probability mass functions of X and Y.

 

[Pere Callahan]

You would have to "integrate out" the dependence on the second variable. Explicitly

$$p(x)=\sum_{y\geq x}p(x,y)$$
and
$$p(y)=\sum_{x\leq y}p(x,y)$$
By the way, you joint pmf doesn't sum to one, but to e³⁷.

 

[Mathemag1c1an]

but how do i integrate the factorials?