The prompt is: Let X1 and X2 have (the same) probability mass function

f(x) := (exp[-n]) * n/x! for x=(0,1,2,3....) where n is a positive constant. Assume that

{X1 = a} and {X2 = b} are independent events for any nonnegative integers a and b.

The question: For any nonnegative integer b, show that:

P(X1 + X2 =b) = the sum from x=0 to b is P(X1 + X2 = b intersect X2 = x) =

the sum from x=0 to b is P(X1 =b-x)P(X2 =x).

I am looking for a little guidance or insight on this problem. I'm stuck on how to get started. Thanks.