Suppose X and Y are independent Poisson random variables with parameters a and b respectively. Find the joint mass function
P[X = k, Y = m]
(exp(-a).a^k)/k! x (exp(-b).b^m)/m!
Find P[X + Y = n]
I got = P[X = k, Y = n - k]
= sum over k to n (exp(-a).a^k)/k! x (exp(-b).b^n - k)/(n-k)!
But I'm not sure how to complete
is this right so far?