Find pX,X+Y(k,n)=P(X=k, X+Y=n)
....I know the pmf for X+Y ~ Pois(λ+μ)
The Attempt at a Solution
As I understand the joint pmf for two independent random variables would be the product of the two individual pmfs. However as X+Y is dependent on X I got really stuck trying to think about this one and how to set it up.
Any help would be great. Thanks :)