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Y~Pois(μ)=> py(k)=e-μμk/k!

Find pX,X+Y(k,n)=P(X=k, X+Y=n)

....I know the pmf for X+Y ~ Pois(λ+μ)

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 :)