I'm completely new to probability, so I'm learning as I go. The convolution theorem isn't something I know or have in any of my materials, but I'll do some research and hopefully that'll point me in the right direction.
X~Pois(λ)=> px(k)=e-λλk/k!
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...
Homework Statement
X~Pois(λ)=> px(k)=e-λλk/k!
Y~Pois(μ)=> py(k)=e-μμk/k!
Find pX,X+Y(k,n)=P(X=k, X+Y=n)
Homework Equations
...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...