> 
> Suppose that $X$ and $Y$ are independent and identically distributed:
>  $$P (X = k) = P (Y = k) = ρ (1 − ρ)^k$$
>  for $k = 0, 1, \dots$ and let $Z := X + Y$. Find the joint distribution of $(X, Z)$ and find the conditional distribution of $X$, given $Z = n$.
> 
> 
> 

I need a little help just setting this up.

If I understand the question, I'm looking for $P (X = k, Z = n)$ and $P (X = k \mid Z = n)$. I'm a little confused, though, because I've never done this when I have a variable defined as a linear function of the other random variables. I also don't really understand what $n$ is.

Any hints or help getting started is appreciated.