I have hit upon the following wall:
I have three absolutely continuous random variables, $X, Y, Z$. $X$ ranges in all $\mathbb R$, while $Y,Z$ are non-negative. $Y$ and $Z$ are statistically dependent. $X$ is independent of both, in every sense.
I know the joint density $f_{YZ}(y,z)$, and the conditional density $f_{Y|Z}(y\mid z)$, as well as the marginal densities of all three.
Let $Q= X-Y$. $f_Q(q)$ is also available.
I need to obtain the conditional density $f_{Q|Z}(q\mid z)$, or $f_{Z|Q}(z\mid q)$.
For some reason, I am stuck, I mean totally stuck, probably a neurological glitch or something. It appears I need the joint density $f_{QZ}(q,z)$, but I cannot reach it.
Is there any hint out there?