$Y=X+\xi X$, $X \sim \operatorname{Unif}[-1, 1]$, $\xi \sim \operatorname{Unif}[0, 1]$. $X$ and $\xi$ are independent.
I need to find $f_{Y\mid X}(y\mid x)$. How to do it? I couldn't find joint probability. Any hints? I think the questions of finding the joint density and the conditional density are equivalent, because it is expressed through each other