I am trying to find $E[Y|X+Y=c]$ where $X$ is a uniform random variable on $[-1,1]$ and $Y$ is a uniform random variable on $[0,1]$ and $X,Y$ are independent.
I know that for discrete events, we have Bayes' Rule of $P(A|B)P(B)=P(A \cap B)$. As far I am aware, this also applies to densities. Density of $X+Y=c$ is $4/9 + 4c/9$ for $c \leq 0.5$ is my guess. However, I struggle to evaluate the numerator.
Can anybody help? Thank you!