It is given that $E[Y/A]$ where $A = {X \in C}, C \in B(R) $; Want to indicate how to compute $E[Y/A]$. Here $X$ and $Y$ are random variables with joint density $f(x,y)$. Any ideas will be very helpful on this problem.
I started doing as follows;
$E[Y/A] = E[Y/X \in C] $.
I don't know how to continue from here.
Thank you.
The conditional expectation is $$\mathbb{E}[Y \mid X \in C] = \dfrac{\displaystyle \int_{y\in \mathbb{R}}\int_{x \in C} y f(x,y) \, dx\, dy}{\displaystyle \int_{y\in \mathbb{R}}\int_{x \in C} f(x,y) \, dx\, dy}$$ though as Ian says there is an issue if the denominator is zero.