Let $$f_{X,Y}(x,y) = 8xy\mathbb{1}_D(x,y)$$ with $D=\{0<x<y<1\}$
I want to find $F_{X,Y}(x,y)$, I do this by integrating:
$$ F_{X,Y}(x,y) = \int_{-\infty}^x \int_{-\infty}^y 8 x y dxdy$$ However now I think I misunderstand because I set up the integral on $D$ in this way: $$ F_{X,Y}(x,y) = \int_{x}^1 \int_{0}^y 8xydxdy$$ This is because x is between 0 and y and y is between x and 1, however I get the wrong result. Is there a mistake in the boundaries of the integral?