Find $k$ such that $f(x,y) = k, 0<x<y<1$ is a probability joint density function. ($f(x,y) = 0$ otherwise).
I'm having trouble with these combined integration limits. Is this correct?
$\displaystyle \int_{0}^{1} \int_{0}^{y} f(x,y) dxdy = \int_{0}^{1} kydy = \frac{k}{2}$.
If $f$ is a joint density, then $\frac{k}{2} = 1 \iff k = 2$.
As @GnuSupporter said in the comments, it is indeed correct. The limits of the inner integral are $0$ and $y$ because $0<x<y$.