I'm working on a problem where $f(x,y)=c(x+y)$ is a joint PDF where $0<x<y<1$. Can someone explain what the region $0<x<y<1$ would look like, or how I can integrate with these bounds? I've tried integrating from $0$ to $x$ and $0$ to $y$ on $x$ and $y$ respectively but that doesn't seem to work.
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The region $0<x<y<1$ looks like the interior of a symmetric right-angle triangle bounded by the lines $x=0$, $y=1$ and $y=x$. If for example you want to find $c$, you could try the integral $$\int_{y=0}^1 \int_{x=0}^y c(x+y) \; dx \; dy$$ and set that equal to $1$ to solve for $c$, though there are other possible approaches. |
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