I have a density function f(x, y) = 1/2 for 0 ≤ x ≤ y ≤ 2 and 0 elsewhere. I am being asked to find the CDF value F(1, 3), but as you can see the three is past the range of the defined triangle, what do I do?
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2$\begingroup$ You want $\int_{y=-\infty}^3 \int_{x=-\infty}^1 f(x,y) \, dx\, dy$ $\endgroup$– HenryCommented Nov 16, 2023 at 11:31
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$\begingroup$ and here by excluding places where $f(x,y)=0$ you get $=\int_{y=0}^1 \int_{x=0}^y f(x,y) \, dx\, dy +\int_{y=1}^2 \int_{x=0}^1 f(x,y) \, dx\, dy$ $\endgroup$– HenryCommented Nov 16, 2023 at 13:15
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$\begingroup$ Or $\int_0^1\int_x^2 f(x,y)\,\mathrm d y\,\mathrm d x$ $\endgroup$– Graham KempCommented Nov 17, 2023 at 1:33
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