Having X~Uniform(0,1), Y~Uniform(0,1) independent what's the pdf of r = |X - Y|. If I want plot f(r=|X - Y|) against X, what should I do?
about the plot, at first I thought of doing, $r^2 = (x - y)^2$, and call $y=\rho$, but it did not work.
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Hint: $|X-Y|\leqslant t$ if and only if $X-Y\leqslant t$ and $Y-X\leqslant t$. – Math1000 Nov 11 '19 at 20:20
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I recommend you look at the highest-voted solution in the post that I linked. I believe it answers everything you ask about. – Math1000 Nov 11 '19 at 20:25
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@Math1000 thank you. – megazord Nov 12 '19 at 13:28