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If $(X<Y)$ are uniform over the region $\{(x,y): 0\lt |y|\lt x \lt 1\}$ then is this region equavalent: $\{(x,y): -x\lt y\lt x \lt 1\}$. I suppose I will justify my thinking here. If the absolute of $y$ is less than $x$, well this is the same property as $|y|\lt 1=-1\lt y\lt1$. That's my reasoning behind my statement. Is it correct?

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Since $x$ is positive, $y$ almost ranges over the interval $(-x,x)$. Since you specified that $0\lt |y|$, to be more precise $y$ ranges over $(-x,0)\cup (0,x)$. – André Nicolas Dec 18 '12 at 4:02
Neither (probability) nor (probability-theory) in there. – Did Dec 19 '12 at 16:22

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