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I'm working on the following problem.

Let $X,Y$ independent, standard normally distributed random variables and define $U=\max\{|X|,|Y|\}$ and $V=\min\{|X|,|Y|\}$. Find the mean of $V/U$.

What approach would work here? I don't really see where to start. Using integrals doesn't seem to work. Any hint or (partial) solution is much appreciated!

Václav Mordvinov
  • 3,268
  • $$ E\left[\frac{X\vee Y}{X\wedge Y} \right] = \int_{[0,\infty)^2}\frac{x\vee y}{x\wedge y}f_{X,Y}(x,y)\ \mathsf d(x\times y) $$ The difficulty, of course, is determining the limits of integration. – Math1000 Nov 21 '17 at 13:20
  • Maybe this is a stupid question, but what do you mean with '$\vee$' and '$\wedge$' in this expression? I don't get what you are doing here. – Václav Mordvinov Nov 21 '17 at 13:49
  • Maximum and minimum, respectively. Just a shorthand notation. – Math1000 Nov 21 '17 at 14:24
  • Okay clear, but then we aren't any closer to the solution right? Since this is just the general approach using integrals, but like I said, I don't see how to find the mean using this. – Václav Mordvinov Nov 21 '17 at 14:29

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