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Compute the Probability for Two Uniform Variables

ImcQuantitative Trader · Technical Screen
HardQuantitative TraderTechnical ScreenSoftware Engineering Fundamentals

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This question evaluates understanding of continuous probability, joint distributions, and order statistics for independent uniform variables, focusing on comparing transformations of random variables.

Let (X) and (Y) be independent random variables, each uniformly distributed on ([0,1]). Define:

  • (L = \max(X,Y))
  • (S = \min(X,Y))

What is the probability that the square of the larger value is greater than the smaller value, that is, (P(L^2 > S))?