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F y(w) >= F x(w), for all w. Prove P{y<x} >= 0.5

I had this question on the exam and boy did it stump me. It was simple to understand why it was true, but I tried several different paths and got nowhere.

Any ideas?

  • 0
    What distribution are we talking about here?2010-10-03
  • 0
    Are $X$ and $Y$ independent?2010-10-03
  • 0
    Any distribution, and I believe they were independent if it matters.2010-10-03

3 Answers 3