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Question about expectations

  1. May 19, 2010 #1
    If X is a random variable and f, g are functions is it possible to prove that:

    [tex]E[f(X)] > E[g(X)] \Rightarrow \exists x: f(x) > g(x)[/tex]
     
  2. jcsd
  3. May 19, 2010 #2

    mathman

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    Yes. Assume it is not true, g ≥ f for all x => E(g) ≥ E(f).
     
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