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Question about expectations

by dabd
Tags: expectations
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dabd
#1
May19-10, 03:07 PM
P: 25
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]
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mathman
#2
May19-10, 03:47 PM
Sci Advisor
P: 6,037
Yes. Assume it is not true, g ≥ f for all x => E(g) ≥ E(f).


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