Question about expectations

dabd

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]

mathman

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

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dabd	Question about expectations Tweet 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]

mathman Recognitions: Science Advisor	Yes. Assume it is not true, g ≥ f for all x => E(g) ≥ E(f).