Can Expectations of Random Variables be Proven to Follow a Certain Pattern?

[dabd]

If X is a random variable and f, g are functions is it possible to prove that:

$$E[f(X)] > E[g(X)] \Rightarrow \exists x: f(x) > g(x)$$

 

[mathman]

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