# Math Help - Inequality

1. ## Inequality

This one is really hard, any help??

2. Does that X really belong in that integrand?

the idea is that g(X)/g(e)>1 so it should be a 1 in the integrand.

3. Ever heard of Chernoff's inequality?

4. What I was saying.........

$E(g(X))= \int_0^{\infty}g(x)dP=\int_0^{a}g(x)dP+\int_a^{\in fty}g(x)dP$

$\ge \int_a^{\infty}g(x)dP =g(a)\int_a^{\infty}{g(x)\over g(a)}dP$

$\ge g(a)\int_a^{\infty}dP$