If a(x) is a function whose expectation exists, and if $\displaystyle a(x) \geq 0$, then $\displaystyle E[a(x)] \geq 0$

So i did this:

$\displaystyle a(x) \geq 0$

$\displaystyle a(x) \times 1 \geq 0$

$\displaystyle a(x) \displaystyle \int_{-\infty}^{\infty} f_{X}(x)dx \geq 0$

$\displaystyle \displaystyle \int_{-\infty}^{\infty} a(x) \; f_{X}(x) \; dx \geq 0$

$\displaystyle E(a(x)) \geq 0$

And do the same for discrete cases....

Is this correct?