Expected Value of a Function of a Continuous Random Variable

Similar to both Expected Values and Expected Values of Continuous Random Variables. This, by contrast, is looking at the average value of some function $g(x)$. Why is this useful? Well $g(x)$ could be $x^2$, which is a measure related to the variance of $x$.

Formula:

$E(g(x))={\int }_{-\infty }^{\infty }g(x)\cdot PDF(x)dx$