What is $E(X^2)$ mean in literal terms? In my probability and statistics class we learned about expected value, or $E(X)$. We also did some work about finding expected values of functions and such, like $E(g(x))$. And in the case of finding the variance, one of the steps involve finding $E(X^2)$. Does this mean anything in real-life terms? 
Using a geometric distribution as an example, is $E(X^2)$ the expected number of times a trial needs to happen until the event $X$ happens twice in a row?

Imagine that $X$ is the side length of a square.  Then $X^2$ is its area.  Now $E(X)$ is the expected side length and $E(X^2)$ its expected area.  It turns out the square of the expected length is not the expected area.  The difference is called variance.
