TITLE: Difference between Variance and 2nd moment
QUESTION [18 upvotes]: I understand that
$Var(X) = E(X^2) - E(X)^2 $
And that the second moment, variance, is
$E(X^2)$
How is variance simultaneously $E(X^2)$ and $E(X^2) - E(X)^2$?

REPLY [28 votes]: $$
\mathbb{E}(X^n) = \text{raw moment}\\
\mathbb{E}\left[\left(X-\mathbb{E}(X)\right)^n\right] = \text{central moment}
$$
where the 2nd central moments represents the variance.
only equal when $\mathbb{E}(X) = 0$ as with $\mathcal{N}(0,1)$.