# Difference between Variance and 2nd moment

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 $E(X^2) - E(X)^2$?

$$\mathbb{E}(X^n) = \text{raw moment}\\ \mathbb{E}\left[\left(X-\mathbb{E}(X)\right)^n\right] = \text{central moment}$$ where the 2nd central moments represents the variance.
only equal when $\mathbb{E}(X) = 0$ as with $\mathcal{N}(0,1)$.
Simple: $$\operatorname{Var}(X)\neq E(X^2)$$
• @slimydummy If $E(X^2)-(E(X))^2=E(X^2)$, so use some algebra and you get... – user223391 Nov 25 '16 at 17:33