Difference between revisions of "Variance"

• $$\text{Var}(X)=\mathbb{E}\left[(X-\mu)^2\right]$$

$$=\mathbb{E}\left[X^2-2X\mu+\mu^2\right]$$

$$=\mathbb{E}\left[X^2\right]-2\mu\mathbb{E}[X]+\mu^2$$

But! $$\mu=\mathbb{E}[X]$$

$$=\mathbb{E}\left[X^2\right]-2\mu^2+\mu^2$$

$$=\mathbb{E}\left[X^2\right]-\mu$$

$$=\mathbb{E}\left[X^2\right]-\mathbb{E}[X]$$

As required.