Definition:Variance/Continuous

Definition
Let $X$ be a continuous random variable.

Then the variance of $X$, written $\operatorname{var} \left({X}\right)$, is a measure of how much the values of $X$ varies from the expectation $\mathbb E \left[{X}\right]$, and is defined as:
 * $\operatorname{var} \left({X}\right) := \mathbb E \left[{\left({X - \mathbb E \left[{X}\right]}\right)^2}\right]$

That is, the expectation of the squares of the deviations from the expectation.

Letting $\mu = \mathbb E\left[{X}\right]$, this is often given as:


 * $\operatorname{var} \left({X}\right) = \mathbb E \left[{\left({X - \mu}\right)^2}\right]$

Also denoted as
In contexts where the standard deviation is of interest, the variance is often denoted ${\sigma^2}_X$.