# Definition:Variance/Continuous

## Definition

Let $X$ be a continuous random variable.

Then the variance of $X$, written $\var X$, is a measure of how much the values of $X$ varies from the expectation $\expect X$, and is defined as:

$\var X := \expect {\paren {X - \expect X}^2}$

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

Letting $\mu = \expect X$, this is often given as:

$\var X = \expect {\paren {X - \mu}^2}$

## Also denoted as

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