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 ${\sigma^2}_X$.

Also see

 * Definition:Variance of Discrete Random Variable