Variance

The variance of a random variable $X$ is defined as $\mathrm{V}\mathrm{a}\mathrm{r}(X):=\mathbf{E}[(X-\mathbf{E}X{)}^2]$, where $\mathbf{E}X$ is the expectation of $X$.

Notation

Since the square root of the variance is the standard deviation, if we have a simple notation for the standard deviation, such as $\sigma$, then we can denote the variance as ${\sigma }^2$.

Questions/things to explain

• vector space interpretation [1] see also the beginning of [2]