Variance

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