variance

let $\text{[math]}$ be a random variable whose expected value is finite $\text{[math]}$ , the variance of $\text{[math]}$ , denoted by $\text{[math]}$ , is defined as
$\text{[math]}$

if $\text{[math]}$ has a finite expected value then
$\text{[math]}$

some important properties:

$\text{[math]}$
$\text{[math]}$ iff $\text{[math]}$ is constant
$\text{[math]}$

let $\text{[math]}$ be a random variable whose distribution law is
$\text{[math]}$ we find the variance:
$\text{[math]}$

variance measures the spread around the mean.