Conditional variance

In statistics, conditional variance is a special form of the variance. If we have a conditional distribution Y|X the conditional variance is defined as

$\operatorname {Var} (Y|X)=E((Y-E(Y|X))^{2}|X),$

where $E$ is the expectation operator. Conditional variances are important parts of ARCH models.

It is also true to say:

$\operatorname {Var} (Y)=E(Var(Y|X))+Var(E(Y|X))$

See also law of total variance.