Conditional variance

In probability theory and statistics, a conditional variance is the variance of a conditional probability distribution. The conditional variance of a random variable Y given the value of a random variable X is

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

where E is the expectation operator. Particularly in econometrics, the conditional variance is also known as the scedastic function or skedastic function. Conditional variances are important parts of ARCH models.

The law of total variance says

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