Conditional variance
= Conditional variance
{title2=$\operatorname{Var}(X\mid\mathcal G)$}
{wiki}
The conditional variance is
$$
\operatorname{Var}(X\mid\mathcal G)
=\mathbb E\!\left[(X-\mathbb E[X\mid\mathcal G])^2\mid\mathcal G\right].
$$
Its expectation is the mean squared error of the conditional-expectation predictor.