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:<math>\operatorname{Var}(Y) = \operatorname{E}(\operatorname{Var}(Y\mid X))+\operatorname{Var}(\operatorname{E}(Y\mid X)),</math>
where, for example, <math>\operatorname{Var}(Y|X)</math> is understood to mean that the value ''x'' at which the conditional variance would is evaluated is allowed to be a [[random variable]], ''X''. In this "law", the inner expectation or variance is taken with respect to ''Y'' conditional on ''X'', while the outer expectation or variance is taken with respect to ''X''. This expression represents the overall variance of ''Y'' as the sum of two components, involving a prediction of ''Y'' based on ''X''. Specifically, let the predictor be the least-mean-squares prediction based on ''X'', which is the [[conditional expectation]] of ''Y'' given ''X''. Then the two components are:
:*the average of the variance of ''Y'' about the prediction based on ''X'', as ''X'' varies;
:*the variance of the prediction based on ''X'', as ''X'' varies.
[[Category:Statistical deviation and dispersion]]
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