Conditional variance: Difference between revisions

Revision as of 01:06, 16 July 2016

Revision as of 12:43, 12 September 2016

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&= \operatorname{E}[ (Y-\operatorname{E}(Y|X)\,\,+\,\, \operatorname{E}(Y|X)-f(X) )^2 ] \\

&= \operatorname{E}[ \operatorname{E}\{ (Y-\operatorname{E}(Y|X)\,\,+\,\, \operatorname{E}(Y|X)-f(X) )^2|X\} ] \\

&= \operatorname{E}[\operatorname{Var}( Y| X )] + \operatorname{E}[(\operatorname{E}(Y|X)-f(X))^2]\,.

\end{align}

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