Conditional variance: Difference between revisions

Revision as of 18:20, 25 April 2016

Revision as of 04:43, 26 April 2016

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By selecting <math>f(X)=\operatorname{E}(Y|X)</math>, the second, nonnegative term becomes zero, showing the claim.

Here, the second equality used the [[Law of total expectation|law of total expectation]].

We also see that the expected conditional variance of ''Y'' given ''X'' shows up as the irreducible error of predicting ''Y'' given only the knowledge of ''X''.