What is an intuitive explanation of why $\displaystyle \text{Var}(Y) = E(\text{Var}(Y|X)) + \text{Var}(E(Y|X)) $? In laymen terms, it is equal to the variance of the conditional expectation plus the expected value of the conditional variance.

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- Oct 17th 2010, 08:32 AMTimeConditional and Total Variance
What is an intuitive explanation of why $\displaystyle \text{Var}(Y) = E(\text{Var}(Y|X)) + \text{Var}(E(Y|X)) $? In laymen terms, it is equal to the variance of the conditional expectation plus the expected value of the conditional variance.

- Oct 17th 2010, 03:44 PMyannyy
my lecturer told me that there is no simple intuitive explanation to this and it has a complex proof to it as well.

Law of total variance - Wikipedia, the free encyclopedia

Theres a proof in there - Oct 17th 2010, 03:45 PMyannyy
my lecturer told me that there is no simple intuitive explanation to this and it has a complex proof to it as well.

Law of total variance - Wikipedia, the free encyclopedia

Theres a proof in there