# Math Help - Conditional and Total Variance

1. ## Conditional and Total Variance

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

2. 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

3. 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