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Answer (1 of 2) Conditional expectation is difficult to work with in the most general case Here is a link to the proof in the general case, but it may not be that informative if you are not familiar with measure theory Law of total expectation I will give you a "proof" in the special caseIs defined for any real valued function g(X) In particular, E(X2jY = y) is obtained when g(X)=X2 and Var(XjY =y)=ECorrelation is a scaled version of covariance; America S Skills Challenge Millennials And The Future Appendix C ƒXƒ|[ƒcŠ ‚è ƒƒ"ƒY ƒ{ƒEƒY Š ‚èã‚°