Conditional expectations and variances

Well, that's all well and good to have a theorem relevant to my research, but we need to get back to Q topics. I promised myself I'd get through Probability Theory by the end of the month.

If X and Y are random variables then:

• E(X) = E(E(X|Y)), provided the expectations exists.
• Var(X) = E(Var(X|Y)) + Var(E(X|Y)), provided the expectations exist.

The proofs for both of these are largely symbol manipulation exercises, but the results are worth knowing. Both results are necessary to prove the blocksum theorem I stated yesterday.