How do i calculate expectation of expectation?

[AndreTheGiant]

When i have stuff like

E(E(X)) or E(E(XY|X)) etc how do i evaluate a double expectation?

and for random vectors stuff like

E(E(X)'Y) or E(X'E(Y)) etc.

 

[brooksy22]

Not too sure about the vector examples, but for the first couple: Always deal with each expectation in turn. For example if E(X) = 4, E(E(x)) = E(4) = 4. The rules of expections should prove very useful as well, like taking constants outside the expectation sign.