Thread: Quick question on conditional expectation

Let x,y be continous random variables.

Prove that E(E(y|x)) = E(y)

I am sure this is a very basic question but still if someone can provide/guide towards a rigourous proof for the same?

Thanks

In fact I realised that the more generic result will hold true

E(E(f(x,y)|x)) = E(f(x,y)), where f(x,y) is a real valued function on (x,y)

E stands for expected value.

Any help/pointers to prove this (in a rigorous way) will be great ! Thanks

It's true in any case, but the continuous case is easy...

which is a function of X

next integrate wrt x and multiply the densities...



Fubini...