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
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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...
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