Prove that if E[Y|X = x] = E[Y] for all x, then X and Y are uncorrelated;

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Prove that if E[Y|X = x] = E[Y] for all x, then X and Y are uncorrelated; give a counterexample to show that the converse is not true.
Prove and use the fact that E[XY] = E[XE[Y|X]].

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A First Course In Probability

ISBN: 9789332519077

9th Edition

Authors: Sheldon Ross

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Question Posted: Oct 22, 2015 03:03 AM

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Prove that if E[Y|X = x] = E[Y] for all x, then X and Y are uncorrelated;

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EXY EEXYX EXEYX Hence if EYX EY th...View the full answer

A First Course In Probability

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