I have a simple-seeming question on conditional expectation. It seems simple, but it has eluded my attempt to answer.(adsbygoogle = window.adsbygoogle || []).push({});

Suppose that two jointly distributed random variables (X,Y) exist with support on positive real line.

From these, it is possible to construct a new random variable, Z=E[X|Y]. Of course, by Bayes rule, E[Z]=E[E[X|Y]]=E[X]. Support of Z is a subset of positive real line.

Suppose now that you are given some third random variable W, and you know that E[W]=E[X]. W hassupport on positive part of real line. Does there exist a random variable V, jointly distributed with X for which W=E[X|V].

Any help is appreciated...

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# Conditional expectations question

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