- #1
Obie
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I have a simple-seeming question on conditional expectation. It seems simple, but it has eluded my attempt to answer.
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...
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...