The discussion centers on proving that if two random variables X and Y satisfy the conditions \(\mathbb{E}(X|Y)=Y\) and \(\mathbb{E}(Y|X)=X\), then X equals Y almost surely (a.s.). Participants seek clarification on the definition of conditional expectation, \(\mathbb{E}(X|Y)\), to facilitate the proof. The consensus is that understanding the properties of conditional expectation is crucial for establishing the equality of the random variables.
PREREQUISITESMathematicians, statisticians, and students of probability theory who are interested in advanced concepts of random variables and conditional expectations.
yavanna said:How can I do this?
Let X,Y r.v., [tex]\mathbb{E}(X|Y)=Y[/tex] and [tex]\mathbb{E}(Y|X)=X[/tex].
Proove that X=Y a.s.