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Math Help - Infinite expectation with finite conditional expected value

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    Infinite expectation with finite conditional expected value

    Give an example of two random variables X and Y where X not equal to Y with EX = \infty but E[X|Y] < \infty
    So I'm scratching my head on this one here... I tried to put in some common dist. like normal dist but it won't work, so perhaps I need to construct a special dist? Perhaps let X be Cauchy?
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    Re: Infinite expectation with finite conditional expected value

    Hello,

    Trivial case :
    If you suppose that X is Y-measurable, for example X=2Y, then E[X|Y]=X, and it then suffices to consider that X follows a Cauchy distribution.
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    Re: Infinite expectation with finite conditional expected value

    That would work, but for my understandings sake, how.do i go about constructing an non-trivial example?
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