Infinite expectation with finite conditional expected value

Give an example of two random variables X and Y where X not equal to Y with $\displaystyle EX = \infty $ but $\displaystyle 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?

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.

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?