# Math Help - Infinite expectation with finite conditional expected value

1. ## 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?

2. ## 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.

3. ## 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?