# Infinite expectation with finite conditional expected value

• April 30th 2012, 09:29 AM
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?
• April 30th 2012, 02:37 PM
Moo
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.
• April 30th 2012, 03:18 PM