Can someone please help me with this question ?!

[Amber Roxanna]

Show that the cauchy random variable
is not an integrable random variable

 

[koupparis]

Umm, take it's pdf and compute E[X]. Where's the problem?

 

[Amber Roxanna]

so i compute the integral of X times the pdf of the cauchy distribution, but from what limits ? -inf to inf ?

 

[koupparis]

Yes, those limits are correct. In general the limits are the domain of the random variable. Look up the Cauchy distribution and you'll see.