Any I.i.d sequence of random variables are uniformly integrable This is an exam question. My teacher says it is true. But I'm thinking it might be false for random variables such as Cauchy. Can anyone confirm that this is false in general?
I think Cauchy distribution would be fine because it is bounded. In general I think it is true, you can take the maximum point of the distribution to use with your delta in your epsilon-delta proof. 

Also, given that all the distributions are the same, you can of course bound the absolute integrals. The absolute integrals are the same as the usual integral as the pdfs are positive functions.
I think Cauchy distribution would be fine because it is bounded. In general I think it is true, you can take the maximum point of the distribution to use with your delta in your epsilon-delta proof. 

Also, given that all the distributions are the same, you can of course bound the absolute integrals. The absolute integrals are the same as the usual integral as the pdfs are positive functions.