Here is my problem:
Let be iid, .
Show that in probability.
This seems like it should be easy. It's in the section from the book on the Weak Law of Large Numbers (among other things.) I thought I should show that is an iid random variable with finite variance and expected value , so then I could use WLLN to say the sum converges in probability to . But when I try that, I find that is not iid.
I feel like this is easy and I'm just missing something basic. Any thoughts?