Let be independent, each with mean 0, and each with finite third moments. Show that:

It gives a hint to use characteristic functions, so here is what I tried doing. I used to represent the sum of the Xi's from 1 to n.

= and

Then, we want to show that .

My first question is if what I have done so far is okay. My second question is, where would I go from here? I can't seem to see it. Thank you!