You need further information to answer your question. For example if Yn = Xn^2 then clearly you don't have independence.
Suppose that are i.d.d. to some distributions and are i.d.d. to .
If all the X's and Y's are indepedent to one aother, does that also mean that the sums is also independent to ?
So I'm trying to prove it by doing it striaght from the definition:
and try to get it to become
But I'm getting stuck on the left hand side, not sure how to break it down...
Any help, please? Thank you!