I apologize in advance for the crappy title but I didn't know how else to describe my problem. I'm trying to solve a problem where Y1, Y2, ... , Yn is a random sample of size n from a normal population with mean = (mu) and variance = (sigma^2).
We are given an estimator for (sigma^2):
(sigma^2) = 1/2k [summation from i=1 to k] (Y2i - Y2i-1)^2
where 2i and 2i-1 above are subscripts of the Y's.
I'm trying to show that the estimator above is consistent using the variance. I know that the mean of each term [(Y2i - Y2i-1)^2]/2 has mean of (sigma^2) but it says in the solution that the variance of each such term is 2(sigma^4) and I can't figure out how they get that.