Let be a random sample of size n from a normal population with mean and variance . Assuming n=2k for some integer k, one possible estimator for is given by:
show that is an unbiased estimator for
so when I expend it out it gives:
That term in the middle is throwing me off.
I know that I eventually have to use the fact that
so taking that into consideration I would get:
I'm not sure if I should have the bottom indicator or if it should just be:
although this doesn't seem correct.