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
Attempt:
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
and
so taking that into consideration I would get:
Mr F says: What follows is wrong. See below.
I'm not sure if I should have the bottom indicator or if it should just be:
although this doesn't seem correct.
.