I am curious if any expert knows what the expected value is of SUM (Xi - X-bar)^2 from 1 to n. Where Xi are a random sample from a distribution?
We have been showing that the expected value of S^2 is sigma squared. But I am wondering how to do this without the n or (n-1) divisor.
We were able to do the formers by re-writing S^2 as SUM(Xi^2)^2 /n - x-bar^2
but this does not work for SUM (Xi - X-bar)^2