I'm trying to prove that the sample variance is an unbiased estimator.
I know that I need to find the expected value of the sample variance estimator $$\sum_i\frac{(M_i - \bar{M})^2}{n-1}$$ but I get stuck finding the expected value of the $M_i\bar{M}$ term. Any clues?
I would also like to calculate the variance of the sample variance. In short I would like to calculate $\mathrm{Var}(M_i - \bar{M})^2$ but again that term rears its ugly head.