In other words, is $S^2$ unbiased for $sigma^2$ for any distribution? I know how to prove this for the normal distribution, but is it possible for me to prove this generally?

Thank you

**Contents**hide

#### Best Answer

I don't know how you managed to prove it via properties of normal RVs, but you can follow the steps for a general derivation here. Note that Bessel corrected formula is the unbiased estimator. Of course, for the distributions we're referring to, the moments should be defined.

### Similar Posts:

- Solved – The derivation of standard deviation
- Solved – When estimating variance, why do unbiased estimators divide by n-1 yet maximum likelihood estimates divide by n
- Solved – Unbiased estimator of standard deviation of a normal distribution, using gamma function
- Solved – Expectation of the sample median for symmetric distributions
- Solved – Unbiased estimator of variance for samples *without* replacement