# Help on Variance of Variance

1. Oct 25, 2005

### phonic

Does anyone know how to calculate the variance of the variance estimator of normal distribution?

$$x_i, i\in\{1,2,...,n\}$$ are n samples of normal distribtuion $$N(\mu, \sigma^2)$$.

And $$S^2 = \frac{n}{n-1} \sum_i (x_i - \bar x)^2$$ is the variance estimator, where
$$\bar x = \frac{1}{n} \sum_i x_i$$.

The question is how to calculate the following variance:
$$E[(S^2- \sigma^2)^2]$$
Where the expectation is respect to sample $$x_i$$.

Thanks a lot!

Last edited: Oct 25, 2005
2. Oct 28, 2005

### EnumaElish

I am pretty sure that one can find this explained in an intermediate probability textbook like Mood, Graybill & Boes.