# What is the name of the distribution of unbiased sample variance for a sample from Gaussian distribution?

Suppose $X_i$'s are iid Gaussian random variables with mean $\mu$ and variance $\sigma^2$.

The distribution of $\sum_i (X_i - \bar{X}_i)^2 / (n-1)$ isn't Chi square. What is its distribution called?

In my case, how do you determine the values of the parameters?

Thanks.

• Doesn't really fit in a comment. Please edit your question, and I'll respond to that in my answer. However, that now sounds rather like routine bookwork, so you should probably add the self-study tag (and read its tag wiki) – Glen_b -Reinstate Monica Sep 15 '14 at 13:56
• In your answer in the link, $S^2 = \frac{(n-1)S^2}{\sigma^2}\cdot \frac{\sigma^2}{(n-1)}\sim \text{Gamma}(\frac{(n-1)}{2},\frac{2\sigma^2}{(n-1)})$. Should it be $S^2 = \frac{(n-1)S^2}{\sigma^2}\cdot \frac{\sigma^2}{(n-1)}\sim \text{Gamma}(\frac{(n-1)}{2},\frac{2\sigma}{\sqrt{n-1}})$ instead? – Jonas Sep 16 '14 at 19:32