Given a random sample of size $n$, from a normal population with variance $\sigma^2$, I am trying to find and identify the distribution of the sample variance, $S^2$.
I know that $\frac{(n-1)S^2}{\sigma^2}$ ~ Chi-Square($n-1$) when the population is normal, but I'm not sure how to express the distribution of $S^2$.
Specifically, I want to figure out how to fill in the parameter for $S$~Chi Square( ... )
If anyone has any suggestions, that would be quite helpful.