Random Variables $\displaystyle X_1,....X_n$ are independent identical normal distrobuted variables with unknown variance $\displaystyle \sigma^2$.

The sample variance is $\displaystyle S^2=\Sigma_{i=1}^n(X_i-\bar{X})^2/(n-1)$ use the result that $\displaystyle \frac{(n-1)S^2}{\sigma^2}\approx \chi^2_v$ to construct a $\displaystyle 100(1-\alpha)%$ two sided random interval (L,U) for $\displaystyle \sigma^2$ where L and U are functions of $\displaystyle S^2$ such that $\displaystyle Pr(L>\sigma^2)=Pr(U<\sigma^2)=\frac{\alpha}{2}$.

State the degrees of freedom of v and express L and U as a function of $\displaystyle S^2$.

Thanks for any help.