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

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

Thanks for any help.