Derive minimum length confidence bounds for a F distribution variance $\sigma^2$ and the ratio of two F distribution population variances $\frac{\sigma_1^2}{\sigma_2^2}$.
What I got so far is $$ P[a < \frac{s_1^2/\sigma_1^2}{s_2^2/\sigma_2^2} < b] $$=$$ P[a < \frac{s_1^2\sigma_2^2}{s_2^2\sigma_1^2} < b]$$ = $$ P[\frac{s_2^2}{s_1^2}a < \frac{\sigma_2^2}{\sigma_1^2} < \frac{s_2^2}{s_1^2}b]$$ = $$ P[\frac{s_1^2}{s_2^2b} < \frac{\sigma_1^2}{\sigma_2^2} < \frac{s_1^2}{s_2^2a}]$$
Is this approach right...How do I move forward with this? Let me know if the question is unclear to you