Prove part (b) of Theorem 9 2 12 Theorem 9 2 12 If FT(t ) is an increasing function of for each t, define L(t) and U(t) by FT(t U(t)) 1 2, FT(t L(t)) 1 Then the random interval L (T), U(T) is a 1 confidence interval for ...

For F T t increasing in there are unique val ...

Prove part (b) of Theorem 9.2.12. Theorem 9.2.12. If FT(t|) is an increasing function of for

Question:

Prove part (b) of Theorem 9.2.12.
Theorem 9.2.12.
If FT(t|θ) is an increasing function of θ for each t, define θL(t) and θU(t) by
FT(t|θU(t)) = 1 - α2, FT(t|θL(t)) = α1.
Then the random interval [θL (T), θU(T)] is a 1 - α confidence interval for θ.