Question 4 (Interval estimation). Assume the same setting as in Question 3. Denote the 100p% quantile of N(0, 1) by Ep. 1. (5%) Prove that 18 = F-1(a/2) F,21(1 - Q/2) T T is a 100(1 - a)% confidence interval for 0. 2. (5%) Find a 100(1 - a) confidence interval I for o = Eo (X1) 3. (5%) Prove that vn(0 -0)/0 N(0. 1) as n - 00. 4. (5%) Construct an asymptotic 100(1 - a)% confidence interval le for 0. 5. (5%) Find the coverage probability of le. 6. (5%) Besides using Io, propose one method that might improve le. State your reason(s)