3. Assume we observe r1, ....In ER with ; # x; for some i, j. Let Yi = Bot BIritei, for ci~ N(0, 02), where Bo, B1 E R and o? > 0 are unknown. (a) Find the UMPU level-a test of Ho : B1 = b vs H1 : B1 b, specifying the null distribution and cutoffs. Hint: You can use the results discussed in class, e.g. page 16 of Lec 9 and page 5-6 of Lec 10. How would you select Z1, q1, and Go in this context? This doesn't require extensive computation. (b) Let B = (Bo, B1) . For v E R2, find the UMPU level-a test of Ho : v B = 0 vs H1 : v 3 0. Hint: WLOG, you can assume |v 2 = 1 (why?). Find a unit vector u e R? which is orthogonal to v. Then, write E [Y] = XB = Xvv B + XuuTB. How would you apply the results from class to this case