28. (i) Under the assumptions of the preceding problem, the uniformly most accurate unbiased (or invariant) confidence intervals for 8 at confidence level 1 - a are fl = max( X(1) +

d, X(II)) - 1 < 8 < min( X(1)' X(II) -

d) = B, where d is the solution of the equation 2d" = a 2d" - (2d - 1)II = a if a < 1/2"- 1 , if a > 1/2"- 1• (ii) The sets Cl : X(II) - X(I) > d and C2 : X(II) - X(I) < 2d - 1 are relevant subsets with coverage probability Po [fl < 8 < BICI] = 1 and Po [fl < 8 < BIC2] = o. (iii) Determine the uniformly most accurate unbiased (or invariant) conditional confidence intervals fl(v) < 8 < B(v) given V = v at confidence level 1 -

a, and compare fl(v), B(v), and B(v) - fl(v) with the corresponding unconditional quantities . [Welch (1939), Pratt (1961), Kiefer (1977a).]