27. Let Xl" ' " x" be independently distributed according to the uniform distribution U(8, 8 + 1). (i) Uniformly most accurate lower confidence bounds fl for 8 at confidence level 1 - a exist and are given by fl = max(X(I) - k, X(II) - 1), where X(I) = min(XI , · · · , XII)' X(II) = max(XI, .. ·, X,,), and (1 - k)" = a . (ii) The set C: x( II) - x(\) 1 - k is a relevant subset with Po(fl 81C) = 1 for all 8. (iii) Determine the uniformly most accurate conditional lower confidence bounds fl(v) given the ancillary statistic V = X(II) - X(I) = v, and compare them with fl. [The conditional distribution of Y = X(1) given V = v is U(8, 8 + 1 - v).] [Pratt (1961), Barnard (1976).]