X1, X2. ..., Xn iid N( $ , 5" ) , find an unbiased estimator of & based on _ Xi, and another based on _ X?); hence, deduce that T = (_ X;, _ X? ) is not complete. You may use this hint from text: (ii) Curved normal family. In the curved exponential family derived from the N(E, 02) family with & = o, we have seen (Example 6.17) that the statistic T = (Xx, Ex-) is minimal sufficient. Ilowever, it is not complete since there exists a function f(7) satisfying (6.12). This follows from the fact that we can find unbiased estimators for & based on either EX; or E X (see Problem 6.21)