Question: 9. Let X , .. . , X; be a sample from (i) the normal distribution N(aa, ( 2 ), with a fixed and 0

9. Let X\ , .. . , X; be a sample from (i) the normal distribution N(aa, ( 2 ), with a fixed and 0 < a < 00; (ii) the uniform distribution U( °-!,° + !), - 00 < ° < 00 ; (iii) the uniform distribution U(O\, 02)' -00 < 0\ < O2 < 00 . For these three families of distributions the following statistics are sufficient: (i), T = (EXi,L\'l); (ii) and (iii), T = (min(X\, ... , Xn ) , max(X\, .. . , Xn }} . The family of distributions of T is complete for case (iii), but for (i) and (ii) it is not complete or even boundedly CO;;Plete. [(i): The distribution of [Xi/ xl does not depend on e.]

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