Unformatted text preview: independent of the minimal suﬃcient statistic in (a). (3) (a) Let ( X 1 ,X 2 ,...,X n ) be i.i.d. U ( θ-1 / 2 ,θ + 1 / 2). Show that ( X (1) ,X ( n ) ) is minimal suﬃcient but not complete. (Hint: What happens to the distribution of X ( n )-X (1) ?) (b) Consider ( X 1 ,X 2 ,...,X n ) i.i.d. N ( θ,θ 2 ). Show that ( ∑ n i =1 X i , ∑ n i =1 ( X i-X ) 2 ) is minimal suﬃcient but not complete. 1...
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- Fall '09
- Statistics, Prime number, minimal sufficient statistic, Keener, Xn i.i.d. fa,b