bst632-spring-2009-homework-problems-01

bst632-spring-2009-homework-problems-01 - Homework 1 for...

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Unformatted text preview: Homework 1 for BST 632: Statistical Theory II – Problems Due Time: 10:45AM Tuesday, on 01/27/2009. Problem 1 (15 points). Verify the following statements. (1) If T ( X) is a sufficient statistic and define T *( X) g (T ( X)) , where g is a one to one function, then T *( X) is a sufficient statistic. (2) If T ( X) is a minimal sufficient statistic and define T *( X) g (T ( X)) , where g is a one to one function, then T *( X) is a minimal sufficient statistic. (3) If T ( X) is a sufficient statistic and define and T *( X) is another statistic and T ( X) g (T *( X)) , then T *( X) is a sufficient statistic. Problem 2 (10 points). Book problem 6.2. Problem 3 (10 points). Book problem 6.3. Problem 4 (10 points). Book problem 6.5. Problem 5 (10 points). Book problem 6.7. Problem 6 (20 points). Book problem 6.9 (a) and (b). Problem 7 (15 points). Book problem 6.12. (Hint: the estimator X / N is unbiased for means that E ( X / N ) .) Problem 8 (10 points). Book problem 6.13. 1 ...
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