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411_hw08 - problem along with Basu’s theorem to find the...

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Stat 411 – Homework 08 Due: Wednesday 03/14 Undergraduates may solve the “Graduate only” problem(s) for possible extra credit. 1. Let X 1 , . . . , X n iid N ( θ 1 , θ 2 ), where θ 2 > 0 is the variance. Find the MVUE of θ 2 1 . 2. Problem 7.7.10 on page 405. (Hint: Use the exponential family form.) 3. Let X 1 , . . . , X n be iid Unif (0 , θ ), a scale parameter problem. Show that U = X (1) /X ( n ) is an ancillary statistic. 4. (Graduate only) Let X 1 , . . . , X n be iid Unif (0 , θ ).
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Unformatted text preview: problem, along with Basu’s theorem, to find the covariance between X (1) and X ( n ) ; that is, calculate C θ ( X (1) ,X ( n ) ) = E θ ( X (1) X ( n ) )-E θ ( X (1) ) E θ ( X ( n ) ) . Hints: (i) For any two random variables Y 1 and Y 2 , with Y 2 non-zero, E ( Y 1 Y 2 ) = E ( Y 2 1 · Y 2 /Y 1 ); (ii) my solution to Problem 4 on Homework 02 might help. 1...
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