HW6 - with mean and variance 2 . (a) Use Slutzkys theorem...

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STA131C, Spring 2007 Prof. W. Polonik HW # 6 due: May 30, 2007 in class 1. Let X 1 , . . ., X n iid Poisson( λ ) , λ > 0 , and defne h λ = X . Show that both statistics T 1 = n ( h λ - λ ) λ and T 2 = n ( h λ - λ ) h λ can be used to construct confdence intervals oF asymptotic level 1 - α. (HINTS: ±irst fnd the large sample (asymptotic) distribution oF the two test statistics. Then use this large sample approximation to construct confdence intervals. Note that the case T 1 requires some special consideration to show that the resulting confdence set actually is a confdence interval.) 2. Let X 1 , . . ., X n iid
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Unformatted text preview: with mean and variance 2 . (a) Use Slutzkys theorem to show that n ( X- ) 2 p 0 as n . (b) Use (a) to show that n ( S 2 n- 2 ) D N (0 , 4 ) as n , where 4 = E( X 1- ) 4- 4 . 3. Let X 1 , . . ., X n iid Beta( , 1) , > , i.e. their common pdF is f ( x ) = x -1 , x [0 , 1] . (a) Show that h = X 1-X is a method oF moment estimator oF . (b) ind the large sample distribution oF n ( - ) . (HINT: Use the -method.)...
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This homework help was uploaded on 04/20/2008 for the course STATS 131C taught by Professor Polonik during the Spring '07 term at UC Davis.

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