SOLUTIONS%20TEST%202%20STA261

SOLUTIONS%20TEST%202%20STA261 - TEST 2 STA261 ( c David...

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TEST 2 STA261 ( c ± David Brenner, 2010) Mar.24, 2010 name SOLUTIONS student number TA (1) Q1 Q2 Q3 Q4 total Instructions: No aids are allowed other than non-programmable calculators. Please show all your work clearly in the space provided to obtain partial credit ; you may use the back of the pages if necessary. TIME ALLOWED : 50 min. DO ANY 3 of the 4 QUESTIONS : approximate grade values are indicated.
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1. Suppose that X,Y IID G (3 ) , θ > 0 a) Let T = X + Y and obtain both ET varT as they depend on θ . W = T/θ G (6) or T = θW, W G (6) (5) ET =6 θ ± varT =6 θ 2 ± b) Obtain a 95% confdence lower bound For the unknown value oF θ . 2 T/θ χ 2 (12) 95 / 100 = P (2 T/θ 21 . 03) = P ( θ 2 T/ 21 . 03) (5) and thereFore LB ( θ : . 95) = 2 T/ 21 . 03 ±
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2. Suppose that X 1 ,...,X 8 IID N (0 2 ) , σ > 0 and let S = ± X 2 1 + · · · + X 2 8 a) Obtain both ES varS as they depend on σ . S
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SOLUTIONS%20TEST%202%20STA261 - TEST 2 STA261 ( c David...

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