FINAL%20STA261%202008

# FINAL%20STA261%202008 - 1 2 3 4 5 7 8 9 10 total/70...

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1 2 3 4 5 7 8 9 10 total/70 UNIVERSITY OF TORONTO Faculty of Arts & Science APRIL-MAY EXAMINATIONS 2008 STA 261H1 S Prof. D. Brenner Duration - 3 hours Examination Aids: Non-programmable Calculators Instructions Please show all your work clearly in the space provided to obtain partial credit; you may use the backs of the pages for rough work. There are three parts to the exam: PARTS A, B and C You are to answer: 4 questions in part A, 1 in part B &2 in part C for a total of 7 questions altogether. All complete questions will be valued equally, but partial grades are shown to the left of each part. Tables for the N (0 , 1) , χ 2 ( m ) ,t ( m ) , & F ( m,n ) are appended. Name Student number TA (1)

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PART A [Do any 4 questions of the 5 provided in this part] 1. Suppose that T G (3 - 1 ) and we observe t =3 / 2. a) Let ± λ = aT - 1 and Fnd the value of the constant a for which E ± λ = λ . (3) b) Obtain var ± λ . (3) c) Obtain a 95% conFdence upper bound for the rate parameter λ . (4)
2. Suppose that X 1 ,X 2 IID X U (0 ) with observed values x 1 =3 ,x 2 =4 and consider the, so-called, maximum likelilood estimator of θ : ± θ = X (2) = max

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FINAL%20STA261%202008 - 1 2 3 4 5 7 8 9 10 total/70...

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