Stat450-midterm-7Feb2017.pdf - UNIVERSITY OF VICTORIA MIDTERM February 2017 STATISTICS 450 CRN 22945 TO BE ANSWERED IN BOOKLETS Instructor Prof M

Stat450-midterm-7Feb2017.pdf - UNIVERSITY OF VICTORIA...

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UNIVERSITY OF VICTORIA MIDTERM February 2017 STATISTICS 450, CRN 22945 TO BE ANSWERED IN BOOKLETS DURATION: 75 minutes Instructor: Prof. M. Lesperance THIS QUESTION PAPER HAS 2 PAGES. Instructions : 1. A Sharp EL-510R or EL-510RN calculator may be used. No other calculator may be used. 2. A formula sheet is provided at the end of the midterm. No other aids such as books, notes, etc. are permitted. 3. DO 5 QUESTIONS IN TOTAL, WITH AT LEAST TWO FROM EACH OF PARTS A AND B. 5 marks each question Part A1. LetY1< Y2< ... < Ynbe the order statistics ofnindependent observations from anexponential distribution with meanθ.(a) What is the p.d.f. ofY1.(b) Find, using integration, the expected value of(1-e-Y1).2. LetYnBinomial(n, p).(a) Write down the moment generating function forYn.(b) Now, letp=λ/nwhereλis a constant. Asn→ ∞,p0. Find the limitingmoment generating function ofYnasn→ ∞. What is the name of this limitingdistribution? Hint: Substitutep=λ/ninto part (a).3. LetYnPoisson(λ= 3n). Use the Central Limit Theorem to show that

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