Stat450-midterm-13Feb2015.pdf - UNIVERSITY OF VICTORIA MIDTERM February 2015 STATISTICS 450 CRN 22904 TO BE ANSWERED IN BOOKLETS Instructor Prof M

Stat450-midterm-13Feb2015.pdf - UNIVERSITY OF VICTORIA...

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UNIVERSITY OF VICTORIA MIDTERM February 2015 STATISTICS 450, CRN 22904 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. Statistical tables are provided. 3. A formula sheet is provided at the end of the midterm. No other aids such as books, notes, etc. are permitted. 4. DO 5 QUESTIONS IN TOTAL, WITH AT LEAST TWO FROM EACH OF PARTS A AND B. 5 marks each question Part A1. Considernrolls of a balanced die.LetXibe the outcome of theith roll and let¯Xn= Σni=1Xi/n.(a) Find anasymptotic approximation(large n) to the distribution of¯Xn.(b) Find c, such that¯Xnpc.2. LetX1:4< X2:4< X3:4< X4:4be the order statistics of a random sample of size 4 fromthe distribution having pdff(x) =e-x,0< x <, zero elsewhere. FindP(3X4:4).3. LetYndenote thenth order statistic of a random sample of sizenfrom a distributionhaving pdf,f(x) = 1, for 0< x < θ, 0< θ <, and zero elsewhere.

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