UNIVERSITY OF VICTORIAMIDTERM February 2015STATISTICS 450, CRN 22904TO BE ANSWERED IN BOOKLETSDURATION: 75 minutesInstructor:Prof. M. LesperanceTHIS QUESTION PAPER HAS 2 PAGES.Instructions:1. A Sharp EL-510R or EL-510RN calculator may be used. No other calculator may beused.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 EACHOF PARTS A AND B.5 marks each questionPart 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¯Xnp→c.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(3≤X4:4).3. LetYndenote thenth order statistic of a random sample of sizenfrom a distributionhaving pdf,f(x) = 1/θ, for 0< x < θ, 0< θ <∞, and zero elsewhere.