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final08 - STAT 455/855 Final Exam 2008 QUEEN'S UNIVERSITY...

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STAT 455/855 -- Final Exam, 2008 Page 1 of 4 QUEEN’S UNIVERSITY DEPARTMENT OF MATHEMATICS AND STATISTICS STAT 455/855 FALL 2008 FINAL EXAMINATION 7:00PM, DECEMBER 4, 2008 GLEN TAKAHARA Instructions : “Proctors are unable to respond to queries about the interpretation of exam questions. Do your best to answer exam questions as written.” “The candidate is urged to submit with the answer paper a clear statement of any assumptions made if doubt exists as to the interpretation of any question that requires a written answer.” This examination is THREE HOURS in length. It is closed-book – no books, notes, or any other resource material is allowed except as indicated in the next item. A standard non-communicating calculator without text storage capabilities and any notes on a single 8 1 2 × 11 inch sheet of paper (both sides) are allowed. Please answer all questions in the booklets provided. Put your student number on the front of all answer booklets and number the answer booklets if more than one answer booklet is used. There are 5 questions. Stat455 students must do questions 1 to 4. Stat855 students must do all 5 questions. Each question is worth 15 marks for a possible total of 60 for Stat455 students and 75 for Stat855 students. Show all your work. You may receive partial credit if you get an answer wrong but show your work, whereas you will receive no credit if you get an answer wrong and do not show your work.
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STAT 455/855 -- Final Exam, 2008 Page 2 of 4 1. (Total 15 marks) Let { X n } n =0 be a discrete time Markov chain with state space S = { 0 , 1 , 2 } and initial distribution (1 / 3 , 1 / 3 , 1 / 3). Consider the three transition probabiilty matrices (i) 1 0 0 0 0 1 0 1 0 , (ii) 1 0 0 0 . 4 . 6 0 .
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