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Unformatted text preview: STAT 455/855  Final Exam, 2009 Page 1 of 4 QUEEN’S UNIVERSITY DEPARTMENT OF MATHEMATICS AND STATISTICS FACULTY OF ARTS AND SCIENCE STAT 455/855 FALL 2009 FINAL EXAMINATION 9:00AM, DECEMBER 14, 2009 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 closedbook – no books, notes, or any other resource material is allowed except as indicated in the next item. • A standard noncommunicating 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. Stat855 students must do all 5 questions. Stat455 students must to 4 of the 5 questions. For Stat455 students, if you answer all 5 questions please indicate which 4 questions you want marked. By default, unless otherwise specified, the first 4 questions will be marked. • 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. STAT 455/855  Final Exam, 2009 Page 2 of 4 1. (Total 15 marks) Let X = { X n : n ≥ } be an irreducible, discrete time Markov chain with countably infinite state space S , transition probability matrix P = (( p ij )) i,j ∈ S , and period d . For each of the following statements say whether it is true or false. Prove....
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 Fall '09
 GLENTAKAHARA
 Probability theory, Markov chain, time Markov chain

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