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Unformatted text preview: STAT 455/855 -- Final Exam, 2003 Page 1 of 4 QUEEN’S UNIVERSITY DEPARTMENT OF MATHEMATICS AND STATISTICS STAT 455/855 FALL 2003 FINAL EXAMINATION 2:00PM, DECEMBER 8, 2003 GLEN TAKAHARA Instructions : • 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 (with a gold sticker for applied science students) 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 do 4 questions, and are graded on only 4 questions. Stat455 students that answer 5 questions must indicate on the answer sheet which 4 are to be graded, otherwise questions 1 to 4 will be graded. Stat455 students may do any 4 questions, but question 5 (which is starred) is intended for Stat855 students. • 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. • “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.” STAT 455/855 -- Final Exam, 2003 Page 2 of 4 1. (Total 15 marks) A game costs k dollars to play and rules are as follows. A fair die is repeatedly rolled until an outcome is rolled which is the same as the previous roll. Let Y denote the number of rolls required (note that Y ≥ 2). If Y ≤ k , the game ends and you lose, so your net profit is...
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- Fall '09
- Markov chain, 3 weeks, net profit, GLEN TAKAHARA