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midterm08 - STAT455/855 Fall 2008 Applied Stochastic...

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STAT455/855 Fall 2008 Applied Stochastic Processes Midterm Exam Instructions: (a) The exam is closed book. No books are allowed. You may use one 8 . 5 × 11 inch sheet of notes and a calculator. (b) There are 3 questions. Stat 855 students must do all of the problems. Stat 455 students must do 2 of questions 1,2 and 3, and if you answer all three of questions 1, 2 and 3, you must specify which two you want graded (the default if you do not specify is questions 1 and 2). (c) Each question is worth 15 marks for a total of 30 marks (Stat455) or 45 marks (Stat855) (d) Show all your work. Partial credit is given. (e) You have 120 minutes. Good luck!
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STAT 455/855 -- Midterm Exam, 2008 Page 2 of 3 1. (15 marks) Let { X n : n 0 } be a Markov chain with state space S = { 1 , 2 , 3 , 4 , 5 , 6 } and transition probability matrix 1 2 3 4 5 6 P = 1 2 3 4 5 6 0 0 1 4 1 2 0 1 4 0 0 0 0 1 0 1 4 1 4 0 0 1 4 1 4 0 0 0 1 0 0 0 1 0 0 0 0 1 2 0 1 2 0 0 0 (a) (5 marks) Identify the equivalence classes and for each class, state whether it is transient or recurrent, and give the period of the class.
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