midterm05 - STAT455/855 Fall 2005 Applied Stochastic...

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Unformatted text preview: STAT455/855 Fall 2005 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 (both sides) and a calculator. (b) 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! STAT 455/855 -- Midterm Exam, 2005 Page 2 of 3 1. (15 marks) (a) (9 marks) Let { X n : n } be the symmetric, simple random walk on the integers; that is, the Markov chain with transition probabilities p i,i +1 = p i,i- 1 = 1 / 2 for all integers i . We are interested in the expected number of steps it takes the walk to reach either state N or- N , where N is a positive integer, starting in state 0....
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midterm05 - STAT455/855 Fall 2005 Applied Stochastic...

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