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# midterm03 - STAT455/855 Fall 2003 Applied Stochastic...

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STAT455/855 Fall 2003 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) 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, 2003 Page 2 of 3 1. (15 marks) Consider the infinite integer lattice Z 2 = { ( x, y ) : x and y are integers } . A particle moves randomly over the lattice: if the particle is at ( x, y ) it’s next move is equally likely to be to ( x + 1 , y ), ( x - 1 , y ), ( x, y + 1) or ( x, y - 1). We are interested in the expected number of moves it makes to get to either the vertical line x = N or the vertical line x = - N , where N
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midterm03 - STAT455/855 Fall 2003 Applied Stochastic...

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