exam_3_m4320_f2010_v1_0

exam_3_m4320_f2010_v1_0 - Exam 3: Math 4320 Fall 2010...

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Exam 3: Math 4320 Fall 2010 Instructions. You may use printed reference material, digital reference material, calculators, and computer algebra systems. You may discuss Exam 3 only with me. Exam 3 is due on Friday, December 10, 2010, at 17:00. Reminder: Please submit a course evaluation at http://www.casa.uh.edu/TeacherEvaluation/ . Problem 1. (10) Let ( X n ) n =0 be a discrete time Markov chain with state space S = { 0 , 1 , 2 } and transition probability matrix P = . 4 . 4 . 2 . 6 . 2 . 2 . 4 . 2 . 4 . (a) (5) Compute the limiting distribution π = ( π 0 1 2 ). (b) (5) Find lim n →∞ P ( X n - 1 = 2 | X n = 1) . Problem 2. (21) Let ( X n ) n =0 be a discrete time Markov chain with state space S = { i Z : 0 6 i 6 7 } and transition probability matrix P = 1 0 0 0 0 0 0 0 1 / 3 1 / 3 0 1 / 3 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 / 2 0 1 / 2 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 . (a)
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This note was uploaded on 10/03/2011 for the course MATH 3364 taught by Professor Staff during the Spring '08 term at University of Houston.

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