Hw5-ORIE3510_S12 - ORIE 3510 Homework 5 Instructor: Mark E....

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ORIE 3510 – Homework 5 Instructor: Mark E. Lewis due 2PM, Wednesday February 29, 2012 (ORIE Hallway drop box) 1. Consider a Markov chain on the states { 1 , 2 , . . . , 9 } with transition matrix 0 . 5 0 0 . 5 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 (a) Is this chain irreducible? (b) Find the period of state 1 and state 8. 2. If { X n , n 0 } is an irreducible Markov chain with period d 2. Is { X dn , n 0 } irreducible? Justify your statement by proof (for YES) or by a counterexample (for NO). 3. Harry plays semipro basketball where he is a defensive specialist. His scoring productivity per game ±uctuates between three states: 1 (scores 0 or 1 points), 2 (scores between 2 and 5 points), 3 (scores more than 5 points). Inevitably, if Harry scores a lot of points in one game,
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This note was uploaded on 03/08/2012 for the course OR&IE 3510 taught by Professor Lewis during the Spring '10 term at Cornell University (Engineering School).

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Hw5-ORIE3510_S12 - ORIE 3510 Homework 5 Instructor: Mark E....

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