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Soinc123 - Solutions to In-Class Homework Problems 1 2 3 1 Problem 30 in chapter 4 Letting Xn be 0 if the nth vehicle is a car and letting it be 1

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Solutions to In-Class Homework Problems 1, 2, 3. 1. Problem 30 in chapter 4. Letting X n be 0 if the n th vehicle is a car and letting it be 1 if the vehicle is a truck gives rise to a two-state Markov chain with transition probability matrix 4 / 51 / 5 3 / 41 / 4 ¸ . The limiting probabilities are the solution of π 0 =4 / 5 π 0 +3 / 4 π 1 π 1 =1 / 5 π 1 +1 / 4 π 1 π 0 + π 1 . Solving these yields π 0 =15 / 19 , π 2 / 19 . That is, 4 out of every 19 vehicles are trucks. 2. Consider the gambler’s ruin problem with p =0 . 3 ,N =7 , and an initial
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This document was uploaded on 10/18/2011.

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