HW_Solution_Chapter 17_EMSE102-202

HW_Solution_Chapter 17_EMSE102-202 - 1 OR Chapter 17...

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1 OR Chapter 17 SOLUTIONS SECTION 17.3 SOLUTIONS 2. To answer both questions we must compute = 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 2 P P P P P P P μ 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 P P P P P P 0 1 2 3 4 = 1 0 0 0 0 ) 1 ( 0 0 0 ) 1 ( 2 0 0 0 ) 1 ( 1 0 0 0 0 1 4 3 2 1 0 ) 1 ( ) 1 ( 2 2 2 2 P P P P P P P P P P P P a. P 23 (2) = 0, P 22 (2) = 2p(1-p) b. To answer this question we must compute P 3 = P 2 * P P 22 (3)=(Row 3 of P 2 )(Column 3 of P) =[(1-p) 2 0 2p(1-p) 0 p 2 ] 0 1 0 0 P P = 0 SECTION 17.4 SOLUTIONS 1. Period of states 1,2, and 3 is 2. To return to any state(other than 0 or 4) the number of wins player has had must equal number of losses. Thus gambler can only return to original state after an even number of plays.
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2 2. Yes, all states communicate and no states are periodic.
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This note was uploaded on 01/02/2010 for the course EMSE 202 taught by Professor Mohaghegh,abeledo during the Spring '07 term at GWU.

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HW_Solution_Chapter 17_EMSE102-202 - 1 OR Chapter 17...

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