MarkovChains-InClass

MarkovChains-InClass - ESI 6321 APPLIED PROBABILITY METHODS...

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1 ESI 6321 APPLIED PROBABILITY METHODS IN ENGINEERING OEM 2009 March 16, 2008 IN-CLASS ASSIGNMENT - SOLUTIONS 17.2.3 A company has two machines. During any day, each machine that is working at the beginning of the day has a 1/3 chance of breaking down. If a machine breaks down during the day, it is sent to a repair facility and will be working two days after it breaks down. (Thus, if a machine breaks down during day 3, it will be working at the beginning of day 5.) Letting the state of the system be the number of machines working at the beginning of the day, formulate a transition probability matrix for this situation. The state of the Markov chain is given by the number of machines that are working at the beginning of the day; the state space is therefore {0,1,2}. If X t =0 , both machines broke down in period t -1 , so that both will be available at the start of period t +1 . This yields the first row of the transition probability matrix. If X t =1 , one of the machines broke down in period t -1 . This means that that machine will definitely be available at the start of period t +1. In addition, the machine that is currently working will be available at the start of period t +1 assuming it does not break down, which happens with probability 2/3 . This yields the second row of the transition probability matrix. If X
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This note was uploaded on 05/12/2010 for the course ESI 6321 taught by Professor Josephgeunes during the Spring '07 term at University of Florida.

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MarkovChains-InClass - ESI 6321 APPLIED PROBABILITY METHODS...

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