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Unformatted text preview: HOMEWORK 4 1. A Markov chain with state space { 1 , 2 , 3 } has transition probability matrix P = 1 / 3 1 / 3 1 / 3 1 / 2 1 / 2 1 Show that state 3 is absorbing and, starting from state 1, find the expected time until absorption occurs. 2. Smith is in jail and has 3 dollars; he can get out on bail if he has 8 dollars. A guard agrees to make a series of bets with him. If Smith bets A dollars, he wins A dollars with probability 0.4 and loses A dollars with probability 0.6. Find the probability that he wins 8 dollars before losing all of his money if (a) he bets 1 dollar each time (timid strategy). (b) he bets, each time, as much as possible but not more than necessary to bring his fortune up to 8 dollars (bold strategy). (c) Which strategy gives Smith the better chance of getting out of jail? 3. A fair coin is tossed repeatedly and independently. Find the expected number of tosses till the pattern HTH appears....
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This note was uploaded on 01/05/2010 for the course ECE 01 taught by Professor All during the Spring '09 term at Aarhus Universitet.
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