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# HW6 - IE 336 Mar 5 2011 Handout#7 Due Mar 11 2011 Homework...

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IE 336 Handout #7 Mar. 5, 2011 Due Mar. 11, 2011 Homework Set #6 1. Consider a Markov chain given by the following transition matrix P = 2 q r 2 p 3 r p 2 q 6 q 2 p 3 r 3 . (a) Compute p , q , and r . Determine the transition diagram. (b) If the vector of state probabilities at time step 4 is p (4) = £ 0 . 2 0 . 6 0 . 2 / determine the vector of state probabilities at time step 8. (c) Compute the vector of steady-state probabilities. 2. Assume the setup of problem 1. (a) If at some point the process is in state 2, determine the average number of steps that will pass before the process leaves state 2. (b) Compute the probability that if the process started from state 3 it will be in state 2 for the first time four steps later. (c) Find the mean first passage time to reach state 2 from state 1. (d) Assume that at some point the process is in state 3. Determine the mean number of steps that will pass before the process returns to state 3. 3. Assume the setup of problem 3 from HW #3.

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