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Unformatted text preview: (3) both From a sequential sample space and by using the equation r ij ( n + 1) = k r ik ( n ) p kj in an eective manner. 3. Consider the Following Markov chain, with states labelled From s , s 1 , . . . , s 5 : S 1/2 1/2 1/4 1 1 S S S S S 1 2 3 4 5 1/4 1/2 1/2 1/2 1/3 1/3 1/3 Given that the above process is in state s just beFore the frst trial, determine by inspection the probability that: (a) The process enters s 2 For the frst time as the result oF the k th trial. Page 1 oF 2 Massachusetts Institute of Technology Department of Electrical Engineering & Computer Science 6.041/6.431: Probabilistic Systems Analysis (Fall 2010) (b) The process never enters s 4 . (c) The process enters s 2 and then leaves s 2 on the next trial. (d) The process enters s 1 for the Frst time on the third trial. (e) The process is in state s 3 immediately after the n th trial. Page 2 of 2...
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