HWII - ECE 493 HOMEWORK ASSIGNMENT II Spring 2007 1. For...

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ECE 493 HOMEWORK ASSIGNMENT II Spring 2007 1. For the Markov chain in Figure 1, determine the following items. (a) P (2) ( i, j ) for every i and j . (b) f (4) 13 , the probability that you reach state 3 for the ﬁrst time after four steps given that you start in state 1. (c) The unique stationary probability distribution π * for the Markov chain. (d) 1 m j = lim n →∞ N jj ( n ) n , the limiting fraction of time you spend in state j , for each state j . (Here, m j = E ( T jj ), the expected ﬁrst return time to state j given that you start in state j .) 2. For the Markov chain in Figure 2, determine the following items. (a) The set S T of transient states and the set S R of recurrent states. (b) The diﬀerent recurrence classes. (c) For each recurrence class C , the unique stationary probability distribution con- centrated on C . (d) For each transient state i and each recurrence class C , the probability R iC that the state of the Markov chain enters C given that it starts in state

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This note was uploaded on 02/01/2010 for the course ECE 496 taught by Professor Delchamps during the Spring '07 term at Cornell University (Engineering School).

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HWII - ECE 493 HOMEWORK ASSIGNMENT II Spring 2007 1. For...

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