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Unformatted text preview: p = 0 . 8, = 0 . 3 and = 0 . 4. (iii) (2 pts.) Display the transition probability matrix for { X n } . (iv) (4 pts.) Determine P [ X n +2 = 1  X n = 1]. (v) (4 pts.) Determine P [ X n +2 = 0  X n = 2]. Problem 21B Consider the Markov chain { X n } with state space { 1 , 2 , 3 , 4 , 5 , 6 } and P = 1 / 3 1 / 6 1 / 2 1 / 6 5 / 6 3 / 8 5 / 8 1 / 4 1 / 4 1 / 2 2 / 3 1 / 3 3 / 4 1 / 4 (i) (5 pts.) Draw the state transition graph. Classify each state as recurrent or transient and identify all classes. (ii) (2 pts.) What is the conditional probability that state 5 occurs before state 3, given that X = 1? (iii) (7 pts.) Determine the stationary distribution of each recurrent class. (iv) (6 pts.) Determine the limiting values of P [ X n = 4  X = 3] , P [ X n = 4  X = 2] and P [ X n = 4  X = 1] as n ....
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 Fall '05
 Ephrimedes

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