Suppose you have a Markov Chain with k transient classes and 2 absorbing states, a and...

 

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Suppose you have a Markov Chain with k transient classes and 2 absorbing states, a and b. Our goal is to figure out the probability of being "absorbed" into state a and the probability of being "absorbed" into state b starting from a transient state. The canonical decomposition for such a system is P = (a) If i and j are both transient, what is the n-step transition probability from j to i? use Q,S,I to express it. (b) Show p can be written in the form below and find S S2 P = (c) Similarly, find S, for general n. (d) Starting in transient state i, what is the probability of being absorbed into state a? use part (c) Suppose you have a Markov Chain with k transient classes and 2 absorbing states, a and b. Our goal is to figure out the probability of being "absorbed" into state a and the probability of being "absorbed" into state b starting from a transient state. The canonical decomposition for such a system is P = (a) If i and j are both transient, what is the n-step transition probability from j to i? use Q,S,I to express it. (b) Show p can be written in the form below and find S S2 P = (c) Similarly, find S, for general n. (d) Starting in transient state i, what is the probability of being absorbed into state a? use part (c)