Problem 4: optional for undergraduates 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 (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 p2 can be written in the form below and find S2 (c) Similarly,find Sn for general n. (d) Starting in transient state i, what is the probability of being absorbed into state a? use part (c) Problem 4: optional for undergraduates 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 (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 p2 can be written in the form below and find S2 (c) Similarly,find Sn for general n. (d) Starting in transient state i, what is the probability of being absorbed into state a? use part (c)