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Finite Math 8.1 to 8.3 Review Sheet Name: 1.A Markov chain has the transition diagram shown below. Find the transition matrix for this Markov chain. 4. A Markov chain has the transition matrix P shown below. The system is initially in state 1. Find the probability that it is in state 2 after two transitions. P= Answer: 5. A Markov chain has the transition Answer: [ ] 2.A Markov chain has the transition matrix P matrix P shown below. Find the probability that the system makes a transition from state 1 to state 2 in two steps. P= shown below. If the system is initially in state 1, find the probability that after one transition it is in state 3. Answer: 6. Transition matrices for three Markov chains are shown below. Which are the transition matrices of regular Markov chains? Answer: A= B= 3.Each day a sales representative is either in the office or out making calls. If she is in the office one day, then she is in the office the next day with probability .3, and if she is out making calls one day then she is in the office the next day with probability .4. Formulate a follows: If she is in the office, then the system is in state 1 and if she is out making calls, then the system is in state 2. The system is observed once each day. C= Answer: 7. A regular Markov chain has the transition matrix P shown below. Find the first coordinate of the stable vector for this Markov chain. P= Answer: Answer: 8. Find the long – run batting average of a softball player who knows that if she gets a hit, then she gets a hit the next time with probability .5, but if she makes an out, then she gets a hit the next time with probability .3. (Assume each time up she either gets a hit or makes an out.) Answer: 1. ANS: PTS: 1 DIF: E REF: 8.1 OBJ: 8-1 To set up and interpret the transition matrix of a Markov chain 2. ANS: .1 PTS: 1 DIF: E REF: 8.1 OBJ: 8-1 To set up and interpret the transition matrix of a Markov chain 3. ANS: PTS: 1 DIF: M REF: 8.1 OBJ: 8-1 To set up and interpret the transition matrix of a Markov chain 4. ANS: .48 PTS: 1 DIF: M REF: 8.2 OBJ: 8-2 To compute new state vectors 5. ANS: .24 PTS: 1 DIF: M REF: 8.2 OBJ: 8-2 To compute new state vectors 6. ANS: A PTS: 1 DIF: M REF: 8.3 OBJ: 8-3 To find regular transition matrices and stable vectors 7. ANS: PTS: 1 DIF: H REF: 8.3 OBJ: 8-3 To find regular transition matrices and stable vectors 8. ANS: .37 PTS: 1 DIF: M REF: 8.3 OBJ: 8-3 To find regular transition matrices and stable vectors