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QUESTION

T is the transition matrix for a 4-state absorbing Markov Chain. State #1 and state #2 are absorbing states.

T is the transition matrix for a 4-state absorbing Markov Chain. State #1 and state #2 are absorbing states.

Use the standard methods for absorbing Markov Chains to find the matrices N = (I - Q)-1 and B = NR. Answer the following questions based on these matrices. (Give your answers correct to 2 decimal places.)

(a) If you start in state #3, what is the expected number of steps needed to reach an absorbing state. (Your answer will come from the matrix N.)

(b) If you start in state #4, what is the expected number of steps needed to reach an absorbing state. (Your answer here will come from the matrix N.)

(c) If you start in state #3, what is the probability that you will eventually land in state #1? (Your answer will come from the matrix B.)

(d) If you start in state #4, what is the probability that you will eventually land in state #1? (Your answer will come from the matrix B.)

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