Please answer parts a, b, c, and d

Consider the Markov chain defined on states S = {0, 1, 2, 3} whose transition probability

matrix is

P : ( 1000

0.2 0.3 0.1 0.4

0.3 0.1 0.5 0.1

0001)

It is known that the process starts in state 1.

(a) Determine the probability that the Markov chain ends in state 0.

(b) Determine the mean time that the process spends in state 1 prior to absorption.

(c) Determine the mean time that the process spends in state 2 prior to absorption.

(d) Determine the mean time to absorption.