Answer the following question

3. A Markov chain on state space {13.3.4.5} has transition matrix a 1 n a o 435 1f5 a 1/6 2,!3 n 1/6 a a 1 a o a n 1 SEEDS The process starts in state 1. (a) Which states are absorbing? (b) Calculate the probabilityr that the process is absorbed at state 4. (c) Calculate the expectation of the time of absorption. (cl) Calculate the expectation of the number of visits to state 2 before absorption. {e} Suppose that you lose 5 for each visit to state 2 and gain 10 for each visit to state 3. Use rst-step analysis to calculate the expectation of the number of pounds you gain before absorption. (f) HEW could you work out the answer to (e) from {c} and {d} 1without doing the rst-step analysis of part (e)