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Question 1 (35 points) Given the following Markov chain one-step transition matrix with three states 0, 1, and 2: P = [0.20 0 0.80 0.70 0.10 0.20 0.60 0.40 0] a) Find the steady-state probabilities. b) If the costs of being in states 0, 1, and 2 are $1700, $2350, and $980 respectively, what is the long-run expected average cost of the system? c) Find the first passage time to state 2 from all 3 states (including state 2 itself), ?i2. d) Find the expected recurrence time of all 3 states.

          Question 1 (35 points)

Given the following Markov chain one-step transition matrix with three states 0, 1, and 2:

P = [0.20 0 0.80
     0.70 0.10 0.20
     0.60 0.40 0]

a) Find the steady-state probabilities.
b) If the costs of being in states 0, 1, and 2 are $1700, $2350, and $980 respectively, what is the long-run expected average cost of the system?
c) Find the first passage time to state 2 from all 3 states (including state 2 itself), ?i2.
d) Find the expected recurrence time of all 3 states.

Question 1 (35 points)

Given the following Markov chain one-step transition matrix with three states 0, 1, and 2:

P = [0.20 0 0.80
0.70 0.10 0.20
0.60 0.40 0]

a) Find the steady-state probabilities.
b) If the costs of being in states 0, 1, and 2 are 1700,2350, and 980 respectively, what is the long-run expected average cost of the system?
c) Find the first passage time to state 2 from all 3 states (including state 2 itself), ?i2.
d) Find the expected recurrence time of all 3 states.

Added by Eileen N.

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