Probability models

b. (13 points) Suppose that Naceur makes on average $10 per ride within zone Z1, $15 per ride within zone Z2, and $2 per minute for rides between zones Z, and Z2 (regardless of whether they start in zone Z, or zone Z2). Determine Naceur's long- run average hourly revenue as a function of the steady-state probabilities ; of the embedded Markov chain { Xn}, where i E S (you do not need to compute the steady-state probabilities of { X,}). (For all n > 0, X,, is the state of the semi- Markov process {X(t) , after n transitions. Thus the embedded Markov chain {Xn} has the same transition probabilities as the semi-Markov process {X(t) } but spends one time unit per visit to each state. ) Explain