Exam 9: Markov Chains and the Theory of Games

Determine whether the matrix is regular. ​ ​

To keep track of the location of its cabs, Zephyr Cab has divided a town into three zones: zone I, zone II, and zone III. Zephyr's management has determined from company records that of the passengers picked up in zone I, 40% are discharged in the same zone, 50% are discharged in zone II, and 10% are discharged in zone III. Of those picked up in zone II, 10% are discharged in zone I, 70% are discharged in zone II, and 20% are discharged in zone III. Of those picked up in zone III, 10% are discharged in zone I, 10% are discharged in zone II, and 80% are discharged in zone III. If the initial distribution vector for the location of the taxis is ​ ​ What will be the distribution after all of them have made one pickup and discharge? ​

Determine whether the given matrix is stochastic. ​