Within a large metropolitan area, 20% of the commuters currently use the public transportation system, whereas the remaining 80% commute via automobile. The city has recently revitalized and expanded its public transportation system. It is expected that 6 months from now 30% of those who are now commuting to work via automobile will switch to public transportation, and 70% will continue to commute via automobile. At the same time, it is expected that 20% of those now using public transportation will commute via automobile and 80% will continue to use public transportation.
Let denote the state "use the public transportation system" and denote the state "commute via automobile".
Construct the transition matrix for the Markov chain that describes the change in the mode of transportation used by these commuters. Find the initial distribution vector for this Markov chain. What percentage of the commuters are expected to use public transportation 6 months from now?
__________ %

Question

Within a large metropolitan area, 20% of the commuters currently use the public transportation system, whereas the remaining 80% commute via automobile. The city has recently revitalized and expanded its public transportation system. It is expected that 6 months from now 30% of those who are now commuting to work via automobile will switch to public transportation, and 70% will continue to commute via automobile. At the same time, it is expected that 20% of those now using public transportation will commute via automobile and 80% will continue to use public transportation.
Let  denote the state "use the public transportation system" and  denote the state "commute via automobile".
Construct the transition matrix for the Markov chain that describes the change in the mode of transportation used by these commuters.       Find the initial distribution vector for this Markov chain.     What percentage of the commuters are expected to use public transportation 6 months from now?
__________ %

Quizplus · Accepted Answer

The Answer of Within a large metropolitan area, 20% of the commuters currently use the public transportation system, whereas the remaining 80% commute via automobile. The city has recently revitalized and expanded its public transportation system. It is expected that 6 months from now 30% of those who are now commuting to work via automobile will switch to public transportation, and 70% will continue to commute via automobile. At the same time, it is expected that 20% of those now using public transportation will commute via automobile and 80% will continue to use public transportation.
Let  denote the state "use the public transportation system" and  denote the state "commute via automobile".
Construct the transition matrix for the Markov chain that describes the change in the mode of transportation used by these commuters.       Find the initial distribution vector for this Markov chain.     What percentage of the commuters are expected to use public transportation 6 months from now?
__________ %

Within a Large Metropolitan Area, 20% of the Commuters Currently