Question

In a large metropolitan area, 30% of the commuters currently use the public transportation system, whereas the remaining 70% 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.

(a) Construct the transition matrix for the Markov chain that describes the change in the mode of transportation used by these commuters.

			P              A
T	=	P A	_____ _____ _____ _____

(b) Find the initial distribution vector for this Markov chain.

X0

=

_____ _____

(c) What percentage of the commuters are expected to use public transportation 6 months from now? (Round your answer to the nearest percent.)
%________

Answer 1