Commuters can get into town by car or bus. Surveys have shown that, for those taking their car on a particular day, 20% take their car the next day and 80% take a bus. Also, for those taking a bus on a particular day, 50% take their car the next day and 50% take a bus. Assume you are starting on a Monday. a) Write a stochastic matrix A and label the states. b) What percentage of the people who initially drive their own car will take their car on Tuesday? c)What percentage of people who initially drive their own car will take their car on Wednesday?
Commuters can get into town by car or bus. Surveys have shown that, for those taking their car on a
particular day, 20% take their car the next day and 80% take a bus. Also, for those taking a bus on a
particular day, 50% take their car the next day and 50% take a bus. Assume you are starting on a Monday.
a) Write a stochastic matrix A and label the states.
b) What percentage of the people who initially drive their own car will take their car on Tuesday?
c)What percentage of people who initially drive their own car will take their car on Wednesday?
d)What percentage of people who initially drive their own car will take their car on Thursday.
e)In the long run, what percentage of the people who initially drive their own car will take their car on any particular day?
f)What is the stable matrix? What is the stable distribution?
g) In the long run, what percentage of the people take their car on a particular day?
h) In the long run, what percentage of the people take the bus on a particular day?
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