Activity 8 Markov chains
ITESM Campus Aguascalientes
MA3002 Advanced Mathematics
January-May 2017
Dr. Juan-Manuel CAMPOS-SANDOVAL
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
1) Suppose that demographic studies show that each year about 6% of a cityʹs population moves to
the suburbs (and 94% stays in the city), while 4% of the suburban population moves to the city
(and 96% remains in the suburbs). In the year 2000, 63.2% of the population of the region lived in
the city and 36.8% lived in the suburbs. What is the distribution of the population in 2002? For
simplicity, ignore other influences on the population such as births, deaths, and migration into and
out of the city/suburban region.
A) 57.7% in the city and 42.3% in the suburbs
B) 59.8% in the city and 40.2% in the suburbs
C) 58.8% in the city and 41.2% in the suburbs
D) 60.9% in the city and 39.1% in the suburbs
1)
2) Suppose that demographic studies show that each year about 8% of a cityʹs population moves to
the suburbs (and 92% stays in the city), while 5% of the suburban population moves to the city
(and 95% remains in the suburbs). In the year 2000, 62.4% of the population of the region lived in
the city and 37.6% lived in the suburbs. What percentage of the population of the region would
eventually live in the city if the migration probabilities were to remain constant over many years?
For simplicity, ignore other influences on the population such as births, deaths, and migration into
and out of the region.
A) 44.2%
B) 50%
C) 38.5%
D) 61.5%
2)
3) Suppose that the weather in a certain city is either sunny, cloudy, or rainy on a given day, and
consider the following:
1) If it is sunny today there is a 70% chance it will be sunny tomorrow and a 30% chance that it
will be cloudy.
2) If it is cloudy today there is a 40% chance it will be sunny tomorrow, a 40% chance that it will be
cloudy, and a 20% chance that it will be rainy.
3) If it is rainy today there is a 40% chance it will be sunny tomorrow, a 30% chance that it will be
cloudy, and a 30% chance that it will be rainy.
3)
Suppose the predicted weather for Friday is 55% sunny, 30% cloudy, and 15% rainy. What are the
chances that Sunday will be rainy?
A) 8.75%
B) 11.5%
C) 10.5%
D) 9.75%
1
4) Suppose that the weather in a certain city is either sunny, cloudy, or rainy on a given day, and
consider the following:
1) If it is sunny today there is a 70% chance it will be sunny tomorrow and a 30% chance that it
will be cloudy.
2) If it is cloudy today there is a 40% chance it will be sunny tomorrow, a 40% chance that it will be
cloudy, and a 20% chance that it will be rainy.
3) If it is rainy today there is a 40% chance it will be sunny tomorrow, a 30% chance that it will be
cloudy, and a 30% chance that it will be rainy.
In the long run, how likely is it that the weather will be rainy on a given day?
A) 12.1%
B) 10.6%
C) 11.3%
2
D) 9.5%
4)
Answer Key
Testname: ACTIVITY_8_MA3002
1)
2)
3)
4)
C
C
D
D
3