Consider the Markov chain with three states, S = {1,2,3,4}, that has the following transition matrix: [o 1/3 1/3 1/3] |1/3 1/3 1/3 P =

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Chapter3: Matrices
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Question 3:
A) Consider the Markov chain with three states, S = {1,2,3,4}, that has the following transition
matrix:
го 1/3 1/3 1/3]
1/3 1/3 1/3 0
1/2 0
P =
1/2
1 0 0
a) Find F), F(2)
b) Find steady state distribution.
B) A new rapid transit system has just started operating. In the first month of operation, it is found
that 25% of commuters are using the system, while 75% still travel by automobiles. The following
transition matrix was determined from records of other rapid transit systems:
[ 4/5 1/5
P = \3/10 7/10]
a) What is the initial state matrix?
b) What percentage of the commuters will be using the new system after 1 month?
c) Find P(X3 = 2|X2 = 1).
d) Find the percentage of commuters using each type of transportation after it has been in
service for a long time.
Transcribed Image Text:Question 3: A) Consider the Markov chain with three states, S = {1,2,3,4}, that has the following transition matrix: го 1/3 1/3 1/3] 1/3 1/3 1/3 0 1/2 0 P = 1/2 1 0 0 a) Find F), F(2) b) Find steady state distribution. B) A new rapid transit system has just started operating. In the first month of operation, it is found that 25% of commuters are using the system, while 75% still travel by automobiles. The following transition matrix was determined from records of other rapid transit systems: [ 4/5 1/5 P = \3/10 7/10] a) What is the initial state matrix? b) What percentage of the commuters will be using the new system after 1 month? c) Find P(X3 = 2|X2 = 1). d) Find the percentage of commuters using each type of transportation after it has been in service for a long time.
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