Question 3:A) Consider the Markov chain with three states, S = {1,2,3,4}, that has the following transitionmatrix:го 1/3 1/3 1/3]1/3 1/3 1/3 01/2 0P =1/21 0 0a) 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 foundthat 25% of commuters are using the system, while 75% still travel by automobiles. The followingtransition matrix was determined from records of other rapid transit systems:[ 4/5 1/5P = \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 inservice for a long time.

Given information: The transition matrix is as given below: 013131313131300120121000

Answered: Consider the Markov chain with three…

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 =

A First Course in Probability (10th Edition)

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Chapter1: Combinatorial Analysis

Section: Chapter Questions

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