Consider the Markov chain X given by the diagram113002135213113CO 2ته استFO 4How likely is it that if the chain is started in state 0, it will pass either state 3 or state 5in the first 10 steps?

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Answered: Consider the Markov chain X given by…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Consider the migration (Markov) matrix A = 0.7 0 0.2 0.1 0.4 0.2 0.2 0.6 0.6 Suppose that, initially, there are 96 residents in location 1, 82 residents in location 2, and 151 residents in location 3. Assume time is measured in years. Find the population in each location after 1 year. Find the population in each location after 2 years.
I need question 4 only
Consider the Markov chain with state space S = {0, 1, 2,...} and transition probabili- ties Poo = 1 - P. P02 = P, and Pr,x+2= P₁ P2,2-1=1-p, for x = 1,2,... For which values of p is this a transient chain?
4
Proposition 9.2.11. A Markov chain is irreducible precisely when it has only on recurrence class and every state is recurrent. one
7
40. A Markov Chain with 4 states is currently equally likely to be in states 3 and 2, but is 4 times as likely to be in state 1 as in 3, and is 2 times as likely to be in 4 as in 1. What is the state vector that describes this situation?
Determine the classes of the Markov chain and whether they are recurrent.
Determine the classes of the Markov chain and whether they are recurrent.
2. Consider a Markov chain {Xn}n≥o having the following transition diagram: 1/2 1 2 5 1/4 3 4 1/2 1/4 6 7 1/2 For this chain, there are two recurrent classes R₁ = {6,7} and R₂ = {1,2,5}, and one transient class R3 = {3,4}. (a) Find the period of state 3. (b) Find f33 and f22. (c) Starting at state 3, find the probability that the chain is absorbed into R₁. (d) Starting at state 3, find the mean absorbation time, i.e., the expected number of steps that the chain is absorbed into R₁ or R₂. Note: there are missing transition probabilities for this chain, but no impact for your solution.
Classify the Markov chain in Figure 1 and calculate the periodicity of every state. 0 10 1 30 1 334 1 02 0 4 2 1 05 Figure 1: Diagram of the Markov chain of Problem 3.
Please do question 4

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Consider the Markov chain X given by the diagram 1 30 116 0 4 213 5 213 113 CO 2 213 FO 4 How likely is it that if the chain is started in state 0, it will pass either state 3 or state 5 in the first 10 steps?