Consider the following Markov chain0 1(0.7 0.3)1(0.3 0.7Starting from state 0, the probability of returning to state 0 in 3 steps equalsа.0.2O b. 0.147О с.None of the choicesd. 0.49

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Answered: Consider the following Markov chain 0 1…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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- Consider a Markov chain on {1,2} with the given transition matrix P shown below. Use two methods to find the probability that, in the long run, the chain is in state 1. First, raise P to a high power. Then directly compute the steady-state vector. P= 0.9 0.2 0.1 0.8 Raise P to a high power. For the purposes of this solution, raise P to the 100th power. p100 (Type an integer or decimal for each matrix element. Round to five decimal places as needed.)
4.43. At a local grocery store there are queues for service at the fish counter (1), meat counter (2), and café (3). For i = 1,2,3 customers arrive from outside the system to station i at rate i, and receive service at rate 4 + i. A customer leaving station i goes to j with probabilities p(i, j) given the following matrix 1 2 3 0 1/4 1/2 2 1/5 0 1/5 3 1/3 1/3 0 1 In equilibrium what is the probability no one is in the system, i.e., 7(0,0,0).
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Consider the following Markov chain 0 1 0.7 0.3) 03 0.7 Starting from state 0, the probability of returning to state 0 in 3 steps equals а. 0.2 b. 0.147 с. None of the choices O d. 0.49