A company has two machines. During any day, each machine that is working atthe beginning of the day has a chance of breaking down. If a machine breaks down during the day, itis sent to a repair facility and will be working two days after it breaks. (Thus, if a machine breaks downduring day 3, it will be working at the beginning of day 5.) Construct a Markov chain for this systemand find a transition probability matrix for this situation. Is this Markov chain ergodic? Why?

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Answered: A company has two machines. During any…

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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Suppose a Markov Chain has transition matrix 40 % % % % 0 % If the system starts in state 3, what is the probability that it goes to state 2 on the next observation, and then goes to state 4 on the following observation? (A) 2 (B) 1 (C) % (D) (E) % (F) (G) 0 (H) % O A O B OD OF
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In a laboratory experiment, a mouse can choose one of two food types each day, type I or type II. Records show that if the mouse chooses type I on a given day, then there is a 75% chance that it will choose type I the next day, and if it chooses type II on one day, then there is a 50% chance that it will choose type II the next day. (a) Find the transition matrix for this Markov chain. Is it regular? Remember this means that all the entries of some power of the matrix are positive. (b) If the mouse chooses type I today, what is the probability that it will choose type I two days from now? (c) If the mouse chooses type II today, what is the probability that it will choose type II three days from now? (d) About what percentage of the time should we expect the mouse to choose type I food? Type II?
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