Machine 1Machine 2Machine 3Machine 4Consider 4 machines in series. If one machine fails, then the system stops until it is repaired. A machinecan fail only when the system is operational. Let p; be the probability that the ith machine fails. Let r;be the probability that the failed ith machine is repaired in the next time epoch. Assume that two (ormore) machines cannot fail simultaneously. Model the failure/repair process as a Markov chain. Writethe probability transition matrix and draw the transition diagram.

For a series system, the probability of failure is Since the 4 machines are in a series system, the…

Answered: Consider 4 machines in series. If one…

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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Each week a student can be either up-to-date or behind. If the student is up-to- date, then the probability of staying up to date is 0.8, otherwise the student falls behind. If the student is behind, then the student will be up-to-date next week with probability 0.6. n-step transition matrix rij (1) = [.8 2 .4] O 0.6×0.8+.2× и
The figure above illustrates a continuous-time Markov process. Suppose the system is currently instate 2. After a small amount of time Δ, what is the probability that the system is in each state?
In a binomial model, give an example of a stochastic process that is both a martingale and Markov.
an 15 A continuous-time Markov chain (CTMC) has three states (1, 2, 3). ed dout of The average time the process stays in states 1, 2, and 3 are 3, 11.9, and 3.5 seconds, respectively. question The steady-state probability that this CTMC is in the second state ( , ) is
For the attached Markov chain with the following transition probability matrix: The Markov chain has only one recurrent class. Determine the period of this recurrent class.
A Markov system with two states satisfies the following rule. If you are in state 1 then of the time you change to state 2. If you are in state 2 then of the time you remain in state 2. state 1 Write the transition matrix for this system using the state vector v state 2 T = Find the long term probability (stable state vector). vs
Shakira's concerts behave like a Markov chain. If the current concert gets cancelled, then there is an 90% chance that the next concert will be cancelled also. However, if the current concert does not get cancelled, then there is only a 50% chance that the next concert will be cancelled. What is the long-run probability that a concert will not be cancelled? a. 1/4 b. 1/10 c. 1/6 d. 1/2 e. 5/6 f. None of the others are correct
Answer the following questions.
A study conducted by the Urban Energy Commission in a large metropolitan area indicates the probabilities that homeowners within the area will use certain heating fuels or solar energy during the next 10 years as the major source of heat for their homes. The following transition matrix represents the transition probabilities from one state to another. Electricity 10.2 Natural Gas Fuel Oil Solar Energy Elec. Gas Oil 0.60 0.05 0.10 0.15 0.85 0.10 0.08 Solar 0 0.10 0.02 0.75 0.08 0.15 0.08 0.05 0.84 Among homeowners within the area, 20% currently use electricity, 35% use natural gas, 40% use oil, and 5% use solar energy as the major source of heat for their homes. In the long run, percentage of homeowners within the area will be using solar energy as their major source of heating fuel? (Round your answer to one decimal place. Assume the trend continues.) X % what
In any given day the air quality in a certain city is either good or bad. Records show that when the air quality is good on one day, then there is a 95% chance that it will be good the next day, and when the air quality is bad on one day, then there is 45% chance it will be bad the next day. a. Give the transition matrix. b. if the air quality is good today, what is the probability it will be good two days from now? c. if the air quality is bad today, what is the probability it will be bad three days from now? d. if the there is 20% chance the air quality is good today, what is the probability it will be good tomorrow?
In a hotel, each employee is in one of three possible job classifications, and changes that classifications (independently) according to a Markov chain with transition probabilities. What percentage of employees are in each classification?

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