(10) Consider a Markov chain with transition matrixаbCda /0 1/2 0 1/2)b| 1P =1d \o1Identify the communication classes, their periods, and whether the class is recurrent ortransient. Find canonical decomposition.

Answered: Image /qna-images/answer/04c168f9-4d54-4b43-b51d-40f550f1a1bd.jpg

Answered: (10) Consider a Markov chain with…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 12EQ: 12. Robots have been programmed to traverse the maze shown in Figure 3.28 and at each junction...

See similar textbooks

Similar questions

Explain how you can determine the steady state matrix X of an absorbing Markov chain by inspection.
12. Robots have been programmed to traverse the maze shown in Figure 3.28 and at each junction randomly choose which way to go. Figure 3.28 (a) Construct the transition matrix for the Markov chain that models this situation. (b) Suppose we start with 15 robots at each junction. Find the steady state distribution of robots. (Assume that it takes each robot the same amount of time to travel between two adjacent junctions.)
ZD In Smalltown, 90% of all sunny days are followed by sunny days, and 80% of all cloudy days are followed by cloudy days. Use this information to model Smalltown's weather as a Markov chain.
(i) Describe how to model the state of the machine as a continuous-time Markov chain with four states. Write down the generator matrix for the chain (ii) Suppose that the machine is running at time 0. What is the probability thatit runs continuously without breaking until at least time 1? (iii) Why is it natural to model this situation as a continuous-time process.
A Markov chain on states {1,2,3,4,5,6} has transition matrix 0 를 0 0 1 0 % 을 0 을 0 0 0 음 2 3 3 4 4 3 1 1 1 1 1 6 Find all communication classes and classify each class as either recurrent or transient.
A Markov Chain has the transition matrix r-[% *]. P = and currently has state vector % % ]: What is the probability it will be in state 1 after two more stages (observations) of the process? (A) % (B) 0 (C) /2 (D) 24 (E) 12 (F) ¼ (G) 1 (H) 224
Suppose that the model pctstck = Bo + Bfunds + Bzrisktol + u satisfies the first four Gauss-Markov assumptions, where pctstck is the percentage of a worker's pension invested in the stock market, funds is the number of mutual funds that the worker can choose from, and risktol is some measure of risk tolerance (larger risktol means the person has a higher tolerance for risk). If funds and risktol are positively correlated, what is the inconsistency in Bj, the slope coefficient in the simple regression of pctstck on funds?
1. A machine can be in one of four states: 'running smoothly' (state 1), 'running but needs adjustment' (state 2), 'temporarily broken' (state 3), and 'destroyed' (state 4). Each morning the state of the machine is recorded. Suppose that the state of the machine tomorrow morning depends only on the state of the machine this morning subject to the following rules. • If the machine is running smoothly, there is 1% chance that by the next morning it will have exploded (this will destroy the machine), there is also a 9% chance that some part of the machine will break leading to it being temporarily broken. If neither of these things happen then the next morning there is an equal probability of it running smoothly or running but needing adjustment. • If the machine is temporarily broken in the morning then an engineer will attempt to repair the machine that day, there is an equal chance that they succeed and the machine is running smoothly by the next day or they fail and cause the machine…
Consider a continuous-time Markov chain with transition rate matrix 0 2 31 Q10 3 2 0/ What are the one-step transition probability matrix of the embedded chain? Enter your answer as a vector of the form ((a₁, b₁, ₁), (a₂, b₂, ₂), (as, bs, cs)) where each of a, b, c, is an integer of the form or a fraction of the form m/n; eg ((1, 1/2, 1/3), (1, 1/2, 1/3), (1, 1/2, 1/3)). Note that there are 8 brackets and 8 commas in total. All should be included. Do not include spaces.
Suppose the transition matrix for a Markov Chain is T = stable population, i.e. an x0₂ such that Tx = x. ساله داد Find a non-zero
A rat is put into the following maze: 2 The rat has a probability of 1/4 of starting in any compartment and suppose that the rat chooses a passageway at random when it makes a move from one compartment to another at each time. Let Xn be the compartment occupied by the rat after n moves. (a) Explain why {Xn} is a MC and find the transition matrix P. (b) Explain why the chain is irreducible, aperiodic and positive recurrent. (c) What is the limit of Pn? Explain.
2. A professor either walks or drives to a university. He never drives two days in a row, but if he walks one day, he is just as likely to walk the next day as to drive his car. Give the transition matrix for this Markov chain.

SEE MORE QUESTIONS

Recommended textbooks for you

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

(10) Consider a Markov chain with transition matrix a C d a /0 1/2 0 1/2) b1 P = C 1 d \o 1 Identify the communication classes, their periods, and whether the class is recurrent or transient. Find canonical decomposition.