Linear Algebra and Its Applications (5th Edition)
5th Edition
ISBN: 9780321982384
Author: David C. Lay, Steven R. Lay, Judi J. McDonald
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Question
Chapter 10.3, Problem 32E
To determine
To find: The communication classes for Markov chain.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
can you please do part d and e , please provide explanations
Long-Run Properties of Markov Chains The leading brewery on the West Coast (labeled A) has hired an OR analyst to analyze its market position. It is particularly concerned about its major competitor (labeled B). The analyst -believes that brand switching can be modeled as a Markov chain using three states, with states A and B representing customers drinking beer produced from the aforementioned breweries and state C representing all other brands. Data are taken monthly, and the analyst has constructed the following (one-step) transition -matrix from past data.
What are the steady-state market shares for the two major -breweries?
2. The day-to-day changes in weather for a certain part of the country form a Markov
process. Each day is sunny, cloudy, or rainy.
• If it is sunny one day, there is a 70% chance that it will be sunny the following
day, a 20% chance it will be cloudy, and a 10% chance of rain.
• If it is cloudy one day, there is a 30% chance it will be sunny the following day, a
50% chance it will be cloudy, and a 20% chance of rain.
• If it rains one day, there is a 60% chance that it will be sunny the following day,
a 20% chance that it will be cloudy and a 20% chance of rain.
(a) Create a transition diagram that describes this scenario.
(b) Create a stochastic matrix that describes this scenario. Is this scenario ergodic
or absorbing? Explain.
(c) Suppose that today, there is a 42% chance of sun, 38% chance of clouds, and 20%
chance of rain. Using matrix multiplication, predict the weather tomorrow, next
Thursday (in 7 days), and in two weeks (in 14 days).
(d) Find the eigenvalues and eigenvectors…
Chapter 10 Solutions
Linear Algebra and Its Applications (5th Edition)
Ch. 10.1 - Fill in the missing entries in the stochastic...Ch. 10.1 - Prob. 2PPCh. 10.1 - In Exercises 1 and 2, determine whether P is a...Ch. 10.1 - In Exercises 1 and 2, determine whether P is a...Ch. 10.1 - Prob. 3ECh. 10.1 - Prob. 4ECh. 10.1 - In Exercises 5 and 6, the transition matrix P for...Ch. 10.1 - Prob. 6ECh. 10.1 - In Exercises 7 and 8, the transition matrix P for...Ch. 10.1 - In Exercises 7 and 8, the transition matrix P for...
Ch. 10.1 - Consider a pair of Ehrenfest urns labeled A and B....Ch. 10.1 - Consider a pair of Ehrenfest urns labeled A and B....Ch. 10.1 - Consider an unbiased random walk on the set...Ch. 10.1 - Consider a biased random walk on the set {1,2,3,4}...Ch. 10.1 - In Exercises 13 and 14, find the transition matrix...Ch. 10.1 - In Exercises 13 and 14, find the transition matrix...Ch. 10.1 - In Exercises 15 and 16, find the transition matrix...Ch. 10.1 - In Exercises 15 and 16, find the transition matrix...Ch. 10.1 - The mouse is placed in room 2 of the maze shown...Ch. 10.1 - The mouse is placed in room 3 of the maze shown...Ch. 10.1 - Prob. 19ECh. 10.1 - In Exercises 19 and 20, suppose a mouse wanders...Ch. 10.1 - Prob. 21ECh. 10.1 - In Exercises 21 and 22, mark each statement True...Ch. 10.1 - The weather in Charlotte, North Carolina, can be...Ch. 10.1 - Suppose that whether it rains in Charlotte...Ch. 10.1 - Prob. 25ECh. 10.1 - Consider a set of five webpages hyperlinked by the...Ch. 10.1 - Consider a model for signal transmission in which...Ch. 10.1 - Consider a model for signal transmission in which...Ch. 10.1 - Prob. 29ECh. 10.1 - Another model for diffusion is called the...Ch. 10.1 - To win a game in tennis, one player must score...Ch. 10.1 - Volleyball uses two different scoring systems in...Ch. 10.1 - Prob. 33ECh. 10.2 - Consider the Markov chain on {1, 2, 3} with...Ch. 10.2 - In Exercises 1 and 2, consider a Markov chain on...Ch. 10.2 - Prob. 2ECh. 10.2 - In Exercises 3 and 4, consider a Markov chain on...Ch. 10.2 - Prob. 4ECh. 10.2 - Prob. 5ECh. 10.2 - In Exercises 5 and 6, find the matrix to which Pn...Ch. 10.2 - In Exercises 7 and 8, determine whether the given...Ch. 10.2 - Prob. 8ECh. 10.2 - Consider a pair of Ehrenfest urns with a total of...Ch. 10.2 - Consider a pair of Ehrenfest urns with a total of...Ch. 10.2 - Consider an unbiased random walk with reflecting...Ch. 10.2 - Consider a biased random walk with reflecting...Ch. 10.2 - Prob. 13ECh. 10.2 - In Exercises 13 and 14, consider a simple random...Ch. 10.2 - In Exercises 15 and 16, consider a simple random...Ch. 10.2 - In Exercises 15 and 16, consider a simple random...Ch. 10.2 - Prob. 17ECh. 10.2 - Prob. 18ECh. 10.2 - Prob. 19ECh. 10.2 - Consider the mouse in the following maze, which...Ch. 10.2 - In Exercises 21 and 22, mark each statement True...Ch. 10.2 - In Exercises 21 and 22, mark each statement True...Ch. 10.2 - Prob. 23ECh. 10.2 - Suppose that the weather in Charlotte is modeled...Ch. 10.2 - In Exercises 25 and 26, consider a set of webpages...Ch. 10.2 - In Exercises 25 and 26, consider a set of webpages...Ch. 10.2 - Prob. 27ECh. 10.2 - Consider beginning with an individual of known...Ch. 10.2 - Prob. 29ECh. 10.2 - Consider the Bernoulli-Laplace diffusion model...Ch. 10.2 - Prob. 31ECh. 10.2 - Prob. 32ECh. 10.2 - Prob. 33ECh. 10.2 - Let 0 p, q 1, and define P = [p1q1pq] a. Show...Ch. 10.2 - Let 0 p, q 1, and define P = [pq1pqq1pqp1pqpq]...Ch. 10.2 - Let A be an m m stochastic matrix, let x be in m...Ch. 10.2 - Prob. 37ECh. 10.2 - Consider a simple random walk on a finite...Ch. 10.2 - Prob. 39ECh. 10.3 - Consider the Markov chain on {1, 2, 3, 4} with...Ch. 10.3 - Prob. 1ECh. 10.3 - In Exercises 16, consider a Markov chain with...Ch. 10.3 - Prob. 3ECh. 10.3 - Prob. 4ECh. 10.3 - Prob. 5ECh. 10.3 - Prob. 6ECh. 10.3 - Consider the mouse in the following maze from...Ch. 10.3 - Prob. 8ECh. 10.3 - Prob. 9ECh. 10.3 - Prob. 10ECh. 10.3 - Prob. 11ECh. 10.3 - Consider an unbiased random walk with absorbing...Ch. 10.3 - In Exercises 13 and 14, consider a simple random...Ch. 10.3 - Prob. 14ECh. 10.3 - In Exercises 15 and 16, consider a simple random...Ch. 10.3 - In Exercises 15 and 16, consider a simple random...Ch. 10.3 - Consider the mouse in the following maze from...Ch. 10.3 - Consider the mouse in the following maze from...Ch. 10.3 - Prob. 19ECh. 10.3 - In Exercises 19 and 20, consider the mouse in the...Ch. 10.3 - Prob. 21ECh. 10.3 - Prob. 22ECh. 10.3 - Suppose that the weather in Charlotte is modeled...Ch. 10.3 - Prob. 24ECh. 10.3 - The following set of webpages hyperlinked by the...Ch. 10.3 - The following set of webpages hyperlinked by the...Ch. 10.3 - Prob. 27ECh. 10.3 - Prob. 28ECh. 10.3 - Prob. 29ECh. 10.3 - Prob. 30ECh. 10.3 - Prob. 31ECh. 10.3 - Prob. 32ECh. 10.3 - Prob. 33ECh. 10.3 - In Exercises 33 and 34, consider the Markov chain...Ch. 10.3 - Prob. 35ECh. 10.3 - Prob. 36ECh. 10.4 - Consider the Markov chain on {1, 2, 3, 4} with...Ch. 10.4 - In Exercises 1-6, consider a Markov chain with...Ch. 10.4 - In Exercises 1-6, consider a Markov chain with...Ch. 10.4 - In Exercises 1-6, consider a Markov chain with...Ch. 10.4 - In Exercises 1-6, consider a Markov chain with...Ch. 10.4 - In Exercises 1-6, consider a Markov chain with...Ch. 10.4 - In Exercises 1-6, consider a Markov chain with...Ch. 10.4 - In Exercises 7-10, consider a simple random walk...Ch. 10.4 - In Exercises 7-10, consider a simple random walk...Ch. 10.4 - In Exercises 7-10, consider a simple random walk...Ch. 10.4 - In Exercises 7-10: consider a simple random walk...Ch. 10.4 - Reorder the states in the Markov chain in Exercise...Ch. 10.4 - Reorder the states in the Markov chain in Exercise...Ch. 10.4 - Reorder the states in the Markov chain in Exercise...Ch. 10.4 - Prob. 14ECh. 10.4 - Prob. 15ECh. 10.4 - Prob. 16ECh. 10.4 - Find the transition matrix for the Markov chain in...Ch. 10.4 - Find the transition matrix for the Markov chain in...Ch. 10.4 - Consider the mouse in the following maze from...Ch. 10.4 - Consider the mouse in the following maze from...Ch. 10.4 - In Exercises 21-22, mark each statement True or...Ch. 10.4 - In Exercises 21-22, mark each statement True or...Ch. 10.4 - Confirm Theorem 5 for the Markov chain in Exercise...Ch. 10.4 - Prob. 24ECh. 10.4 - Consider the Markov chain on {1, 2, 3} with...Ch. 10.4 - Follow the plan of Exercise 25 to confirm Theorem...Ch. 10.4 - Prob. 27ECh. 10.4 - Prob. 28ECh. 10.4 - Prob. 29ECh. 10.5 - Prob. 1PPCh. 10.5 - Consider a Markov chain on {1, 2, 3, 4} with...Ch. 10.5 - Prob. 1ECh. 10.5 - Prob. 2ECh. 10.5 - In Exercises 13, find the fundamental matrix of...Ch. 10.5 - Prob. 4ECh. 10.5 - Prob. 5ECh. 10.5 - Prob. 6ECh. 10.5 - Prob. 7ECh. 10.5 - Prob. 8ECh. 10.5 - Prob. 9ECh. 10.5 - Prob. 10ECh. 10.5 - Prob. 11ECh. 10.5 - Prob. 12ECh. 10.5 - Consider a simple random walk on the following...Ch. 10.5 - Consider a simple random walk on the following...Ch. 10.5 - Prob. 15ECh. 10.5 - Prob. 16ECh. 10.5 - Prob. 17ECh. 10.5 - Prob. 18ECh. 10.5 - Prob. 19ECh. 10.5 - Consider the mouse in the following maze from...Ch. 10.5 - In Exercises 21 and 22, mark each statement True...Ch. 10.5 - Prob. 22ECh. 10.5 - Suppose that the weather in Charlotte is modeled...Ch. 10.5 - Suppose that the weather in Charlotte is modeled...Ch. 10.5 - Consider a set of webpages hyperlinked by the...Ch. 10.5 - Consider a set of webpages hyperlinked by the...Ch. 10.5 - Exercises 27-30 concern the Markov chain model for...Ch. 10.5 - Exercises 27-30 concern the Markov chain model for...Ch. 10.5 - Exercises 27-30 concern the Markov chain model for...Ch. 10.5 - Exercises 27-30 concern the Markov chain model for...Ch. 10.5 - Exercises 31-36 concern the two Markov chain...Ch. 10.5 - Exercises 31-36 concern the two Markov chain...Ch. 10.5 - Exercises 31-36 concern the two Markov chain...Ch. 10.5 - Prob. 34ECh. 10.5 - Prob. 35ECh. 10.5 - Prob. 36ECh. 10.5 - Consider a Markov chain on {1, 2, 3, 4, 5, 6} with...Ch. 10.5 - Consider a Markov chain on {1,2,3,4,5,6} with...Ch. 10.5 - Prob. 39ECh. 10.6 - Let A be the matrix just before Example 1. Explain...Ch. 10.6 - Prob. 2PPCh. 10.6 - Prob. 1ECh. 10.6 - Prob. 2ECh. 10.6 - Prob. 3ECh. 10.6 - Prob. 4ECh. 10.6 - Prob. 5ECh. 10.6 - Prob. 6ECh. 10.6 - Major League batting statistics for the 2006...Ch. 10.6 - Prob. 8ECh. 10.6 - Prob. 9ECh. 10.6 - Prob. 10ECh. 10.6 - Prob. 11ECh. 10.6 - Prob. 12ECh. 10.6 - Prob. 14ECh. 10.6 - Prob. 15ECh. 10.6 - Prob. 16ECh. 10.6 - Prob. 17ECh. 10.6 - In the previous exercise, let p be the probability...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Similar questions
- Explain how you can determine the steady state matrix X of an absorbing Markov chain by inspection.arrow_forwardTOPIC: MARKOV CHAINSA market research firm conducted a household survey regarding preferences for three brands of detergents.three brands of detergents. The survey was conducted by interviewing the same housewives at the beginning of two consecutive months.consecutive months. The results of the survey are as follows: Beginning of month 1: 200 respondents showed a preference for the "Ace" brand, 120 for the "Bold" brand, and 180 for the "Clean" brand.for the "Clean" brand. A) With the above data, write a transition probability matrix and indicate how many housewives were loyal to each brand during that period.were loyal to each brand during that period.arrow_forwardCentral topic markov chains: Every summer the Yates de los Lagos owners association decides if its annual regatta will be held in June, July or August. If it takes place in June, the probability of good weather is ¾; and if these conditions exist, the regatta of the next year it will be done in June with probability 2/3, in July with probability 1/6 or in August with probability 1/6; but if there is bad weather, next year's regatta will take place in July or August with equal probabilities. If the competition is held in July, good and bad weather have equal probabilities; if there is good weather, the next year's regatta will be held in July; If there is bad weather, the next regatta will take place in August with probability of 2/3 or in June with probability of 1/3. If the regatta takes place in August, the probability of good weather is 2/5; and if there are good conditions atmospheric conditions, next year's regatta will take place in July or August, with equal probabilities; but…arrow_forward
- Each item is inspected and is declared to either pass or fail. The machine can work in automatic or manual mode. If it outputs two failed items in a row in automatic mode, it is switched to manual. Once it produces two passing items in a row in manual mode, it is switched back to automatic. Sup- pose that failure rate is a in automatic and b in manual. You modeled the system as a Markov chain with a diagram given below, where states represent the mode and the status of the previously man- ufactured item, so for example, state “manual-1 success” represents that the machine is in manual mode and the previous item passed.arrow_forwardScenario: Researchers were interested in how social situations can influence stress-induced eating. They grouped participants according to self-reported stress-induced eating habits: consistently eating more (hyperphagics) or eating less (hypophagics) when stressed. Each participant was then exposed to one of three social situations: (1) a social inclusion condition, where subjects were told that a confederate partner had approved of a video they had made answering some questions and was looking forward to meeting them, (2) a neutral condition, where they were told their partners could not meet them because their partners had to cancel their participation, or (3) a social exclusion condition, where they were told that their partner had decided not to meet them after viewing their video. Subjects were then given an ice cream taste test and the amount of ice cream consumed was measured. what is the most appropriate graph if every main effect and interaction is significant? Group of…arrow_forwardScenario: Researchers were interested in how social situations can influence stress-induced eating. They grouped participants according to self-reported stress-induced eating habits: consistently eating more (hyperphagics) or eating less (hypophagics) when stressed. Each participant was then exposed to one of three social situations: (1) a social inclusion condition, where subjects were told that a confederate partner had approved of a video they had made answering some questions and was looking forward to meeting them, (2) a neutral condition, where they were told their partners could not meet them because their partners had to cancel their participation, or (3) a social exclusion condition, where they were told that their partner had decided not to meet them after viewing their video. Subjects were then given an ice cream taste test and the amount of ice cream consumed was measured. Question: In this particular scenario, how many hypotheses are there? 0 1 2 3arrow_forward
- Draw the state diagram for the Markov Model and show the transition probabilities on the diagram.arrow_forwardScenario: Researchers were interested in how social situations can influence stress-induced eating. They grouped participants according to self-reported stress-induced eating habits: con-sistently eating more (hyperphagics) or eating less (hypophagics) when stressed. Each partici-pant was then exposed to one of three social situations: (1) a social inclusion condition, where subjects were told that a confederate partner had approved of a video they had made answering some questions and was looking forward to meeting them, (2) a neutral condition, where they were told their partners could not meet them because their partners had to cancel their participa-tion, or (3) a social exclusion condition, where they were told that their partner had decided not to meet them after viewing their video. Subjects were then given an ice cream taste test and the amount of ice cream consumed was measured. Question: Which of the following best describes the scenario? Group of answer choices…arrow_forwardConsider a game where you need to fill a 5-digit number by spinning a wheel. Every time you spin the wheel a random digit shows up between 0 – 9 with equal probability. You are to decide where to place the digit in your number. Once you choose a location for the digit you cannot change it. Your objective is to maximize the number you get. (a) Set this up as a Markov Decision Process, identify the states, actions, and transition matrices.arrow_forward
- TOPIC: MARKOV CHAINS A housewife always uses one of three brands of detergent: "A", "B" or "C". Which one she buys depends inwhich of the three manufacturers is running a promotional campaign (with gifts such as combs, ornaments, etc.),etc.). Companies undertake such campaigns at random, regardless of whether or not competitors are running other campaigns at the same time.not running other campaigns at the same time. Brand "A" company runs a campaign ½ of the time, brand "B" runs a campaign 1/3 of the time, and brand "B" runs a campaign 1/3 of the time, and brand "C" runs a campaign 1/3 of the time.1/3 of the time, and "C" promotes 1/3 of the time. If the lady buys brand "A" on a certain occasion, the next time she will also buy brand "A".If she buys brand "A" on a certain occasion, the next time she will also buy brand "A", if your company is promoting or if neither of the other two is doing so.or she buys brand "B" if it is on promotion, but brand "A" is not, or she buys brand "C" if…arrow_forwardWe will use Markov chain to model weather XYZ city. According to the city’s meteorologist, every day in XYZ is either sunny, cloudy or rainy. The meteorologist have informed us that the city never has two consecutive sunny days. If it is sunny one day, then it is equally likely to be either cloudy or rainy the next day. If it is rainy or cloudy one day, then there is one chance in two that it will be the same the next possibilities. In the long run, what proportion of days are cloudy, sunny and rainy? Show the transition matrix.arrow_forwardPlease describe the steps you used to get the solution to the problem provided in the image below.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:9781305658004
Author:Ron Larson
Publisher:Cengage Learning
Finite Math: Markov Chain Example - The Gambler's Ruin; Author: Brandon Foltz;https://www.youtube.com/watch?v=afIhgiHVnj0;License: Standard YouTube License, CC-BY
Introduction: MARKOV PROCESS And MARKOV CHAINS // Short Lecture // Linear Algebra; Author: AfterMath;https://www.youtube.com/watch?v=qK-PUTuUSpw;License: Standard Youtube License
Stochastic process and Markov Chain Model | Transition Probability Matrix (TPM); Author: Dr. Harish Garg;https://www.youtube.com/watch?v=sb4jo4P4ZLI;License: Standard YouTube License, CC-BY