Assume that a website www.funwithmath1600.ag has three pages: Page A: KingAlgebra • Page B: Learn1600 andWin • Page C: Linear AlgbraIsEverywhere Each page has some links to the other pages of this website and no pages links to any page outside this website. • Page A has three links to page B and only one link to page C. • Page B has three links to page A and two links to page C. • Page C has one link to page A and two links to page B. A student decides to explore this website starting from page A. Since reading content is always a boring task (is it?!) they decide to choose one of the links in page A with equal probability and click on the link to see the next page. As a result, on the next step, they will end up on page B with probability 3/4 and on the page C with probability 1/4. This process is then continued by the student with the same rule: Go the next page by clicking, with equal probability, on one of the existing links that are on the present page. (Use only fractions in your calculations; no decimals please). (a) Use a Markov chain to model the probability of the student being on one of the pages of this website after n clicks. In particular, find the transition matrix, the initial state vector and explain the meaning of entries on each state vector.
Assume that a website www.funwithmath1600.ag has three pages: Page A: KingAlgebra • Page B: Learn1600 andWin • Page C: Linear AlgbraIsEverywhere Each page has some links to the other pages of this website and no pages links to any page outside this website. • Page A has three links to page B and only one link to page C. • Page B has three links to page A and two links to page C. • Page C has one link to page A and two links to page B. A student decides to explore this website starting from page A. Since reading content is always a boring task (is it?!) they decide to choose one of the links in page A with equal probability and click on the link to see the next page. As a result, on the next step, they will end up on page B with probability 3/4 and on the page C with probability 1/4. This process is then continued by the student with the same rule: Go the next page by clicking, with equal probability, on one of the existing links that are on the present page. (Use only fractions in your calculations; no decimals please). (a) Use a Markov chain to model the probability of the student being on one of the pages of this website after n clicks. In particular, find the transition matrix, the initial state vector and explain the meaning of entries on each state vector.
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter9: Systems Of Linear Equations
Section9.5: Multiplication With The Addition-or-subtraction Method
Problem 31P
Related questions
Question
100%
Transcribed Image Text:Assume that a website www.funwithmath1600.ag has three pages:
• Page A: King Algebra
• Page B: Learn1600andWin
Page C: Linear
AlgbraIsEverywhere
Each page has some links to the other pages of this website and no pages links to any page
outside this website.
• Page A has three links to page B and only one link to page C.
• Page B has three links to page A and two links to page C.
• Page C has one link to page A and two links to page B.
A student decides to explore this website starting from page A. Since reading content is
always a boring task (is it?!) they decide to choose one of the links in page A with equal
probability and click on the link to see the next page. As a result, on the next step, they
will end up on page B with probability 3/4 and on the page C with probability 1/4. This
process is then continued by the student with the same rule:
Go the next page by clicking, with equal probability, on one of the existing links
that are on the present page.
(Use only fractions in your calculations; no decimals please).
(a) Use a Markov chain to model the probability of the student being on one of the pages
of this website after n clicks. In particular, find the transition matrix, the initial state
vector and explain the meaning of entries on each state vector.
(b) Use your model to find the probability that the student ends up on page B after 5
clicks.
Transcribed Image Text:(c) Find the steady state of this stochastic process.
(d) Explain why one can use this information to rank the pages of this website and what
would the ranking be??
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 6 steps with 27 images
Recommended textbooks for you
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Intermediate Algebra
Algebra
ISBN:
9781285195728
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Intermediate Algebra
Algebra
ISBN:
9781285195728
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning