(4)Assume that a website www.funwithmath1600.ag has three pages:Page A: KingAlgebraPage B: Learn1600andWin• Page C: LinearAlgbraIsEverywhereEach page has some links to the other pages of this website and no pages links to any pageoutside 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 isalways a boring task (is it?!) they decide to choose one of the links in page A with equalprobability and click on the link to see the next page. As a result, on the next step, theywill end up on page B with probability 3/4 and on the page C with probability 1/4. Thisprocess is then continued by the student with the same rule:Go the next page by clicking, with equal probability, on one of the existing linksthat 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 pagesof this website after n clicks. In particular, find the transition matrix, the initial statevector 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 5clicks.(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 whatwould the ranking be??

Answered: Image /qna-images/answer/fb8862f4-6c4d-4ceb-ba8c-76fcf2d7799d.jpg

Answered: (a) Use a Markov chain to model the…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Pleaese show all work and clearly state the answers in complete English sentences.
Determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text.(a) A stochastic matrix can have negative entries.(b) A Markov chain that is not regular can have a unique steady state matrix.
De termine if P = is a regular stochastic matrix.
I need help solving part B please.. The computer center at Rockbottom University has been experiencing computer downtime. Let us assume that the trials of an associated Markov process are defined as one-hour periods and that the probability of the system being in a running state or a down state is based on the state of the system in the previous period. Historical data show the following transition probabilities. To From Running Down Running 0.90 0.10 Down 0.20 0.80 (a) If the system is initially running, what is the probability of the system being down in the next hour of operation? The asnwer for part A is .10! (b) What are the steady-state probabilities of the system being in the running state and in the down state? (Enter your probabilities as fractions.) Running?1= ? Down?2= ?
Please describe the steps you used to get the solution to the problem provided in the image below.
3. A fair die is thrown repeatedly and independently. The process is said to be in state j at time n if j is the highest integer obtained in the first n throws. (a) Explain why the process described above is Markov. (b) Write down the transition matrix for the model. (c) How will the process behave in the long-run?
Help with the second bullet point, in the long run what fration of the games will the team win?
Plz don't give solution in image format and give me solutions as soon as possible
Please provide steps for how you got the solution to the problem provided in the photos below. I previously asked this on here and the answer provided was confusing and wrong.
An individual can contract a particular disease with probability 0.17. A sick person will recover dur- ing any particular time period with probability 0.44 (in which case they will be considered healthy at the beginning of the next time period). Assume that people do not develop resistance, so that pre- vious sickness does not influence the chances of contracting the disease again. Model as a Markov chain, give transition matrix on your paper. Find the probability that a healthy individual will be sick after two time periods.
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?
Please help me with this math homework question. I really can not figure this out.

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