Assume that a website www.funwithmath1600.ag has three pages:
• Page A: KingAlgebra
• Page B: Learn1600andWin
• Page C: LinearAlgbraIsEverywhere
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
(b) Use your model to find the probability that the student ends up on page B after 5 clicks.
(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?
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