Science:Math Exam Resources/Courses/MATH307/December 2012/Question 05 (c)
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Question 05 (c) 

Consider an internet with six sites. The stochastic matrix describing the behaviour of a web surfer (with damping factor zero) is (c) Introduce a damping factor of 1/2 so that the surfer now moves according to the stochastic matrix (1/2)P + (1/2)Q where Q is the stochastic matrix describing a surfer picking any site at random (including the current site). Beginning equal probabilities of being at each site, what are the probabilities of being at each site after one step? 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

Science:Math Exam Resources/Courses/MATH307/December 2012/Question 05 (c)/Hint 1 
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Solution 

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Science:Math Exam Resources/Courses/MATH307/December 2012/Question 05 (c)/Solution 1 