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

MATH307 December 2012

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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

${\displaystyle P={\begin{bmatrix}0&0&{\frac {1}{3}}&0&0&0\\{\frac {1}{2}}&0&{\frac {1}{3}}&0&0&0\\0&{\frac {1}{3}}&0&0&0&{\frac {1}{2}}\\{\frac {1}{2}}&{\frac {1}{3}}&0&0&{\frac {1}{2}}&0\\0&{\frac {1}{3}}&0&1&0&{\frac {1}{2}}\\0&0&{\frac {1}{3}}&0&{\frac {1}{2}}&0\end{bmatrix}}}$

(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?

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