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

Consider an internet with six sites. The stochastic matrix describing the behaviour of a web surfer (with damping factor zero) is

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

(b) If we begin with equal probabilities of being at each site, what are the probabilities of being at each site after one step? What is the probability of being at site 6 after two steps?