# problems4.6 - Math 307: Problems for section 4.5 December...

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Math 307: Problems for section 4.5December 20, 20091.Suppose that there is a fixed population of cola drinkers each with a favourite amongCoke, Pepsi and Thums Up. Every month 3% of the Coke drinkers switch to Pepsi while5% switch to Thums Up. Every month 2% of the Pepsi drinker switch to Coke while 3%switch to Thums Up.Every month 1% of the Thums Up drinkers switch to Coke and1% switch to Pepsi. What are the eventual market shares of these drinks? (You can useMATLAB/Octave to compute things, but explain what you are doing in your solution.)2.A flea hops randomly on vertices of a triangle, hopping to each of the other vertices withequal probability (never remaining at the same vertex). The flea starts at vertex1. Whatis the probability that the flea is at vertex1again afternhops?3.Show that the product of twon×nstochastic matrices is also stochastic.4.Find the rank for each site withα= 1and0.85for an internet that is linked in the followingwayYou can useeig

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Term
Fall
Professor
RICHARDFROESE
Tags
Math, Pepsi drinker switch, eventual market shares, MATLAB Octave function metropolis m