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Unformatted text preview: Tutorial #10 - MAT 1332A - Fall 2009 November 23, 2009 Find the eigenvalues and eigenvectors of A = 1- 8 4 . Solution: 1 = 2 + 2 i , v 1 = 1 2 + 2 i ; 2 = 2- 2 i , v 2 = 1 2- 2 i On any given day, a student is either healthy or ill. Of the students who are healthy today, 95% will be healthy tomorrow. Of the students who are ill today, 55% will still be ill tomorrow. (a) What is the transition matrix for this situation? (b) Suppose 20% of the students are ill on Monday. What fraction of per- centage of the students are likely to be ill on Tuesday? On Wednes- day? (c) If a student is well today, what is the probability that he or she will be well two days from now? (d) Find the steady-state vector for the Markov chain. Solution : (a) From : H I To : P = . 95 . 45 . 05 . 55 Healthy Ill Note that the sum of the entries in each column is 1. (b) Recall that the sum of the entries of a state vector is always 1. Let x (0) be the state vector on Monday. So x (0) = . 80 . 20 . Then....
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