tutorial10 - Tutorial #10 - MAT 1332A - Fall 2009 November...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

Page1 / 3

tutorial10 - Tutorial #10 - MAT 1332A - Fall 2009 November...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online