homework 3 solutions - Engineering Math Homework 3...

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Engineering Math Homework 3 Solutions Spring 2009 1. number of people with serious symptoms in month number of people with mild symptoms in month number of people with 4 4 4 4 4 no symptoms in month 4 B œ Þ&!B  Þ"!C  Þ!&D B B C œ Þ%!B  Þ'!C  Þ#&D C C D œ Þ"!B  Þ$!C  Þ(!D D D œ Þ&! Þ"! Þ!& Þ%! Þ'! Þ#& Þ"! Þ$! Þ(! 4" 4 4 4 4" 4 4" 4 4 4 4" 4 4" 4 4 4 4" Ô× Ô × Ô × ÕØ Õ Ø Õ Ø 4 so the stochastic matrix is Þ&! Þ"! Þ!& Þ%! Þ'! Þ#& Þ"! Þ$! Þ(! 2. Ô × Ô × Ô × Õ Ø Õ Ø Õ Ø B #)!! B Þ&! Þ"! Þ!& #)!! ")#! C #)!! C Þ%! Þ'! Þ#& #)!! $&!! D #)!! D Þ"! Þ$! Þ(! #)!! $!)! œœ œ !" Ô × Ô × Õ Ø Õ Ø B Þ&! Þ"! Þ!& ")#! "%"% C Þ%! Þ'! Þ#& $&!! $&*) D Þ"! Þ$! Þ(! $!)! $$)) # # # After two months, people have serious symptoms, people have mild symptoms, "%"% $&*) and people have no symptoms. $$)) 3. Ô × Ô × Õ Ø Õ Ø Þ&! Þ"! Þ!& B ! Þ%! Þ%! Þ#& C ! Þ"! Þ$! Þ$! D ! œ Ô × Õ Ø Þ&! Þ"! Þ!& l ! "! # " l ! Þ % ! Þ % # &l ! ) )&l ! Þ"! Þ$! Þ$! l ! " $ $ l ! qqqqqqÄ Ð#!ÑV" Ð#!ÑV# Ð"!ÑV$
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This note was uploaded on 01/28/2010 for the course ESE 317 taught by Professor Hastings during the Fall '08 term at Washington University in St. Louis.

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