# Find ex t for all states x 167 roll a fair die

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Unformatted text preview: ar 70% of programmers remain in that position 20% are promoted to project manager and 10% are ﬁred (state X). 95% of project managers remain in that position while 5% are ﬁred. How long on the average does a programmer work before they are ﬁred? 1.63. At a nationwide travel agency, newly hired employees are classiﬁed as beginners (B ). Every six months the performance of each agent is reviewed. Past records indicate that transitions through the ranks to intermediate (I) and qualiﬁed (Q) are according to the following Markov chain, where F indicates workers that were ﬁred: BIQF B .45 .4 0 .15 I 0 .6 .3 .1 Q0 01 0 F0 00 1 (a) What fraction are eventually promoted? (b) What is the expected time until a beginner is ﬁred or becomes qualiﬁed? 74 CHAPTER 1. MARKOV CHAINS 1.64. At a manufacturing plant, employees are classiﬁed as trainee (R), technician (T) or supervisor (S). Writing Q for an employee who quits we model their progress through the ranks as a Markov chain with transition probability R T S Q RT .2 .6 0 .55 0 0 0 0 SQ 0 .2 .15 .3 1 0 0 1 (a) What fraction of recruits eventually make supervisor...
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## This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).

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