The lawyers at a law firm are either associates or partners. At the end of each year,

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The lawyers at a law firm are either associates or partners. At the end of each year, 30% of the associates leave the firm, 20% are promoted to partner, and 50% remain associates. Also, 10% of the partners leave the firm at the end of each year. Assume that a lawyer who leaves the firm does not return.
(a) Draw the transition diagram for this Markov process. Label the states A, P, and L.
(b) Set up an absorbing stochastic matrix for the Markov process.
(c) Find the stable matrix.
(d) What is the expected number of years that an associate will be in the firm before leaving?
(e) In the long run, what percent of the lawyers will be associates?
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Finite Mathematics and Its Applications

ISBN: 978-0134768632

12th edition

Authors: Larry J. Goldstein, David I. Schneider, Martha J. Siegel, Steven Hair

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