Gambler’s Ruin Exercises 19 and 20 refer to Example 7.
Job Mobility 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?
Want to see the full answer?
Check out a sample textbook solutionChapter 8 Solutions
Finite Mathematics & Its Applications (12th Edition)
- CAPSTONE Explain how to find the nth state matrix of a Markov chain. Explain how to find the steady state matrix of a Markov chain. What is a regular Markov chain? What is an absorbing Markov chain? How is an absorbing Markov chain different than a regular Markov chain?arrow_forwardExplain how you can determine the steady state matrix X of an absorbing Markov chain by inspection.arrow_forwardConsider the Markov chain whose matrix of transition probabilities P is given in Example 7b. Show that the steady state matrix X depends on the initial state matrix X0 by finding X for each X0. X0=[0.250.250.250.25] b X0=[0.250.250.400.10] Example 7 Finding Steady State Matrices of Absorbing Markov Chains Find the steady state matrix X of each absorbing Markov chain with matrix of transition probabilities P. b.P=[0.500.200.210.300.100.400.200.11]arrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning