Operations Research : Applications and Algorithms
4th Edition
ISBN: 9780534380588
Author: Wayne L. Winston
Publisher: Brooks Cole
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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.
Draw the transition diagram for this Markov process. Label the states A, P, and L.
Set up a stochastic matrix for the Markov process.
Find the state of the matrix that changes no more.
In the long run, what percent of the lawyers will be associates?
(c.) Assume that the probability of rain tomorrow is 0.5 if it is raining today, and assume that the probability of its being clear (no rain) tomorrow is 0.9 if it is clear today. Also assume that these probabilities do not change if information is also provided about the weather before today.(i) Explain why the stated assumptions imply that the Markovian property holds for the evolution of the weather.(ii) Formulate the evolution of the weather as a Markov chain by defining its states and giving its (one-step) transition matrix
:Determine the probability transition matrix ∥Pij∥ for the following Markov chains. Pleaseprovide the solutions step by step and provide a short explanation for each step.
=> 3 black balls and 3 white balls are placed in two urns so that each urncontains 3 balls. At each step one ball is selected at random from each urn and thetwo balls interchange. The state of the process is the number of white balls in thefirst urn.
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Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole
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