A certain firm has noticed that employees' salaries from year to year can be modeled by Markov analysis. The matrix of transition probabilities follows.
(a) Set up the matrix of transition probabilities in the form:
I 0
A B
(b) Determine the fundamental matrix for this problem.
(c) What is the probability that an employee who has received a raise will eventually quit?
(d) What is the probability that an employee who has received a raise will eventually be fired?
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Salary in Next Year
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Salary in Current Year
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Remains Unchanged
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Receives Raise
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Quits
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Fired
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Remains Unchanged
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0.2
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0.4
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0.3
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0.1
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Receives Raise
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0.5
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0.3
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0.0
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0.2
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