CAS Exam MAS-I Spring 2019, Question 9

Study guide: Exam MAS-I

You are given the following information about a 40-state Markov chain:

• The states are numbered: \{0,1,\ldots,39\}
• P_{m,n} is the one-step transition probability from State m to State n
• P_{0,0} = \frac{1}{2}
• P_{0,i} = \frac{1}{78} for i = 1,2,\ldots 39
• P_{i,0} = \frac{1}{39} for i = 1,2,\ldots 39
• P_{i,i+1} = \frac{38}{39} for i = 1,2,\ldots 38
• P_{39,1} = \frac{38}{39}

Calculate the long run probability of being in State 0.

• A) Less than 0.1
• B) At least 0.1, but less than 0.2
• C) At least 0.2, but less than 0.3
• D) At least 0.3, but less than 0.4
• E) At least 0.4

Answer this question and see the worked solution

Concepts tested

• Markov Chain
• Stationary Distribution

More questions from this set

• CAS Exam MAS-I Spring 2019, Question 8
• CAS Exam MAS-I Spring 2019, Question 10