A study of armed robbers yielded the approximate transition probability matrix shown below. The matrix gives the probability that a robber currents free, on probation, or in jail would, over a period of a year, make a transition to one of the states. То Probation From Free Jail Free Probation Jail 0.1 0.2 0.9 0.7 0.2 0.3 0.0 0.5 0.1 Assuming that transitions are recorded at the end of each one-year period: i) For a robber who is now free, what is the expected number of years before going to jail? ii) What proportion of time can a robber expect to spend in jail?
A study of armed robbers yielded the approximate transition probability matrix shown below. The matrix gives the probability that a robber currents free, on probation, or in jail would, over a period of a year, make a transition to one of the states. То Probation From Free Jail Free Probation Jail 0.1 0.2 0.9 0.7 0.2 0.3 0.0 0.5 0.1 Assuming that transitions are recorded at the end of each one-year period: i) For a robber who is now free, what is the expected number of years before going to jail? ii) What proportion of time can a robber expect to spend in jail?
A First Course in Probability (10th Edition)
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![A study of armed robbers yielded the approximate transition probability matrix
shown below. The matrix gives the probability that a robber currents free, on
probation, or in jail would, over a period of a year, make a transition to one of the
states.
То
From
Free
Probation
Jail
Free
0.7
0.2
0.1
Probation
0.3
0.5
0.2
Jail
0.0
0.1
0.9
Assuming that transitions are recorded at the end of each one-year period:
i) For a robber who is now free, what is the expected number of years before
going to jail?
ii) What proportion of time can a robber expect to spend in jail?
[Note: You may consider maximum four transitions as equivalent to that of steady
state if you like.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feadc2ada-b74a-49cb-9e62-321f17cf11ad%2Fd30dbf3a-73bd-45cf-a889-d77926783fe5%2Ftreooim_processed.png&w=3840&q=75)
Transcribed Image Text:A study of armed robbers yielded the approximate transition probability matrix
shown below. The matrix gives the probability that a robber currents free, on
probation, or in jail would, over a period of a year, make a transition to one of the
states.
То
From
Free
Probation
Jail
Free
0.7
0.2
0.1
Probation
0.3
0.5
0.2
Jail
0.0
0.1
0.9
Assuming that transitions are recorded at the end of each one-year period:
i) For a robber who is now free, what is the expected number of years before
going to jail?
ii) What proportion of time can a robber expect to spend in jail?
[Note: You may consider maximum four transitions as equivalent to that of steady
state if you like.]
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