A study of armed robbers yielded the approximate transition probability matrixshown below. The matrix gives the probability that a robber currents free, onprobation, or in jail would, over a period of a year, make a transition to one of thestates.ТоFromFreeProbationJailFree0.70.20.1Probation0.30.50.2Jail0.00.10.9Assuming 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 beforegoing 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 steadystate if you like.]

I) Given the robber is free now, let the expected number of years before it is going to jail here be…

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?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 9EQ

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