Essay
On any particular day,an individual can take one of two routes to work.Route A has a 25% chance of being congested,whereas route B has a 40% chance of being congested.The probability of the individual taking a particular route depends on his previous day's experience.If one day he takes route A and it is not congested,he will take route A again the next day with probability 0.8.If it is congested,he will take route B the next day with probability 0.7.On the other hand,if he takes route B one day and it is not congested,he will take route B again the next day with probability 0.9.Similarly,if route B is congested,he will take route A the next day with probability 0.6.
a.Construct the transition matrix for this problem.(Hint: There are four states corresponding to the route taken and the congestion.The transition probabilities are products of the independent probabilities of congestion and next-day choice.)
b.What is the long-run proportion of time that route A is taken?
Correct Answer:
Verified
b.0.3...View Answer
Unlock this answer now
Get Access to more Verified Answers free of charge
Correct Answer:
Verified
b.0.3...View Answer
Unlock this answer now
Get Access to more Verified Answers free of charge
Q16: State j is an absorbing state if
Q17: A unique matrix of transition probabilities should
Q18: Absorbing state probabilities are the same as<br>A)steady-state
Q19: Markov process models<br>A)study system evolution over repeated
Q20: The probability that a system is in
Q22: A state is said to be absorbing
Q23: If the probability of making a transition
Q24: At steady state,<br>A)π<sub>1</sub>(n + 1)> π<sub>1</sub>(n).<br>B)π<sub>1</sub> =
Q25: When absorbing states are present,each row of
Q26: Markov process trials<br>A)are used to describe future