3. Car owners are required to have car insurance to ensure that any damage they cause to themselves or other drivers can be repaired. Suppose that there are three car insurance companies A, B and C to choose from. Each of these insurance companies sells annual policies, so it is only possible to change insurer once a year. Moreover, new customers are required to stay with their insurer for a minimum of two years. When it is possible for a car owner to change their insurance company, the probability that they will not choose to do so is 0.8, 0.7 and 0.9 if the current insurer is company A, B or C respectively. If, when it is possible for a car owner to change their insurance company, they choose to do so, then the probability of selecting either of the alternate firms is 0.5. chain. S = {A, B, C}. the states of an alternate state space which does result in a Markov Hint: There are six states The one-step transition matrix for the Markov chain model is, 0 1 0 0 0 0 0 0.8 0.1 0 0.1 0 0 0 0 1 0 0 P = 0.15 0 0 0.7 0.15 0 0 0 0 0 0 1 0.05 0 0.05 0 0 0.9 Determine all stationary distributions for this Markov chain and justify your answer. Calculate the long term expected proportions of drivers using each of the companies above and justify your answer. You may use without proof that irreducible Markov chains with finite state spaces are positive recurrent.
3. Car owners are required to have car insurance to ensure that any damage they cause to themselves or other drivers can be repaired. Suppose that there are three car insurance companies A, B and C to choose from. Each of these insurance companies sells annual policies, so it is only possible to change insurer once a year. Moreover, new customers are required to stay with their insurer for a minimum of two years. When it is possible for a car owner to change their insurance company, the probability that they will not choose to do so is 0.8, 0.7 and 0.9 if the current insurer is company A, B or C respectively. If, when it is possible for a car owner to change their insurance company, they choose to do so, then the probability of selecting either of the alternate firms is 0.5. chain. S = {A, B, C}. the states of an alternate state space which does result in a Markov Hint: There are six states The one-step transition matrix for the Markov chain model is, 0 1 0 0 0 0 0 0.8 0.1 0 0.1 0 0 0 0 1 0 0 P = 0.15 0 0 0.7 0.15 0 0 0 0 0 0 1 0.05 0 0.05 0 0 0.9 Determine all stationary distributions for this Markov chain and justify your answer. Calculate the long term expected proportions of drivers using each of the companies above and justify your answer. You may use without proof that irreducible Markov chains with finite state spaces are positive recurrent.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:3. Car owners are required to have car insurance to ensure that any damage they cause to
themselves or other drivers can be repaired. Suppose that there are three car insurance
companies A, B and C to choose from. Each of these insurance companies sells annual
policies, so it is only possible to change insurer once a year. Moreover, new customers
are required to stay with their insurer for a minimum of two years.
When it is possible for a car owner to change their insurance company, the probability
that they will not choose to do so is 0.8, 0.7 and 0.9 if the current insurer is company
A, B or C respectively. If, when it is possible for a car owner to change their insurance
company, they choose to do so, then the probability of selecting either of the alternate
firms is 0.5.
chain.
S = {A, B, C}.
the states of an alternate state space which does result in a Markov
Hint: There are six states
The one-step transition matrix for the Markov chain model is,
0
1
0
0
0
0
0
0.8 0.1
0
0.1
0
0
0
0
1
0
0
P =
0.15 0
0
0.7 0.15
0
0
0
0
0
0
1
0.05
0 0.05 0
0
0.9
Determine all stationary distributions for this Markov chain and justify your answer.
Calculate the long term expected proportions of drivers using each of the companies
above and justify your answer. You may use without proof that irreducible Markov
chains with finite state spaces are positive recurrent.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
