An automobile insurance company charges vehicle insurance premium depending on whether the customer

had accidents during the previous two years. Each year insurance holders have an accident with a

probability of 0.10. Accidents in different years are independent events. The next year's premium is

determined according to the following rules:

1. If an insurance holder had accidents in each of the past two years, they pay additional INR 1000.

2. If an insurance holder had accident in the current year, but not the previous year, they pay an

additional INR 600.

3. If an insurance holder had an accident last year but not the current year, they pay an extra INR 300.

4. If an insurance holder had no accidents in the past two years, they are given a discount of INR 200.

2.1 Formulate the above problem using Markov chain. Clearly identify the states and the state

transition probability matrix (TPM).

2.2 A customer in the current year has not committed any accident in the past two years. What will be

the expected additional insurance premium for this customer in year t+3?