In most of Europe and Asia annual automobile insurance is determined by the bonus malus system. Each policyholder is given a number (state) and the policy premium is determined as a function of this...

Extracted text: In most of Europe and Asia annual automobile insurance is determined by the bonus malus system. Each policyholder is given a number (state) and the policy premium is determined as a function of this state. A policy holder's state changes from year to year in response to the number of claims made by the policy holder. Suppose the number of daims made by a particular policyholder in any given year, is a Poisson random variable with parameter A. Let. s;(k) be the next state of a policyholder who was in state i in the previous year and who made k claims in that year. The following table is a simplified Bonus-Malus system having 4 states. Next state if Annual State Premium O claims 1 claim |2 claims 3 or more claims 1 200 1 2 4 2 250 1 3 4 4 3 400 2 4 4 4 4 600 3 4 4 4 For A =2 A. Find the mean time to retum to state 1 (if you start in state 1): drestime (round to 2 decimals) B. Find the expected annual premium for a random person after it has been with the insurance company for a while: decimals) (round to 2