Question 3 [18 marks] An insurance company has 2 types of policyholders: 60% are of risk type A and 40% are of risk type B. A and B types are associated with the number of claims NA and NB, respectively, where NA ~ Poisson()A = 0.1) and NB ~ Poisson(AB = 0.3) (during the lifetime of the insurance policy). Determining the type of a policyholder (type A or B) is done based on his/her claim submission. Claim arrivals (conditional on the risk type) occur independently. (a) [9 marks] Compute conditional probability that an arbitrary chosen policyholder is of risk type A if he /she did not submit any claims in a given claim period. What is this probability for the policyholder of type B? (b) [9 marks] Compute conditional probability that an arbitrary chosen policyholder is of risk type A if he/she submitted exactly one claim in a given claim period. What is this probability for the policyholder of type B? Solution