An insurance company believes that their policyholders fall

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An insurance company believes that their policyholders fall into two demographic profiles, A and B. The fraction of policyholders that are of demographic A is ? (with 0 < ? < 1) and the fraction of policyholders that are of demographic B is 1- ? . In any given year, the probability that a person of demographic A will file a claim is pA and the probability that a person of demographic B will file a claim is pB. A policyholder is chosen at random: let C1 be the event that this policyholder makes a claim in year 1 and C2 be the event that this policyholder makes a claim in year 2. Under what circumstances (in terms of pA and pB) are the events C1 and C2 independent? Prove your answer.

Reference no: EM13628282

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