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QUESTION 1 120 Marks (a) An insurance company has three classes of policyholders where the claim amount distribution for each class follows (X + 8)a+1 x > 0 with parameters a and 9. You are given: 200 1 Risk Class ao Low 200 Medium 2 High 100 A third of the policyholders is considered Low risk class. For a randomly selected policyholder, the probability that he will claim an amount less than 100 is 06. A policyholder made a claim that exceeds 150. Calculate the probability that this policyholder is from a high risk class. (12 marks) (b) Let X be a random variable with pdf /(x) - 2xefor x > 0 Let /.(x) define as below: (x)- $(x) E[X] Find mean of S. (*) (8 marks) QUESTION 1 120 Marks (a) An insurance company has three classes of policyholders where the claim amount distribution for each class follows (X + 8)a+1 x > 0 with parameters a and 9. You are given: 200 1 Risk Class ao Low 200 Medium 2 High 100 A third of the policyholders is considered Low risk class. For a randomly selected policyholder, the probability that he will claim an amount less than 100 is 06. A policyholder made a claim that exceeds 150. Calculate the probability that this policyholder is from a high risk class. (12 marks) (b) Let X be a random variable with pdf /(x) - 2xefor x > 0 Let /.(x) define as below: (x)- $(x) E[X] Find mean of S. (*) (8 marks)