5. (a) A large pool of adults earning their first driver's license includes 50% low-risk drivers, 30% moderate-risk driv

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5 A A Large Pool Of Adults Earning Their First Driver S License Includes 50 Low Risk Drivers 30 Moderate Risk Driv 1 (37.33 KiB) Viewed 31 times

5. (a) A large pool of adults earning their first driver's license includes 50% low-risk drivers, 30% moderate-risk drivers, and 20% high-risk drivers. Because these drivers have no prior driving record, an insurance company considers each driver to be randomly selected from the pool. This month, the insurance company writes four new policies for adults earning their first driver's license. Calculate the probability that these four will contain at least two more high-risk drivers than low-risk drivers. (10 marks) (b)An actuary has discovered that policyholders are three times as likely to file two claims as to file four claims. The number of claims filed has a Poisson distribution. Calculate the variance of the number of claims filed. (10 marks)