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Within a certain period of time, let n be the number of health claims (the amount the insurance company pays the insured) of an insurance company, and suppose that the sizes of the claims areXi,... , Xn i.i.d Negative Expo nential with parameter ?. Let P be the premium charged or each policy (the amount the insured pays up front and let Sn-Xi+...+Xn. Assume the total amount of the claims should not exceed the total premium for the rn policies sold with probability p. You may assume n >30, and that X, are independent. (a) Write down the approximate distribution of Sn (b) Describe P(S nP) in words. (c) Find a general equation for P. (d) What should the premium P be if A 1/500, n 5000, and p 0.98?

math   Statistics-And-Probability   
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