※ 引述《jackoyu (偉下列資料正確填寫並回숩》之銘言： : 2. : Insurance policies are often sold with a deductible of d. When the loss x, : is at or below d, the insured will not make a claim and the insurance pays : nothing. When the loss is above d, the insured will make a claim and the : insurance pays the claim amount, x-d. : Suppose the losses have an exponential distribution with mean 1000. There is : a deductible of 100. 寫寫看= = : 1) What is the expected claim amount? x~Exp(1/1000) E[X-d] = E[X] - 100 = 900 : 2) A loss is occurred, what is the probability that the insured will make a : claim ? P(X>100) = e^-(1/1000)*100 = e^-0.1 : 3) There losses are occurred, assume the losses are independent. What is the : probability that exactly one claim is made. ~Pois(1/1000) = e^-(1/1000)[x/1000] : 4) One hundred claims are made, assume the losses are independent. What is the : probability that the average claim amount is over 1000e^(-0.1). average claim amount E(Xdad) = 1000 V(Xdad) = 1m/100 P(Z > (1000e^0.1-1000)/(1000/10)) = P(Z>(e^0.1-1)/10) --

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