※ 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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