2. The number of accidents incurred by an insured driver in a single year has a geometric distribution with mean 5. If an accident occurs, the probability that the damage amount exceeds the deductible is 0.3. The number of claims and the damage amounts are independent. What is the probability that there will be at most one damage exceeding the deductible in a single year?
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$X$ follows a geometric distribution with mean 5. The probability mass function of $X$ is given by $P(X=k) = (1-p)^{k-1}p$, where $p$ is the probability of success (having an accident). The mean of a geometric distribution is $\frac{1}{p}$, so we have $\frac{1}{p} Show more…
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Lien L.
330. A loss under a liability policy is modeled by an exponential distribution The insurance company will cover the amount of that loss in excess of a deductible of 2000. The probability that the reimbursement is less than 6000, given that the loss exceeds the deductible, is 0.50. Calculate the probability that the reimbursement is greater than 3000 but less than 9000, given that the loss exceeds the deductible. 0.28 0.35 0.50 0.65 0.72
Sri K.
An auto insurance company insures your car for one year against damage due to collision with another vehicle or object. Your policy has an annual deductible of $400. During the year, there is a 90% chance that you will not have a collision and a 10% chance that you will have exactly one collision. Assume that the damage from a collision is approximated by an exponential distribution with a mean of $1600. (a) What is the probability that the insurer will not pay you anything, including the possibility that you don't have a collision? (Ans 0.92212) (b) Given that you have a collision, what is the probability that the insurer won't pay you more than $600, including the possibility that the damage doesn't exceed the deductible? (Ans 0.46474) (c) Given that you have a collision, determine the expected value of the insurance payment, including the possibility that the damage doesn't exceed the deductible. (Ans $1246.08) (d) Given that you have damage that exceeds the deductible, what is the probability that the insurer won't pay you more than $600? (Ans 0.31271) (e) Given that you have damage that exceeds the deductible, determine the expected value of the insurance payment. (Ans $1600) (f) What is the probability that the insurer won't pay you more than $600, including the possibility that you don't have a collision or that you have damage that doesn't exceed the deductible. SOLVE 2 WAYS, using answers from parts (a) - (e). (Ans 0.94647) (g) Determine the expected value of the insurance payment, including the possibility that you don't have a collision or that you have damage that doesn't exceed the deductible. SOLVE 2 WAYS, using answers from parts (a) - (e). (Ans $124.61)
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