29. 汽車行駛高速公路及快速公路,車輛行駛於設有爬坡道之長陡坡路段,其時速低於最低速限時, 除有特殊狀況外,應行駛何車道,並禁止變換車道
(A)外側車道
(B)中線車道
(C)爬坡道。

30. 標線為白色菱形劃設於車道,表示何種意義(A)讓路線(B)車種專用車道標線(C)指向線。

51. An auto insurance company insures an automobile worth 15,000 for one year under a policy with a 1,000 deductible. During the policy year there is a 0.04 chance of partial damage to the car and a 0.02 chance of a total loss of the car. If there is partial damage to the car, the amount X of damage (in thousands) follows a distribution with density function Calculate the expected claim payment. (A) 320 (B) 328 (C) 352 (D) 380 (E) 540

52. An insurance company’s monthly claims are modeled by a continuous, positive random variable X, whose probability density function is proportional to  for 0 ＜ x＜∞  . Calculate the company’s expected monthly claims. (A) 1/6 (B) 1/3 (C) 1/2 (D) 1 (E) 3

53. An insurance policy is written to cover a loss, X, where X has a uniform distribution on [0, 1000]. The policy has a deductible, d, and the expected payment under the policy is 25% of what it would be with no deductible. Calculate d. (A) 250 (B) 375 (C) 500 (D) 625 (E) 750

54. An insurer's annual weather-related loss, X, is a random variable with density functionCalculate the difference between the 30th and 70th percentiles of X. (A) 35 (B) 93 (C) 124 (D) 231 (E) 298

55. A recent study indicates that the annual cost of maintaining and repairing a car in a town in Ontario averages 200 with a variance of 260. A tax of 20% is introduced on all items associated with the maintenance and repair of cars (i.e., everything is made 20% more expensive). Calculate the variance of the annual cost of maintaining and repairing a car after the tax is introduced. (A) 208 (B) 260 (C) 270 (D) 312 (E) 374

56. A random variable X has the cumulative distribution function Calculate the variance of X. (A) 7/72 (B) 1/8 (C) 5/36 (D) 4/3 (E) 23/12

57. The warranty on a machine specifies that it will be replaced at failure or age 4, whichever occurs first. The machine’s age at failure, X, has density function Let Y be the age of the machine at the time of replacement. Calculate the variance of Y. (A) 1.3 (B) 1.4 (C) 1.7 (D) 2.1 (E) 7.5

58. A probability distribution of the claim sizes for an auto insurance policy is given in the table below:  Calculate the percentage of claims that are within one standard deviation of the mean claim size. (A) 45% (B) 55% (C) 68% (D) 85% (E) 100%

59. The owner of an automobile insures it against damage by purchasing an insurance policy with a deductible of 250. In the event that the automobile is damaged, repair costs can be modeled by a uniform random variable on the interval (0, 1500). Calculate the standard deviation of the insurance payment in the event that the automobile is damaged. (A) 361 (B) 403 (C) 433 (D) 464 (E) 521

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