43. Let X be a continuous random variable with density function

 Calculate the expected value of X.
(A) 1/5
(B) 3/5
(C) 1
(D) 28/15
(E) 12/5

44. A device that continuously measures and records seismic activity is placed in a remote region. The time, T, to failure of this device is exponentially distributed with mean 3 years. Since the device will not be monitored during its first two years of service, the time to discovery of its failure is X = max(T, 2). Calculate E(X). (A)(B)(C) 3 (D) (E) 5

45. A piece of equipment is being insured against early failure. The time from purchase until failure of the equipment is exponentially distributed with mean 10 years. The insurance will pay an amount x if the equipment fails during the first year, and it will pay 0.5x if failure occurs during the second or third year. If failure occurs after the first three years, no payment will be made. Calculate x such that the expected payment made under this insurance is 1000. (A) 3858 (B) 4449 (C) 5382 (D) 5644 (E) 7235

46. An insurance policy on an electrical device pays a benefit of 4000 if the device fails during the first year. The amount of the benefit decreases by 1000 each successive year until it reaches 0. If the device has not failed by the beginning of any given year, the probability of failure during that year is 0.4. Calculate the expected benefit under this policy. (A) 2234 (B) 2400 (C) 2500 (D) 2667 (E) 2694

47. A company buys a policy to insure its revenue in the event of major snowstorms that shut down business. The policy pays nothing for the first such snowstorm of the year and 10,000 for each one thereafter, until the end of the year. The number of major snowstorms per year that shut down business is assumed to have a Poisson distribution with mean 1.5. Calculate the expected amount paid to the company under this policy during a one-year period. (A) 2,769 (B) 5,000 (C) 7,231 (D) 8,347 (E) 10,578

48. A manufacturer’s annual losses follow a distribution with density function  To cover its losses, the manufacturer purchases an insurance policy with an annual deductible of 2. Calculate the mean of the manufacturer’s annual losses not paid by the insurance policy. (A) 0.84 (B) 0.88 (C) 0.93 (D) 0.95 (E) 1.00

49. An insurance company sells a one-year automobile policy with a deductible of 2. The probability that the insured will incur a loss is 0.05. If there is a loss, the probability of a loss of amount N is K/N, for N = 1, . . . , 5 and K a constant. These are the only possible loss amounts and no more than one loss can occur. Calculate the expected payment for this policy. (A) 0.031 (B) 0.066 (C) 0.072 (D) 0.110 (E) 0.150

50. An insurance policy reimburses a loss up to a benefit limit of 10. The policyholder’s loss, Y, follows a distribution with density function:  Calculate the expected value of the benefit paid under the insurance policy. (A) 1.0 (B) 1.3 (C) 1.8 (D) 1.9 (E) 2.0

1. 基隆市「慶安宮」又稱雞籠媽祖廟位於(A)忠一路(B)忠二路(C)忠三路。

2. 基隆市義五路與愛七路是(A)雙向道(B)同方向單行道(C)不限制、行駛路線。

3. 基隆「潮境公園」位於(A)仁愛區(B)中正區(C)暖暖區。

112年 - SOCIETY OF ACTUARIES_EXAM P PROBABILITY_EXAM P SAMPLE QUESTIONS 251-319#119927

112年 - SOCIETY OF ACTUARIES_EXAM P PROBABILITY_EXAM P SAMPLE QUESTIONS 201-250#119925

112年 - SOCIETY OF ACTUARIES_EXAM P PROBABILITY_EXAM P SAMPLE QUESTIONS 151-200#119924

112年 - SOCIETY OF ACTUARIES_EXAM P PROBABILITY_EXAM P SAMPLE QUESTIONS 101-150#119921

112年 - SOCIETY OF ACTUARIES_EXAM P PROBABILITY_EXAM P SAMPLE QUESTIONS 51-100#119910

112年 - SOCIETY OF ACTUARIES_EXAM P PROBABILITY_EXAM P SAMPLE QUESTIONS 1-50#119899