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

60. A baseball team has scheduled its opening game for April 1. If it rains on April 1, the game is postponed and will be played on the next day that it does not rain. The team purchases insurance against rain. The policy will pay 1000 for each day, up to 2 days, that the opening game is postponed. The insurance company determines that the number of consecutive days of rain beginning on April 1 is a Poisson random variable with mean 0.6. Calculate the standard deviation of the amount the insurance company will have to pay. (A) 668 (B) 699 (C) 775 (D) 817 (E) 904

61. An insurance policy reimburses dental expense, X, up to a maximum benefit of 250. The probability density function for X is:where c is a constant. Calculate the median benefit for this policy. (A) 161 (B) 165 (C) 173 (D) 182 (E) 250

62. The time to failure of a component in an electronic device has an exponential distribution with a median of four hours. Calculate the probability that the component will work without failing for at least five hours. (A) 0.07 (B) 0.29 (C) 0.38 (D) 0.42 (E) 0.57

63. An insurance company sells an auto insurance policy that covers losses incurred by a policyholder, subject to a deductible of 100. Losses incurred follow an exponential distribution with mean 300. Calculate the percentile of losses that exceed the deductible. (A) 600 (B) 700 (C) 800 (D) 900 (E) 1000

64. Claim amounts for wind damage to insured homes are mutually independent random variables with common density function where x is the amount of a claim in thousands.  Suppose 3 such claims will be made. Calculate the expected value of the largest of the three claims. (A) 2025 (B) 2700 (C) 3232 (D) 3375 (E) 4500

65. A charity receives 2025 contributions. Contributions are assumed to be mutually independent and identically distributed with mean 3125 and standard deviation 250. Calculate the approximate 90th percentile for the distribution of the total contributions received. (A) 6,328,000 (B) 6,338,000 (C) 6,343,000 (D) 6,784,000 (E) 6,977,000

66. Claims filed under auto insurance policies follow a normal distribution with mean 19,400 and standard deviation 5,000. Calculate the probability that the average of 25 randomly selected claims exceeds 20,000. (A) 0.01 (B) 0.15 (C) 0.27 (D) 0.33 (E) 0.45

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