QWD
Sample Multiple Choice Questions v4.1.pdf

Iii the annual hurdle rate used for profit

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(iii) The annual hurdle rate used for profit calculations is 10%. (iv) The profit vector is (−165, 100, 125). (v) The profit margin for this insurance is 6%. Calculate the probability that (50) will survive one year. (A) 0.95 (B) 0.96 (C) 0.97 (D) 0.98 (E) 0.99 [This was Question 15 on the Spring 2015 Multiple Choice exam.]
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July 3, 2018 Page 148 12.4. For a fully discrete 3-year term life insurance policy on (40) you are given: (i) All cash flows are annual. (ii) The annual gross premium is 1000. (iii) Profits and premiums are discounted at an annual effective interest rate of 12%. (iv) The profit vector: Time in years Profit 0 -400 1 150 2 274 3 395 (v) The profit signature: Time in years Profit 0 -400 1 150 2 245 3 300 Calculate the profit margin. (A) 4.9% (B) 5.3% (C) 5.9% (D) 6.6% (E) 9.7%
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July 3, 2018 Page 149 LM.1. An employer is modelling time to retirement of workers using the Kaplan-Meier estimator. You are given the following information. (i) There are 1000 workers in force at time 0. (ii) At time 10, there are 600 workers remaining. (iii) The Kaplan-Meier estimate of the survival function for retirement at time 10 is 1000 ˆ (10) 0.8 S (iv) The next retirement after time 10 occurred at time 12, when 100 workers retired. (v) During the period from time 10 to time 12, a total of 200 workers dropped out for various other reasons. Calculate 1000 ˆ (12) S , the Kaplan-Meier estimate of the survival function (12). S (A) 0.40 (B) 0.45 (C) 0.50 (D) 0.55 (E) 0.60
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July 3, 2018 Page 150 LM.2. In a study of 1,000 people with a particular illness, 200 died within one year of diagnosis. Calculate a 95% (linear) confidence interval for the one-year empirical survival function. (A) (0.745, 0.855) (B) (0.755, 0.845) (C) (0.765, 0.835) (D) (0.775, 0.825) (E) (0.785, 0.815)
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July 3, 2018 Page 151 LM.3. A cohort of 100 newborns is observed from birth. During the first year, 10 drop out of the study and one dies at time 1. Nine more drop out during the next six months, then, at time 1.5, three deaths occur. Compute the Nelson-Åalen estimator of the survival function, (1.5). S (A) 0.950 (B) 0.951 (C) 0.952 (D) 0.953 (E) 0.954
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July 3, 2018 Page 152 LM.4. You are given the following data based on 60 observations: Calculate the upper limit of the 80% confidence interval for S (21) using the Kaplan-Meier estimate and Greenwood’s approximation. (A) 0.249 (B) 0.283 (C) 0.311 (D) 0.335 (E) 0.351 i y i s i b i 1 5 5 7 2 8 6 7 3 13 7 7 4 16 6 5 5 21 6 4
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July 3, 2018 Page 153 LM.5. In a study of workplace retention for a large employer, the following grouped data were collected from 100 new entrants. Time to exit Number of employees 0 5 years 28 5 10 years 19 10 20 years 15 20 30 years 30 Over 30 years 8 Calculate the probability that an employee exits within the first 12 years, using the ogive empirical distribution function. (A) 0.49 (B) 0.50 (C) 0.51 (D) 0.52 (E) 0.53
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July 3, 2018 Page 154 LM.6. Assume the Markov model of unemployment illustrated in the following diagram. Transition intensities are assumed to be constant for the lives under consideration. In a study of 5 lives, over a one-year observation period, you are given the following information.
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