Chapter 2 and 3 Exam Prep Questions

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Allan Powell
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1 1 You are given the following mortality table: q for males q for females A life insurance company currently has 1000 males insured and 1000 females insured All 2000 insureds are age 90 All lives are independent Determine the probability that a randomly selected insured selected at the start of the third year will die during the third year 2 You are given: i 10 q Calculate q 60 ii 20 q iii q You are given the following: i p7 090 ii p iii p8 070 iv p90 00 v p9 02 Calculate 10 q 80

2 4 You are given: Calculate q 3/4 You are given: i Deaths are uniformly distributed between integral ages ii q 01 iii q 1 02 i Deaths follow a constant force of mortality between integral ages ii q 01 iii q 1 02 Calculate 06 0 q 02 6 You are given: i Deaths follow a constant force of mortality between ages and 1 ii Deaths are uniformly distributed between ages 1 and 2 iii q 01 iv q 1 02 Calculate 06 0 q 02 7 You are given that l 100,000 and q 0 If you assume that deaths follow a constant force of mortality between integral ages, then 03d Calculate 0 q 02 assuming uniform distribution of deaths between integral ages

3 8 You are given that mortality follows Makeham s law with A 0004, B 00003, and c 107 You are also given that under this law e Calculate e 61 9 Connor who is now age 22 is subject to substandard mortality Standard mortality follows mortality in the Illustrative Life Table Connor s force of mortality at any time is equal the force of mortality for the Illustrative Life Table plus 001 Calculate the probability that Connor will be alive at age 6 10 The probability of an ipad becoming useless due to any cause (being dropped, mechanical failure, etc) is 20% in each year Let K is the random variable representing number of complete years before an ipad becomes useless Calculate EK [ ] and the Var[ K ] 11 You are given: a Mortality follows Gompertz Law B b ln( c) c 30 p Calculate 10 q There have been 1,000,000 people eposed to a disease Based on scientific studies, 70% of people eposed to this disease end up actually contracting the disease For those eposed, the probability of surviving 10 years if the person does not contract the disease is 09 The probability of surviving 10 years if a person does contract the disease is 06 Calculate the variance of the number of survivors at the end of 10 years

4 13 You are given the following three select and ultimate mortality table: [] q [ ] q[ ] 1 q[ ] 2 3 q You are given that l [0] 100,000 Calculate d [2] 14 You are given that: i e 60 ii q 01 iii Deaths are uniformly distributed between integral ages Calculate e 1 1 Hua s mortality follows Gompetz Law with B and c 11 The probability that Hua will live for t years is Edyta s mortality follows Makeham s Law with B and c 11 The probability that Edyta will live for t years is Hua and Edyta are both currently age 20 Calculate the probability that Edyta will live for 2t years 16 You are given 2 for 0 t p t t ct You are also given Calculate

5 17 You are given: a e30 48 b e4 3 c e60 23 d e 14 30:1 e e 140 4:1 f e 12 60:1 Find the probability that (30) dies prior to age You are given 2 for 0 t 80 p t t t Calculate Var[ T 0] 19 You are given: a q90 02 b q91 03 c q92 c d q93 10 e Var[ K90] Determine c 20 You are given 0001t t Calculate 10 q 21 You are given that 30 q 0 (0)( 30 p 0 ) (3)( 1 q 0 ) Calculate 1 p 6

6 You are given that for Calculate 0 p 0 23 Mortality follows the Illustrative Life Table Assuming Uniform Distribution of Deaths between integral ages and that 0 s 1, 1000 q 1 s Calculate s

7 Mortality Table A l Mortality follows Mortality Table A above Calculate the Var[ K 7] 2 You are given that t q t 2 for 0 t Calculate e 2: 3 26 You are given that 100 for Calculate q 0

8 Epected Value = 4 and Variance = , Answers

1. Datsenka Dog Insurance Company has developed the following mortality table for dogs: l x

1. Datsenka Dog Insurance Company has developed the following mortality table for dogs: Age l Age 0 000 5 100 1 1950 6 1000 1850 7 700 3 1600 8 300 4 1400 9 0 l Datsenka sells an whole life annuity based