1 You are given the following mortality table: q for males q for females 90 020 010 91 02 01 92 030 020 93 040 02 94 00 030 9 060 040 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 q0 0100 Calculate 10 10 q 60 ii 20 q0 0226 iii 20 10 q0 0148 3 You are given the following: i p7 090 ii p80 080 iii p8 070 iv p90 00 v p9 02 Calculate 10 q 80
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 03 240939 Calculate 0 q 02 assuming uniform distribution of deaths between integral ages
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 e60 167 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 000262301 ln( c) c 30 p30 0471003492 Calculate 10 q 40 12 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
13 You are given the following three select and ultimate mortality table: [] q [ ] q[ ] 1 q[ ] 2 3 q 3 0 0020 0031 0043 006 3 1 002 0037 000 006 4 2 0030 0043 007 0072 3 003 0049 006 0091 6 4 0040 00 0076 0113 7 004 0061 0090 0140 8 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 00004 and c 11 The probability that Hua will live for t years is 096238 Edyta s mortality follows Makeham s Law with B 00004 and c 11 The probability that Edyta will live for t years is 08794 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 0 1 0004 t ct You are also given 29 0 100 Calculate
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 60 18 You are given 2 for 0 t 80 p t 0 1 0004 t 00001 t Calculate Var[ T 0] 19 You are given: a q90 02 b q91 03 c q92 c d q93 10 e Var[ K90] 1038864 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
2 3 22 You are given that 110 3 3 for 0 110 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 9 3676786 Calculate s
Mortality Table A l 7 2000 76 1600 77 960 78 00 79 200 80 0 24 Mortality follows Mortality Table A above Calculate the Var[ K 7] 2 You are given that t q t 2 for 0 t 10 0 001 Calculate e 2: 3 26 You are given that 100 for 0 100 Calculate 10 20 q 0
1 0244 2 0172 3 028 4 017297 007909 6 0074724 7 004082 8 1617 9 04118 10 Epected Value = 4 and Variance = 20 11 024430 12 19,09 13 274898 14 611 1 073437 16 80 17 012609 18 4602 19 06 20 009398 21 07 22 090609 23 03 24 1331 2 404 26 0448 Answers