You are given
for [math]0 \lt t \lt 100[/math].
Calculate [math]\stackrel{\circ}{e}_{\text {75:1010 }}[/math].
- 6.6
- 7.0
- 7.4
- 7.8
- 8.2
- Created by Admin, Jan 15'24
You are given:
i) [math]\mu_{x+t}=\beta t^{2}, t \geq 0[/math]
ii) [math]l_{x}=1000[/math]
iii) [math]l_{x+10}=400[/math]
Calculate [math]1000 \beta[/math].
- 2.75
- 2.80
- 2.85
- 2.90
- 2.95
- Created by Admin, Jan 15'24
(i) An excerpt from a select and ultimate life table with a select period of 3 years:
[math]x[/math] | [math]l_{[x]}[/math] | [math]l_{[x]+1}[/math] | [math]l_{[x]+2}[/math] | [math]l_{x+3}[/math] | [math]x+3[/math] |
---|---|---|---|---|---|
60 | 80,000 | 79,000 | 77,000 | 74,000 | 63 |
61 | 78,000 | 76,000 | 73,000 | 70,000 | 64 |
62 | 75,000 | 72,000 | 69,000 | 67,000 | 65 |
63 | 71,000 | 68,000 | 66,000 | 65,000 | 66 |
(ii) Deaths follow a constant force of mortality over each year of age
Calculate [math]1000_{2 \mid 3} q_{[60]+0.75}[/math].
- 104
- 117
- 122
- 135
- 142
- Created by Admin, Jan 15'24
You are given:
(i) An excerpt from a select and ultimate life table with a select period of 2 years:
[math]x[/math] | [math]l_{[x]}[/math] | [math]l_{[x]+1}[/math] | [math]l_{x+2}[/math] | [math]x+2[/math] |
---|---|---|---|---|
50 | 99,000 | 96,000 | 93,000 | 52 |
51 | 97,000 | 93,000 | 89,000 | 53 |
52 | 93,000 | 88,000 | 83,000 | 54 |
53 | 90,000 | 84,000 | 78,000 | 55 |
(ii) Deaths are uniformly distributed over each year of age
Calculate [math]10000_{2.2} q_{[51]+0.5}[/math].
- 705
- 709
- 713
- 1070
- 1074
- Created by Admin, Jan 16'24
The SULT Club has 4000 members all age 25 with independent future lifetimes. The mortality for each member follows the Standard Ultimate Life Table.
Calculate the largest integer [math]N[/math], using the normal approximation, such that the probability that there are at least [math]N[/math] survivors at age 95 is at least [math]90 \%[/math].
- 800
- 815
- 830
- 845
- 860
- Created by Admin, Jan 16'24
You are given:
[math]x[/math] | [math]l_{x}[/math] |
---|---|
60 | 99,999 |
61 | 88,888 |
62 | 77,777 |
63 | 66,666 |
64 | 55,555 |
65 | 44,444 |
66 | 33,333 |
67 | 22,222 |
[math]a={ }_{3.42 .5} q_{60}[/math] assuming a uniform distribution of deaths over each year of age [math]b={ }_{3.4 \mid 2.5} q_{60}[/math] assuming a constant force of mortality over each year of age Calculate 100,000(a-b).
- -24
- 9
- 42
- 73
- 106
- Created by Admin, Jan 16'24
You are given the following extract from a table with a 3-year select period:
[math]x[/math] | [math]q_{[x]}[/math] | [math]q_{[x]+1}[/math] | [math]q_{[x]+2}[/math] | [math]q_{x+3}[/math] | [math]x+3[/math] |
---|---|---|---|---|---|
60 | 0.09 | 0.11 | 0.13 | 0.15 | 63 |
61 | 0.10 | 0.12 | 0.14 | 0.16 | 64 |
62 | 0.11 | 0.13 | 0.15 | 0.17 | 65 |
63 | 0.12 | 0.14 | 0.16 | 0.18 | 66 |
64 | 0.13 | 0.15 | 0.17 | 0.19 | 67 |
[math]e_{64}=5.10[/math]
Calculate [math]e_{[61]}[/math].
- 5.30
- 5.39
- 5.68
- 5.85
- 6.00
- Created by Admin, Jan 16'24
For a mortality table with a select period of two years, you are given:
[math]x[/math] | [math]q_{[x]}[/math] | [math]q_{[x]+1}[/math] | [math]q_{x+2}[/math] | [math]x+2[/math] |
---|---|---|---|---|
50 | 0.0050 | 0.0063 | 0.0080 | 52 |
51 | 0.0060 | 0.0073 | 0.0090 | 53 |
52 | 0.0070 | 0.0083 | 0.0100 | 54 |
53 | 0.0080 | 0.0093 | 0.0110 | 55 |
The force of mortality is constant between integral ages.
Calculate [math]1000_{2.5} q_{[50]+0.4}[/math].
- 15.2
- 16.4
- 17.7
- 19.0
- 20.2
- Created by Admin, Jan 16'24
A club is established with 2000 members, 1000 of exact age 35 and 1000 of exact age 45 . You are given:
(i) Mortality follows the Standard Ultimate Life Table
(ii) Future lifetimes are independent
(iii) [math] N[/math] is the random variable for the number of members still alive 40 years after the club is established
Using the normal approximation, without the continuity correction, calculate the smallest [math]n[/math] such that [math]\operatorname{Pr}(N \geq n) \leq 0.05[/math].
- 1500
- 1505
- 1510
- 1515
- 1520
- Created by Admin, Jan 16'24
A father-son club has 4000 members, 2000 of which are age 20 and the other 2000 are age 45. In 25 years, the members of the club intend to hold a reunion.
You are given:
(i) All lives have independent future lifetimes.
(ii) Mortality follows the Standard Ultimate Life Table.
Using the normal approximation, without the continuity correction, calculate the [math]99^{\text {th }}[/math] percentile of the number of surviving members at the time of the reunion.
- 3810
- 3820
- 3830
- 3840
- 3850
- Created by Admin, Jan 16'24