sadikxwhfnc
Keen member
Hi,
I am attempting the CS2 Assignment X2 of the 2019 Textbook and I do not understand the solution to Qn 2.2.
The question is as follows:
In a certain population, the force of mortality at age x is given by:
70 < x <= 75 : 0.02
75 < x <= 80 : 0.04
80 < x <= 85 : 0.07
Find the probability that a life now aged exactly 73 will die between exact age 79 and exact age 82.
The solution is as follows:
Required probability = 6P73 * 3Q79
6P73 = 2P73 * 4P75 = exp(-2 * 0.02) * exp(-4 * 0.04) = exp (-0.2)
I have two questions with regard to the solution:
1. Why is 2P73 * 4P75 = exp(-2 * 0.02) * exp(-4 * 0.04) used instead of 3P73 * 3P76 = exp(-3 * 0.02) * exp (-3 * 0.04)??
This is because I thought that the force of mortality for age 73, 74 , and 75 is 0.02??
2. What is wrong with the method I used to solve as follow:
I find the probability of death at age = 79 , 80 , 81 , and 82.
P(Age = 79) = exp(-3*0.02) * exp(-3*0.04) * (1 - exp(-0.04)) = 0.032751
P(Age = 80) = exp(-3*0.02) * exp(-4*0.04) * (1 - exp(-0.04))
P(Age = 81) = exp(-3*0.02) * exp(-5*0.04) * (1 - exp(-0.07))
P(Age = 82) = exp(-3*0.02) * exp(-5*0.04) * * exp(-1 * 0.07) * (1 - exp(-0.07))
Many thanks for your help in advance.
I am attempting the CS2 Assignment X2 of the 2019 Textbook and I do not understand the solution to Qn 2.2.
The question is as follows:
In a certain population, the force of mortality at age x is given by:
70 < x <= 75 : 0.02
75 < x <= 80 : 0.04
80 < x <= 85 : 0.07
Find the probability that a life now aged exactly 73 will die between exact age 79 and exact age 82.
The solution is as follows:
Required probability = 6P73 * 3Q79
6P73 = 2P73 * 4P75 = exp(-2 * 0.02) * exp(-4 * 0.04) = exp (-0.2)
I have two questions with regard to the solution:
1. Why is 2P73 * 4P75 = exp(-2 * 0.02) * exp(-4 * 0.04) used instead of 3P73 * 3P76 = exp(-3 * 0.02) * exp (-3 * 0.04)??
This is because I thought that the force of mortality for age 73, 74 , and 75 is 0.02??
2. What is wrong with the method I used to solve as follow:
I find the probability of death at age = 79 , 80 , 81 , and 82.
P(Age = 79) = exp(-3*0.02) * exp(-3*0.04) * (1 - exp(-0.04)) = 0.032751
P(Age = 80) = exp(-3*0.02) * exp(-4*0.04) * (1 - exp(-0.04))
P(Age = 81) = exp(-3*0.02) * exp(-5*0.04) * (1 - exp(-0.07))
P(Age = 82) = exp(-3*0.02) * exp(-5*0.04) * * exp(-1 * 0.07) * (1 - exp(-0.07))
Many thanks for your help in advance.