Actuary Certification Actuary Certification Life Contingencies 1

Question 1

What does the curtate future lifetime K(x) represent for a life aged x?

Accepted Answer

The integer part of the future lifetime

Answer

K(x) is the curtate future lifetime, defined as the greatest integer less than or equal to the complete future lifetime T(x).

Question 2

The probability that a life aged 30 survives to age 40 is denoted as:

Accepted Answer

10p30

Answer

The notation nPx represents the probability that a life aged x survives at least n more years, so 10p30 is the probability of surviving from 30 to 40.

Question 3

Which life table function gives the expected number of deaths between exact ages x and x+1 out of a cohort of l0 lives?

Accepted Answer

dx

Answer

dx = lx − lx+1 represents the number of deaths between ages x and x+1 in the life table cohort.

Question 4

The force of mortality μ(x) is best described as:

Accepted Answer

The instantaneous rate of mortality at exact age x

Answer

The force of mortality μ(x) is the instantaneous hazard rate of death, analogous to an intensity in a Poisson process.

Question 5

Under the Uniform Distribution of Deaths (UDD) assumption, qx+t for 0 < t < 1 equals:

Accepted Answer

t · qx

Answer

Under UDD, deaths are uniformly distributed within each year of age, so the probability of death in the first t years of age x is t·qx.

Actuary Certification Practice Test

Actuary Certification Practice Test

Actuary Certification Actuary Certification Life Contingencies 1