Q UIZ 2
1. You are given:
0.04 if 0 < x < 40,
(x) =
0.05 if x > 40.
Calculate e25:25 .
(A) 15.6
(B) 17.6
(C) 19.6
(D) 21.6
(E) 23.6
2. For T , the future lifetime random variable for (0):
(a) > 70;
(b
Homework 1
1. Suppose that the probability that a 30-year-old will die before reaching
age 40 is 0.05, the probability that a 40-year-old will die before reaching age
50 is 0.07, and the probability t
1. L IFE I NSURANCE
1.1. Introduction. In this section, we develop formulae for the valuation
of traditional insurance benefits. In particular, we consider whole life, term
and endowment insurance.
Be
1. S URVIVAL M ODELS
1.1. Survival function. We are interested in properties of a positive random variable X, which we interpret as age-at-death or age-at-failure.
Definition 1.1. The survival functio
Q UIZ 3
1. You are given the survival function
s(x) = 1 (0.01x)2 , 0 x 100.
Calculate e30:50 , the 50-year temporary complete expectation of life
of (30).
(A) 27
(B) 30
(C) 34
(D) 37
(E) 41
2. For (x)
1. For a special fully continuous last survivor insurance of 1 on (x) and (y),
you are given:
(i) Tx and Ty are independent, (ii) = 0.06.
(iii) For (x), x+t = 0.08, and for (y), y+t = 0.04, t > 0.
Cal
1. Consider the following life table:
x
52
53
54
lx 89,948 89,089 88,176
Calculate 0.2q52.4 assuming UDD.
(A) 0.001911 (B) 0.001914 (C) 0.001917 (D) 0.001920 (E) 0.001923
2. For a 4-year college, you
1. For a whole life insurance of 1 on (41) with death benefit payable at the
end of the year of death, you are given:
(a) i = 0.05; p40 = 0.9972;
(b) A41 A40 = 0.00822;
(c) 2A41 2A40 = 0.00433;
(d) Z
Q UIZ 1
1. An actuary for a medical device manufacturer initially models the
failure time for a particular device with an exponential distribution
with mean 4 years. This distribution is replaced with
Homework 2
Exercise 2.1. Suppose that (x) =
Find .
2x
,
2 x2
Exercise 2.2. You are given that t q35 =
and e45 .
for 0 x , and 20 q40 =
50t+t2
7475
5
12
.
for 0 t 65. Find (45)
Exercise 2.3. The futur