Math 419A Problem Set 1
Due by 5PM on Thursday, September 17
Show all work and use proper actuarial notations.
1. Consider the lifetime (of a newborn) random variable with force of mortality defined by
µx =
1
√
16 x
for x ≥ 0
(a) Find a simplified expression for the survival function S0 (x)
(b) Show that S0 (x) is a valid survival function.
(c) Calculate
20|10 q20
and interpret this probability.
2. You are given:
• The probability that (35) survives to reach age 50 is 0.83.
• The probability that (35) dies between age 50 and 65 is 0.15.
Calculate the probability that (35) survives to reach age 65.
3. For a population which contains equal numbers of males and females at birth, you are given
that
• for males, µm
x = 0.10 for x ≥ 0.
• for females, µfx = 0.08 for x ≥ 0.
Calculate q60 for this population.
1