Math 520, Life Contingencies I, Exam 2, 29 November 2012
There are three problems on this exam for a total of 100 points.
You may not use your book or notes, but you may use a calculator.
1.
You are given the following excerpt from a life table in which i
Math 520 Life Contingencies I
Final Exam: 18 December 2012
This is a closedbook, closednotebook exam. You may use a calculator.
Show your work, and circle your answer if your answer is not obvious.
1. In this question, I ask you several questions about
Chapter 34.2 Review Problems
1. If the force of mortality is constant and equal to ln(10/9) from ages 76 to 80, how
many of 1000 persons ages 76 are expected to survive to age 80? (Answer: 656.1)
2. What is
d
dt 1t px+t ?
(Answer:
1t px+t
(x + t)
3. Mort
Math 520, Life Contingencies I, Exam 1, 14 October 2010
Each problem is worth 20 points.
You may not use your book or notes, but you may use a calculator.
1.
You are given the following mortality table:
x
lx
qx
dx
80
1000
0.020
20
81
980
0.0306
30
82
950
HW10 Solutions  Math 520 Fall 2013
Math 520, Fall 2013  Homework 10
Assigned 11/03/2013
Ungraded Not to be Turned In
1. (Similar to 5.7)
Establish a backward recursive formula for an nyear temporary life annuity issued to
(x). Determine the starting va
Name: _
Uniqname: _
Note to Math 520 Fall 2016 students: The following practice test is Test 2
from the Fall 2013 Math 520 course. During 2013, the material covered
excluded section 5.4 and Chapters 12. However, this material will be covered
in the 2016
Homework 3 Solutions, Math 520 F13
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Math 520, Fall 2013  Homework 4 Solutions
Due September 26, 2013
Graded problems: 1a (10 total pts for lx and ex), 1b (2 pts), 1c (2 pts), 3 (6 pts)
1. Solution.
a) Using Makehams law, for x 13,
1
1
0
0
ln s(x+1) ln s(x) = ( x y ) dy = A Bc x y dy =
Bx
c
HW6 Solutions  Math 520 Fall 2013
Page 1 of 4
10/08/2013
HW6 Solutions  Math 520 Fall 2013
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10/08/2013
HW6 Solutions  Math 520 Fall 2013
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10/08/2013
HW6 Solutions  Math 520 Fall 2013
Math 520, Fall 2013  Homework 6
Assigned 10/0
HW8 Solutions  Math 520 Fall 2013
Math 520, Fall 2013  Homework 8
Due October 24, 2013
Show your work to receive credit
Express numeric answers as fractions or decimals
1. Problem 4.19.
(6 points for part (c) )
2. (2 points)
In class, we proved that, un
Math 520, Section 001, Life Contingencies I, Exam 1, 10 September 2015
There are four problems on this exam for a total of 100 points.
You may not use your book or notes, but you may use a calculator.
SHOW ALL YOUR WORK.
1.
Suppose a continuous random var
Math 520, Section 001, Life Contingencies I, Exam 2, 8 October 2015
There are ve problems on this exam for a total of 100 points.
You may not use your book or notes, but you may use a calculator.
SHOW ALL YOUR WORK.
1.
Suppose q90 = 0.40 and q91 = 0.70.
(
NAME:
Quiz 3: Suppose the ageatdeath random variable X has survival function given by
s(x) = ecx for x 0, for some constant c > 0.
(a) Calculate
ex = E[T (x)].
SOLUTION: t px =
s(x+t)
s(x)
= ect , so
ex =
R
0
t px
dt =
R
0
ect dt = 1c .
(b) Calculate
NAME:
Quiz 7: Ann, who is 30 years old, buys a whole life annuity of $1 per year payable
continuously. Suppose that mortality follows de Moivres Law with = 90 and that the
force of interest = 0.04. Let Y denote the present value random variable of the ann
Math 520, Life Contingencies I, Final Exam, 17 December 2010
There are six problems for a total of 100 points.
You may not use your book or notes, but you may use a calculator.
1. Let X represent the ageatdeath of a newborn. For a certain population, th
Math 520, Life Contingencies, Exam 2, 7 December 2010
There are 4 problems.
You may not use your book or notes, but you may use a calculator.
1.
Serge buys a 3year endowment insurance policy that pays $10,000 at the end of year of death
or at time 3, whi
NAME:
Quiz 1: Given the survival function s(x) =
100x
100
for 0 x 100, compute the survival
function and probability density function for T (20), the future lifetime of (20).
SOLUTION: t p20 = sT (20) (t) = P[T (20) > t] = P[X > 20 + tX > 20] =
d
sT (20)
Math 520, Section 001, Life Contingencies I, Exam 3, 5 November 2015
There are four problems on this exam for a total of 100 points.
You may not use your book or notes, but you may use a calculator.
SHOW ALL YOUR WORK.
1.
Suppose (90) buys a twoyear term
Math 520, Section 001, Life Contingencies I, Final Exam, 22 December 2015
There are ve problems on this exam for a total of 100 points.
You may not use your book or notes, but you may use a calculator.
SHOW ALL YOUR WORK.
1.
Consider a 20year endowment i
Math 520, Section 001, Life Contingencies I, Exam 4, 3 December 2015
There are three problems on this exam for a total of 100 points.
You may not use your book or notes, but you may use a calculator.
SHOW ALL YOUR WORK.
1.
Suppose (40) buys a continuous,
HW9 Solutions  Math 520 Fall 2013
Math 520, Fall 2013  Homework 9
Assigned 10/27/2013
Ungraded Not to be Turned In
1. (Similar to 4.20)
You are given that the assumptions of problem 4.20 hold.
Note that Ax =
0
e t t p x ( x t ) dt =
=
e
k 0
a. Show tha
HW11 Solutions  Math 520 Fall 2013
Math 520, Fall 2013  Homework 11 Solutions
Due Thursday, November 14, 2013
A subset of this assignment will be graded
Show your work to receive credit
Express numeric answers as fractions or decimals
1. Problem 5.38
2.
Math 520, Fall 2013  Homework 9
Assigned 10/27/2013
Ungraded Not to be Turned In
1. (Similar to 4.20)
You are given that the assumptions of problem 4.20 hold.
Note that Ax =
0
e t t p x ( x t ) dt =
=
e
k 0
a. Show that
k 1
k
k
k
px x (k )
k 1
k
k 0
k