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
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
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
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
Page 3 of 4
10/08/2013
HW6 Solutions  Math 520 Fall 2013
Math 520, Fall 2013  Homework 6
Assigned 10/0
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
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
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