STAT 479
Spring 2013
Test 1
February 12, 2013
1. (10 points) The random variable X is the loss under a medical insurance policy and is
distributed as a 2 point mixture distribution. The 2 point mixture distribution is a
combination of a gamma distribution
STAT 479
Quiz 9
Spring 2013
April 18, 2013
1. You have the following sample:
3
15
25
50
100
You want to test the following hypothesis:
H0: The data comes from the Pareto distribution with 5 and 180 .
H1: The data does not come from the Pareto distribution
STAT 479
Quiz 8
Spring 2013
April 11, 2013
1. You are given the following sample of losses from a health insurance policy:
600
1000
2000
Your boss believes that losses are distributed as a Normal distribution.
The Company has a reinsurance agreement that
STAT 479
Quiz 7
Spring 2013
April 4, 2013
1. You are given the following random sample:
8 8 12 15
The data is smoothed using a uniform kernel with a bandwidth of 3.
Using the smoothed distribution, calculate F (11) .
Solution:
K y ( x)
x y b
for y b x y
STAT 479
Quiz 5
Spring 2013
February 28, 2013
1. Claims for medical insurance coverage is distributed as an exponential distribution with
500 .
Siyun creates a discrete distribution of claims by using the Method of Mass Dispersal with a
span of 50.
Yuxi
STAT 479
Spring 2013
Quiz 4
February 21, 2013
1. Cao Casualty Company sells stop loss insurance which covers the Beckley Family medical
bills. The stop loss insurance pays for aggregate claims in excess of 1000.
There are three members of the Beckley fami
STAT 479
Quiz 1
January 19, 2012
. Wang Dental Insurance Company has received the following sample of claims:
80 80 100 80 120
Wang believes that dental claims are distributed as a Gamma distribution with a = 33 and
c9 = 2.8.
VARSAM is the variance o
Stat 479
Fall 2010
Quiz 7
October 25, 2010
1. An urn contains four balls. Each ball has a unique number on it. The numbers on
the balls are 2, 4, 6, and 8.
Two balls are drawn from the urn without replacement and the maximum number
drawn is used to estima
Stat 479
Fall 2010
Quiz 8
November 2, 2010
1. You are given the following information on 23 lives in a one year mortality study.
Life
Time of Entry
1
2
3
4
5
6
7-20
21
22
23
0
0
0
0
0
0
0
.2
.5
.7
Time of
Termination
.5
.2
.6
.6
.8
.7
1
.6
.9
1
Calculate
1.
Stat 479
Fall 2010
Quiz 9
November 18, 2010
You are given the following random sample from an Exponential distribution:
3 6 8 10 20
Using percentile matching at the 80th percentile, estimate 6. . You are given the following random sample from a Par
Stat 479
Fall 2010
Quiz 9
November 18, 2010
1. You are given the following random sample from an Exponential distribution:
3 6 8 10 20
Using percentile matching at the 80th percentile, estimate .
2. You are given the following random sample from a Pareto
Stat 479
Test 1
September 30, 2010
1. The number of student from Interest Theory that visit my office during office hours is distributed
as a Poisson distribution with a mean of 2 per hour.
The number of students from Loss Models that visit my office duri
STAT 479
Test 2
November 9, 2010
1. You are given the following grouped claim information:
Amount of Claim
0 5000
5000 10,000
10,000 25,000
25,000 100,000
100,000 +
Total
Number of Claims
8
12
3
2
1
26
Calculate E ( X 10,000) and E ( X 40,000) .
Total Amo
Homework Problems
Stat 479
Chapter 2
1.
Model 1 is a uniform distribution from 0 to 100. Determine the table entries for a
generalized uniform distribution covering the range from a to b where a < b.
2.
Let X be a discrete random variable with probability
Stat 479
Spring 2013
Quiz 3
January 31, 2013
1.
The number of coins dropped into a wishing well per ten minute period follows a Poisson
distribution with a mean of 1. The coins dropped in the wishing well are distributed as follows:
Coin
Penny
Nickel
Dime
STAT 479
Spring 2013
Quiz 2
January 24, 2013
1. Losses represented by the random variable of X are uniformly distributed from 0 to the
maximum loss. You are given that Var[ X ] 62,208 .
Calculate TVaR0.75 ( X ) .
Solution:
Var[ X ]
(b a)2
62, 208 (b 0)2
STAT 479
Spring 2013
Quiz 1
January 17, 2013
1. Purdue provides health insurance for all the students who take STAT 479. Purdue buys this
insurance from GAO Insurance Company. During the last five years, GAO has incurred the
following total losses:
Year
2
STAT 479
Spring 2013
Test 1
February 12, 2013
1. (10 points) The random variable X is the loss under a medical insurance policy and is
distributed as a 2 point mixture distribution. The 2 point mixture distribution is a
combination of a gamma distribution