STOR 472Exam 1
February 11, 2013
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(1) A meteorologist has constructed the following table by tabulating the number of major snowstorms in
Chapel H
STOR 472Exam 1
February 8, 2012
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Print here
(1) A health insurer will pay your medical expenses this year subject to a deductible of 200. The
probability that y
Our first exam will be on Monday, Feb.11. Focus your preparation for the exam on the following
problems. They incorporate the major ideas from the first seven classes. The problems on the exam will
test the same concepts.
HW 1: 5
HW 2: 2,3,4,5
HW 3: 2,4
H
Homework Assignment 11:
(1) An insurer offers group term insurance on 250 mutually independent lives for a premium of 285. The probability of a claim is 0.02 for each life. The distribution of the number of lives by benefit amount is: Benefit Amount Numbe
Homework Assignment 10:
(1) An insurance company is selling the one-year term insurance that pays an extra benefit in case of
accidental death that is described on page 29. The company wishes to have at least a 95% probability
that premiums with a relativ
Homework Assignment 9:
(1) An insurer has a portfolio of 32 independent policies. The probability of a claim is 1/6. The benefit
amount given that there is a claim has a gamma distribution with = 2 and = 6. Let S be the total
claims for the portfolio. Usi
Homework Assignment 8:
(1) The probability of a fire in a certain structure in a given time is 0.05. If a fire occurs,
the damage to the structure is uniformly distributed between 0 and 20. The claim
random variable, X, represents the fire damage to the s
Homework Assignment 7:
(1) Losses have an inverse exponential distribution. The mode is 10,000. Calculate the
median.
(Ans 28,854. Recall from class lecture that if X has an exponential distribution, then
Y = X-1 has an inverse exponential distribution. F
Homework Assignment 6:
(1) For 2003, loss sizes follow a uniform distribution with f(x) = 1 / 2500, 0 < x < 2500.
Inflation of 3% impacts all losses uniformly from 2003 to 2004. In 2004 a deductible of 100
is applied to all losses. Determine the expected
Homework Assignment 5:
(1) You are given:
(i)
Losses follow an exponential distribution with the same mean in all years.
(ii)
The loss elimination ratio this year is 70%.
(iii)
The deductible for the coming year is 4/3 of the current deductible.
Use the m
Homework Assignment 4:
(1) An insurance policy is written to cover a loss X, where X has a uniform distribution
on [0, 1000]. At what level must a deductible be set in order for the expected
payment to be 25% of what it would be with no deductible? (Try t
Homework Assignment 3:
(1) A company establishes a fund of 120 from which it wants to pay an amount, C, to any of its 20
employees who achieve a high performance level during the coming year. Each employee has a 2%
chance of achieving a high performance l
Homework Assignment 2:
(1) A random loss has the following probability distribution:
Amount of Loss: 0
Probability
: .5
1
.1
2
.1
3
.1
5
.1
6
.05
7
.025
9
.025
An insurer will pay nothing if the loss is 2, and will pay the loss minus 2 if the loss is > 2,
Homework Assignment 1:
(1) An insurance companys monthly claims are modeled by a continuous, positive random
variable X. The probability density function of X is proportional to (1+x) -4 where 0<x< .
Determine the companys expected monthly claims. (Ans )
Homework Assignment 25:
(1) Using the table on page 449, calculate the expected value of the reinsurers payment for each of the following reinsurance arrangements: (a) The reinsurer pays 50% of aggregate claims in excess of 2. The maximum amount the reins
Homework Assignment 24:
(1) Aggregate claims has a compound Poisson distribution with = 1 and p(1) = p(2) = 0.5. For a premium of 4.0, an insurer will pay total claims and a dividend equal to the excess, if any, of 75% of the premium over 100% of the clai
Homework Assignment 23:
(1) An insurance company sold one-year term life insurance on a group of 2,300 independent lives as given below: Class Benefit Amount Prob of Death Number of Policies 1 1 0.10 500 2 2 0.02 500 3 3 0.02 500 4 2 0.10 300 5 2 0.10 500
Homework Assignment 22:
(1) Do Exercise 14.5 on page 462. (In part (b), the first method refers to the approximation we developed in class.) (2) Consider a group life insurance contract with an accidental death benefit. Assume that for all members the pro
Homework Assignment 20:
(1)
(a) If the adjustment coefficient R = 2, find u so that (u) < 0.05. (b) Suppose that X has a Gamma(2,3) distribution and that the adjustment coefficient R = 1. Find , the relative security loading. (c) Suppose that X is exponen
Homework Assignment 19:
(1) A continuous-time surplus process has a compound Poisson claims process. (i) The claim amount distribution is inverse Gaussian with = 1.0 and = 0.02. (ii) The relative security loading is positive. (iii) The adjustment coeffici
Homework Assignment 18:
For a claim number process cfw_N(t), t 0, you are given that the waiting times between successive claims are independent and identically distributed with distribution function F(t) = 1 e-2t. Determine the probability that exactly 3
Homework Assignment 17:
(1) For an allosaur with 10,000 calories stored at the start of a day: (i) The allosaur uses calories uniformly at a rate of 5,000 per day. If his stored calories reach 0, he dies. (ii) Each day the allosaur eats 1 actuary (10,000
Homework Assignment 16:
(1) You are the agent for a baseball player who desires an incentive contract that will pay the following amounts: Type of hit Probability of hit per time at bat Compensation per hit Single 0.14 x Double 0.05 2x Triple 0.02 3x Home
Homework Assignment 15:
(1) The random variable S follows a binomial distribution with n = 3 and p = 1/3. The following procedure simulates S: Generate a uniform random number U on [0,1] and let 0, if U a 1, if a < U b 2, if b < U c 3, if c < U
S=
Determi
Homework Assignment 14: (1) Do Exercise 12.13 on page 394. (2) Lucky Lisa finds coins on her way to class at a Poisson rate of 0.5 coins per minute. The denominations are randomly distributed: (i) (ii) (iii) 60% of the coins are pennies; 20% of the coins
Homework Assignment 13: (1) Prescription drug losses, S, are modeled assuming the number of claims has a geometric distribution with mean 4, and the amount of each prescription is 40. Calculate E[(S-100)+]. (Ans 92.16) (2) Do Exercise 12.10 on page 394. [
Homework Assignment 12: (1) In a clinic, physicians volunteer their time on a daily basis to provide care to those who are not eligible to obtain care otherwise. The number of physicians who volunteer in any day is uniformly distributed on the integers 1
Homework Assignment 11:
(1) An insurer offers group term insurance on 250 mutually independent lives for a premium of 285. The probability of a claim is 0.02 for each life. The distribution of the number of lives by benefit amount is: Benefit Amount Numbe