Risk Management Homework Assignments

RMI 2101 Fall 2018

Homework Assignment 6 24 Points

Due Dates

Hard Copy – Monday, October 8, 2018 AT THE BEGINNING OF CLASS

Electronic Copy – Turnitin no later than 4 PM on Thursday, October 11, 2018

Be careful to follow the Guidelines for Homework Document on Canvas/Course Documents.

1. The Civil Air Patrol (CAP) owns airplanes used for search and rescue missions. During

their activities, CAP sustains losses in the form of property damage to their airplanes. The CAP owns 150 planes in Pennsylvania (PA), and it has the following data for the number of accidents per airplane per year in PA.

# of accidents per airplane per year

# of airplanes of having this # of accidents

0 85

1 45

2 20

a. What is the random variable illustrated here? [1 point]

b. Derive the probability distribution based on this data. Be careful to label exactly

what you are defining as the probability distribution. Round your calculation to 2 decimals. [3 points]

c. Calculate the expected value of frequency per airplane. What is the unit of

measurement? Round your calculation to 2 decimals. [2 points] d. CAP has calculated the variance of frequency per airplane to be equal to 0.5064

in PA. Prove that CAP calculated the correct variance for frequency. Show all work! What is the unit of measurement? [4 points]

e. How much risk is present for CAP in PA? What is the unit of measurement?

Round your calculation to 2 decimals. [2 points] 2. Assume initially that when accidents occur, they are non-random and equal to $13,000.

a. Calculate the expected loss per airplane in PA. [1 point] b. Calculate the expected loss for ALL airplanes in PA. [1 point]

3. Now based on the information in PA, CAP has constructed the following information related to the dollar amount of losses for 105 reported accidents.

a. Calculate the expected value of severity per airplane. Round your calculation to

2 decimals. [4 points]

$ amount of losses # of accidents having this $ amount of losses

$500 7

$1,000 10

$3,000 2

$6,000 6

$9,000 8

$13,000 18

$16,000 13

$19,000 15

$23,000 9

$26,000 6

$29,000 4

$33,000 3

$36,000 1

$39,000 2

$50,000 1

$80,000 0

b. Calculate the expected loss per airplane. [2 points]

4. The CAP also has the following data for the number of accidents per airplane in New Jersey (NJ). CAP has 60 airplanes in NJ. It is known that the variance of frequency per airplane in NJ is 0.2989.

# of accidents per airplane per year

# of airplanes of having this # of accidents

0 40

1 18

2 2

Which state is riskier for CAP, PA or NJ? And why? Show all calculations and explain your numerical results. Round your calculation to 2 decimals. [4 points]