Risk Management Homework Assignments

RMI 2101 Fall 2018

Homework Assignment 5 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. Temple football team is playing against East Carolina on Saturday, October 6, 2018.

Suppose that Temple has a 46.5% chance of winning the game. College football games

cannot end in a tie.

a. What is the random variable associated with this game? [1 point]

b. What is the mutually exclusive event in this case? [1 point]

c. Construct a well-labeled probability distribution table based on the outcomes of

this game. [2 points]

2. After East Carolina, Temple will play against three other teams as listed in the table

below.

Date GAME Win Probability1

October 6 East Carolina 46.5%

October 20 Cincinnati 72.8%

November 1 UCF 18.6%

November 10 Houston 65.0%

a. What is the probability that Temple wins ALL four games? [1 point]

b. What is the probability that Temple loses ONLY ONE of the four games? Be sure

to show your work. (Hint: they could lose to East Carolina AND win the others,

OR they could lose to Cincinnati AND win the others …) [5 points]

1 The win probabilities are randomly assigned and refer to the probability of Temple winning the game.

3. On Thursday, ABC Grocery is expecting to receive Package A containing $150 worth of food. Based on his past experience with the delivery service, the manager estimates that this package has a chance of 10% being lost in shipment. On Friday, ABC Grocery expects Package B to be delivered. Package B contains $400 worth of food. This package has a 30% chance of being lost in shipment. a. What are the possible outcomes for ABC Grocery’s total dollar amount of losses

for package A and B? For each dollar amount of losses, describe under what circumstances it would occur. In other words, what event(s) must happen for each dollar amount of losses to occur? Please note that this asks about total dollar amount of losses, not number of losses. [2 points]

b. For each of the possible outcomes you identify in part [a], derive the probability of the outcome occurring. [4 points]

c. Construct [in table form] the probability distribution for total dollar amount of losses for package A and B. [2 points]

d. Calculate the expected value of total dollar amount of losses. What is the unit

of measurement? [2 points]

e. The manager has calculated the variance for the total dollar amount of losses to be 35,625. Since you want to be sure you are using correct numbers in your evaluation, prove that the manager calculated the correct variance for total dollar amount of losses. Show all work! What is the unit of measurement? [4 points]