Risk Management

Hint: Read the questions carefully and be sure that what you write answers the questions. Many times
students give correct information in an answer but that information is not the answer to the question.
Be careful as your writing skills, proper grammar, punctuation, capitalization etc. constitute part of the
homework grade.
Please show your work for each problem and bold/make clear the final answer.
***Please round ALL Final Answer VALUES to the nearest 2 decimal places
1. After witnessing the recent storm that took place in the tri-state area, as a risk manager you
want to reevaluate the potential frequency and severity of future storms in these areas. You use
new models to predict future weather patterns on 90 counties within the tri-state. Conclusions
were formed to contrast the probability distribution for number of hurricanes per county per
year within the tri-state area.

# of hurricanes per county per year Probability
0 0.05
1 0.15
2 0.18
3 0.30
4 0.30
5 0.02
a. Calculate the expected frequency of hurricanes per county per year. (2 points)
b. Calculate the variance. (2 points)
2. Now assume that when hurricanes do occur, they are non-random and losses due to clean ups
are equal to $1900.
 Calculate the expected losses per county per year? (2 points)
 Calculate the expected losses for ALL counties in the tri-state per year. (1 point)
 Calculate the expected loss for ALL counties in the tri-state for the next 5 years. (1
point)
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3. You would like to compare your data for future hurricanes in the tri-state area with the
frequency of hurricanes that occur in the south. You have collected the following data on 100
counties in the south.
# of hurricanes per county per year # of counties having these losses
0 73
2 15
4 ???
6 4
8 2
a. Calculate the probability distribution for frequency based on the information provided
above. (2 points)
b. Which location faces the most risk for hurricanes between the north and south?
Show/explain how you came to this answer. (2 points)
4. From past information, you have constructed the following distribution related to dollar
amount of losses when hurricanes do occur in the south.
$ amount of losses Probability of dollar loss
250 0.20
780 0.30
1500 0.35
1800 0.15
a. Calculate the expected value of severity for the south. (1 point).
b. Calculate the expected loss per county per year. (1 point)
5. Janie loves shopping from online small business thrift stores. Earlier this month she ordered
from two stores, let’s call them store A and B. The only downside Janie has noticed shopping
from these stores is sometimes her orders get lost in the mail. Below is the information on how
much she spent at each store and the probability it gets lost in the mail.
 Store A: $150 with a loss probability of 0.10
 Store B: $275 with a loss probability of 0.05
a. Create a probability distribution including all possible losses. (3 points)
b. Calculate the coefficient of variation. (3 points)
6. Five students are enrolled in RMI 2101. Colleen has a 3.0 GPA, EJ has a 3.5 GPA, Chelsea has a
3.7 GPA, Nicole has a 2.5 GPA, and Shanan has a 3.33 GPA. Colleen has a variance of 1, EJ has a
variance of 0.40, Chelsea has a variance of 0.7, Nicole has a variance of 1.2, and Shanan has a
variance of 0.95. Who faces the most risk? You must show the calculation for each student. (5
points)
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7. Henry lives in a not so safe area where break-ins are pretty common. When break-ins do occur,
damage is caused to doors and windows while also personal property is stolen. Below is a
probability distribution for the possible losses associated with a single break-in in a year.
a. What is the maximum possible loss? (1 point)
b. What is the expected loss? (1 point)
c. What is the variance? (1 point)