RMI 2101

Spring 2018

Homework Assignment 3 (Answer Key)

30 points

Due on Feb 22nd, 2018 at 5:30 PM EST on BlackBoard/SafeAssign

No hard copies will be accepted in class. All homework must be submitted on SafeAssign and time stamped by 5:30 PM EST on the due date.

Carefully follow the Instructions – Homework Guidelines and Submitting Homework to SafeAssign located in the Homework Section of BlackBoard. Hint: Read the questions carefully and be sure that you answer the questions asked. Many times students give correct information in an answer but that information is not the answer to the question.

This assignment is entirely math orientated. As such you will need to show all of your work to receive full credit for the answers you provide. Provide your answers using Word docs only.

1. Use this Probability Distribution (PD) to answer the three questions below: Jimmy’s Coffee House would like to estimate the number of worker’s compensation claims for the upcoming year using accumulated data from the past 10 years. Upon review of this data it has been determined that Jimmy’s has had between 0 and 2 claims annually. The loss distribution for Jimmy’s Coffee House is as follows:

# of Worker’s Compensation Losses per Year	Probability of having this # of losses
0	.1
1	.7
2	.2

a. Calculate the expected number of losses per year ( mean ). (3 points)

b. Calculate the variance for the Jimmy’s Coffee House frequency distribution. Hint – first, construct a Probability Distribution Table now that the mean has been determined. (8 points)

c. Jimmy’s Coffee House wants to know how their risk compares to that of their competitor, Lulu’s Café. Lulu’s Café expects on average 1 accident per year with a variance of .60. Who faces more risk, Jimmy’s or Lulu’s? Hint: Jimmy’s and Lulu’s have different means. Show your work. (6 points)

2. Elite Limousine Service (ELS) uses a fleet of 1,000 vehicles to provide limousine and party bus services. From past information, the Chief Risk Officer for ELS has constructed the following loss distribution for the number of accidents per vehicle per year. Hint: frequency .

# of accidents per vehicle per year	# of vehicles having these losses
0	300
1	500
2	200

Find the expected number of accidents per vehicle per year, i.e. calculate the E(F). (4 points)

3. Now assume from past information, ELS has constructed the following probability distribution (PD) for the dollar amount of loss when accidents do occur .Hint: severity.

$ amount of losses	Probability of dollar losses
2,000	.40
8,000	.35
15,000	.25

a. Find the expected cost per accident, i.e., calculate the E(S). (3 points)

b. Calculate the expected loss per vehicle per year. (hint E(S) x E(F )) (3 points)

c. Calculate the expected loss for all vehicles per year . (3 points)

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