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(Solved) FINC 6366 Problem Set I 1) Rick's Toy Store faces the following


Please see the attachment and answer Question 2 and question 3 Complete.


FINC 6366

 

Problem Set I

 

1) Rick?s Toy Store faces the following probability distribution of fire losses in its store over the

 

next year:

 

Probability

 


 

0.70

 


 

0.20

 


 

0.10

 


 

Loss

 


 

$0

 


 

$30,000

 


 

$70,000

 


 

a. Calculate the expected value and standard deviation of Rick?s losses for the year.

 

b. Assume that Rick pools his losses with Mark?s store, which has an identical loss distribution.

 

Mark?s losses are independent of Rick?s. Rick and Mark agree to split the total losses in the

 

pool equally. Show the revised probability distribution for the mean loss from the pool.

 

c. Calculate the expected value and standard deviation of the pooled mean losses

 

d. Insures combine a large number of exposure units in the process of risk pooling. Describe the

 

effect of increasing the size of the risk pool on the mean loss of the pool and on the standard

 

deviation of the mean loss in the pool. In your answer, assume that the losses of all the

 

exposure units in the pool are independent and homogeneous.

 

2) Maria is analyzing the workers? compensation (WC) losses of the employees in the firm that

 

occurred over a one-year period, based on the following data:

 

Number of WC Claims

 

Filled/Worker

 


 

Number of Workers

 


 

Total Number of Claims

 


 

0

 


 

800

 


 

0

 


 

1

 


 

240

 


 

240

 


 

2

 


 

30

 


 

60

 


 

a. Use the information in the table to find the average frequency of losses per worker.

 

b. Use the information in the table to estimate a probability distribution for the frequency

 

distribution of losses per worker in a year.

 


 

3) You are given the following table:

 

Range of Loss Amount Midpoint

 

Dollar Number of Losses

 

Amount of Loss

 


 

Total $ Amt. of Losses

 


 

$1-2000

 


 

$1,000

 


 

200

 


 

$200,000

 


 

$2000-10,000

 


 

$6,0000

 


 

30

 


 

$180,000

 


 

Greater than $12,000

 


 

NA

 


 

0

 


 

0

 


 

a. Use the information in the table to find the average severity per claim

 

b. Use the information in the table to estimate a probability distribution for the loss severity per

 

claim.

 

c. Using your answers from question 3, part (a) and question 2, part ( b), use convolution to find

 

the average loss.

 


 

 


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DATE ANSWERED

Oct 15, 2019

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