Please see the attachment and answer Question 2 and question 3 Complete.
Problem Set I
1) Rick?s Toy Store faces the following probability distribution of fire losses in its store over the
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
Number of Workers
Total Number of Claims
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
Greater than $12,000
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
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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