Problem Set I 1) Rick’s Toy Store faces the following probability distribution o
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Question
Problem Set I
1) Rick’s Toy Store faces the following probability distribution of fire losses in its store over the next year:
Probability
0.50
0.40
0.10
Loss
$0
$20,000
$70,000
Calculate the expected value and standard deviation of Rick’s losses for the year.
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.
Calculate the expected value and standard deviation of the pooled mean losses
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
500
0
1
270
270
2
50
100
Use the information in the table to find the average frequency of losses per worker.
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 Amount of Loss
Number of Losses
Total $ Amt. of Losses
$1-2,000
$1,000
300
$300,000
$2,000-10,000
$6,000
15
$90,000
Greater than $12,000
NA
0
0
Use the information in the table to find the average severity per claim
Use the information in the table to estimate a probability distribution for the loss severity per claim.
Using your answers from question 3, part (a) and question 2, part( b), use convolution to find the average loss.
Probability
0.50
0.40
0.10
Loss
$0
$20,000
$70,000
Explanation / Answer
Rick’s Toy Store:
Expected Loss = 0.50 x 0 + 0.40 x 20,000 + 0.10 x 70,000 = $ 15,000
Variance of the loss = 0.50 x (0-15,000)2 + 0.40 x (20,000-15,000)2 + 0.10 x (70,000-15,000)2 = $ 425 x 106
Standard deviation of the loss = sqrt(Variance) = $ 20,615.53
For the pooled loss, the mean loss is the average of the losses of both Rick's store and Mark's store. The probability distribution of the mean loss of the pooled account is as per the below table:
Expected value of the mean loss = 0.25 x 0 + 0.2 x 10,000 + 0.05 x 35,000 + 0.2 x 10,000 + 0.16 x 20,000 + 0.04 x 45,000 + 0.05 x 35,000 + 0.04 x 45,000 + 0.01 x 70,000 = 15,000
Variance = 212.5 x 106
Standard deviation = $ 14,577.38
Rick's store Mark's store Mean Loss Probability 0 0 0 0.25 0 20000 10000 0.20 0 70000 35000 0.05 20000 0 10000 0.20 20000 20000 20000 0.16 20000 70000 45000 0.04 70000 0 35000 0.05 70000 20000 45000 0.04 70000 70000 70000 0.01Related Questions
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