You are given the following table: Range of Loss Amount Midpoint Dollar Amount o
ID: 3204156 • Letter: Y
Question
You are given the following table:
Range of Loss Amount
Midpoint Dollar Amount of Loss
Number of Losses
Total $ Amt. of Losses
$1-2000
$1,000
200
$200,000
$2000-10,000
$6,000
30
$180,000
Greater than $12,000
NA
0
0
1. Use the information in the table to find the average severity per claim
2. Use the information in the table to estimate a probability distribution for the loss severity per claim.
3. Using your answers from question 3, part (a) and question 2, part ( b), use convolution to find the average loss.
Range of Loss Amount
Midpoint Dollar Amount of Loss
Number of Losses
Total $ Amt. of Losses
$1-2000
$1,000
200
$200,000
$2000-10,000
$6,000
30
$180,000
Greater than $12,000
NA
0
0
Explanation / Answer
Solution:
1.Average severity per claim
=Total amount of loss/Number of losses
=380,000/500
=$760
2.Probability distribution
Range of Loss amount
Total amount of loss
Probability
$1-2000
$200,000
0.53
$2000-10000
$180,000
0.47
Greater than $12,000
0
0
3.Convolutions
Average severity per claim=$760
Probability distribution is: 0. 0.8, 0.2
Let X be the loss with K as the integer
Let the probability distribution be m1 (K)
Let average loss be M1A
M1A=M1K*X
M1A= (0*760) + (0.8*760) + (0.2*760)
Range of Loss amount
Total amount of loss
Probability
$1-2000
$200,000
0.53
$2000-10000
$180,000
0.47
Greater than $12,000
0
0
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