1) Ricks Toy Store faces the following probability distribution of fire losses in its store over the next year:

1. Calculate the expected value and standard deviation of Ricks losses for the year.
2. Assume that Rick pools his losses with Marks store, which has an identical loss distribution. Marks losses are independent of Ricks. 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.
3. Calculate the expected value and standard deviation of the pooled mean losses
4. 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.

Probability	0.70	0.20	0.10
Loss	$0	$30,000	$70,000

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 Amount of Loss	Number of Losses	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

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.