1. SGWhas experienced the following workers compensation losses at two of their cleaning plants over 10-year period shown below. (20)

year 1 2 3 4 5 6 7 8 9 10

plant #1 losses 800 400 200 0 400 600 200 600 0 800

plant #2 losses 400 400 600 200 0 200 0 800 800 600

SGW is considering whether to purchase insurance or to self-insurance these losses.

1) Based on the experience of plant #1 losses only, estimate the expected loss and the standard deviation of the loss.

2) SGW is considering buying insurance from XYZ company, an insurer that is able to pool the loss experience of plant #1 with other firms that are independent of each other. Estimate the expected lossand the standard deviationof the mean loss distribution when XYZ insures 100, 900, and 2500 independent and homogeneous plants. For now, disregard the loss experience of SGW's plant #2.

3)If XYZ could pool an unlimited number of independent and homogeneous exposure units, what premium would XYZ charge to cover their underlying losses.

4) Are SGW's plants independent of each other? Explain why or why not with the correlation coefficientof the losses between the two plants.

5) Suppose that SGW had 100 plants with loss records that are homogeneous to those shown in question (1), and that the correlation of the losses among the 100 plants equals 0.1. Calculate the standard deviationof the mean loss per policy for the pool of 100 plants. Compare this value to the standard deviation for the pool of 100 independent and homogeneous plants found in question (2).

6) In question (5), as the number of plants self-insured by SGW grows to infinity, what is the residual uncertainty for SGW?