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Explain how probability distributions can be used to calculate the expected value, variance, and standard deviation of a loss exposure.

RISK ASSESSMENT AND POLLING

After studying this chapter, you should be able to

■ Explain how probability distributions can be used to calculate the expected value, variance, and standard deviation of a loss exposure.

■ Explain how risk managers and insurers can use prior loss data to estimate probability distributions for the frequency and severity of losses.

■ Calculate the average loss, given probability distributions for the frequency of losses and the severity of losses.

■ Use the process of convolution to calculate the average loss.

■ Demonstrate how the process of risk pooling can be used to reduce risk.

■ Describe the characteristics of the normal distribution that are useful in risk pooling.

■ Use confidence intervals to demonstrate how insurers and risk managers can use risk pooling to decrease their cost of risk management.