Consider a car owner who has an 80% chance of no accidents in a year, a 20%
chance of being in a single accident in a year, and no chance of being in more than one accident
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in a year. For simplicity, assume that there is a 50% probability that after the accident the car
will need repairs costing 500, a 40% probability that the repairs will cost 5000, and a 10%
probability that the car will need to be replaced, which will cost 15,000. Combining the frequency
and severity distributions forms the following distribution of the random variable X, loss due to
accident: