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In: Statistics and Probability

Consider a portfolio of insurance policies, on which the number of claims has a binomial distribution...

Consider a portfolio of insurance policies, on which the number of claims has a binomial distribution with parameters n = 1,000 and p = 0.01.

The claim size distribution is assumed to be exponential with mean $100.

Claim amounts are assumed to be independent random variables, and the claim amounts are independent of the number of claims.

The insurer takes out an individual excess of loss reinsurance contract with a retention level of $200.

Calculate the mean of the aggregate annual claims paid by the insurer, net of reinsurance.

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