Policy holders of an insurance company have accidents at times of a Poisson processwith rate . The

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Policy holders of an insurance company have accidents at times of a Poisson processwith rate . The distribution of the time R until a claim is reported is random with P.R  r/ D G.r/ and ER D .

(a) Find the distribution of the number of unreported claims.

(b) Suppose each claim has mean  and variance 2. Find the mean and variance of S the total size of the unreported claims.

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