Aggregate claims from a risk have a compound negative binomial distribution, with negative binomial parameters k=100 and p=0.5. The individual claim amount distribution is Pareto with parameters α=3 and λ=400. The insurer of this risk effects excess of loss reinsurance with retention level 400 with Reinsurance Company A. (a) Show that the distribution of the number of (non-zero) claims for Reinsurance Company A is negative binomial with parameters 100 and 8 / 9. (b) Show that the distribution of

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