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Each life within a group medical expense policy has loss amounts which follow a compound Poisson process with . Given a loss, the probability that it is for Disease 1 is 1/16.
Loss amount distributions have the following parameters: Code:
Mean per loss Std. Dev. per loss  Disease 1 5 50 Other Diseases 10 20 A vaccine which will eliminate Disease 1 and costs 0.15 per person has been discovered. Define: A = the aggregate premium assuming that no one obtains the vaccine, and B = the aggregate premium assuming that everyone obtains the vaccine and the cost of the vaccine is a covered loss. Calculate A/B.  Why are we able to multiply 0.16 () by each of the probabilities for Disease 1 or Other diseases?
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Yes, that is why the problem states that it is a "compound Poisson", i.e. it can be separated into proportional Poisson's. Conversely, you can add Poisson's together. (I learned this after getting that exact problem wrong.)
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