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Suppose that Y is the number of insurance claims made by an indi- vidual policyholder in one year. We assume that Y|X = x ~

Suppose that Y is the number of insurance claims made by an indi- vidual policyholder in one year. We assume that Y|X = x ~ Pois(2) where X ~ Gamma(a,0). (a) Work out the probability that the policyholder makes exactly y claims in a year. (b) What is the expected number of claims in a year?

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