An insurance company supposes that each person has an accident parameter and that the yearly number of accidents of someone whose accident parameter is λ is Poisson distributed with mean λ. They also suppose that the parameter value of a newly insured person can be assumed to be the value of a gamma random variable with parameters s and α. (a) If a newly insured person has n accidents in her first year, find the conditional density of her accident parameter. (b) Also, determine the expected number of accidents that she will have in the following year.

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