An insurance company supposes that each person has an accident parameter and that the yearly number of accidents of someone whose accident parameter is \lambda is poisson distributed with mean \lambda. 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 \alpha. if a newly insured person has n accidents in her first year, find the conditional density of her accident parameter. also, determine the expected number of accidents that she will have in the following year.
hint: you don’t actually have to evaluate any integrals to do this problem; recognize the form of the conditional density as one of the distributions we’ve looked at, then plug in the proper constants.