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An insurance company supposes that the number of accidents that each of its policyholders will have...

An insurance company supposes that the number of accidents that each of its policyholders will have in a year is Poisson distributed. The rate parameter of the Poisson is also a random variable which has an exponential distribution with parameter 2.3. What is the probability that a randomly chosen policyholder has exactly 3 accidents next year?(Hint: You can use the following result for thenth moment of exponential random variable: If Z ∼Exp(μ) , then E (Zn )= n!/μn)

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