The poisson mean lambda of a randomly chosen person has a, Applied Statistics

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The poisson mean lambda of a randomly chosen person has a

An insurance company supposes that the number of accidents that each of its policyholders will have this year is Poisson distributed, with a mean depending on the policyholder: the Poisson mean Λ of a randomly chosen person has a Gamma distribution with the Γ(2, 1)-density function fΛ(λ) = λe^-λ (λ > 0). Find the expected value of Λ for a policyholder having x accidents this year (x = 0, 1, 2, . .).

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