Question: Let X and Y be two real-valued random variables such that 1. Y follows a Gamma distribution with parameters a and 1, i.e., with p.d.f.

Let X and Y be two real-valued random variables such that 1. Y follows a Gamma distribution with parameters a and 1, i.e., with p.d.f. ye / r(a), y>0 where I' is the Gamma function and a >0. 2. Conditionally to Y = y, X follows a Poisson distribution with parameter Ay, with A >0.\f

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