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Let X1 and X2 be two Poisson random variables. Suppose is distributed as Poisson(A1), and X2 is distributed as Poisson (2), where A1, A2

Let X1 and X2 be two Poisson random variables. Suppose is distributed as Poisson(A1), and X2 is distributed as Poisson (2), where A1, A2 > 0. Suppose X1 and X2 are independent. Let Y = X1+X2. What is the distribution of Y? Hint: The moment generating function of Poisson(A) is exp (\(et - 1)).

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