13:43 a Suppose X ~ Poisson(A,), Y ~ Poisson(A2), and X and Y are independent. Using the fact that the moment generating function of Poisson(A) is eMe'-1), derive the distribution of X + Y. Prove that...

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Extracted text: 13:43 a Suppose X ~ Poisson(A,), Y ~ Poisson(A2), and X and Y are independent. Using the fact that the moment generating function of Poisson(A) is eMe'-1), derive the distribution of X + Y. Prove that the moment generating function of Poisson(A) is indeed ee-1). (Hint: You will likely use Taylor series for exponential function in the proof.)