Question: Problem 5.29 Suppose X1, X2 are independent Poisson random variables with parameters 1, 2. Show that X1 + X2 is a Poisson random variable with

Problem 5.29 Suppose X1, X2 are independent Poisson random variables with parameters λ1, λ2. Show that X1 + X2 is a Poisson random variable with parameter λ = λ1 +λ2. Hint: Compute the moment generating function MX1+X2 (s) using Theorem 5.2 and Equation 3.69.

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