Question: Consider X 1 , X 2 , ., X n independent Poisson random variables with parameters 1 , 2 ,

Consider X₁, X₂, •., X n independent Poisson random variables with parameters μ₁, μ₂, • • • , μ n. Use the properties of moment-generating functions to show n that the random variable Σⁿ_{i = 1}Xi is a Poisson random variable with mean Σⁿ_{i = 1}μ i and variance Σⁿ_{i = 1}μi.

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