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.