Question: 17.1 Consider X1,X2, . . . , Xn independent Poisson random variables with parameters 1, 2 , . . . , n. Use the properties

17.1 Consider X1,X2, . . . , Xn independent Poisson random variables with parameters μ1, μ2 , . . . , μn. Use the properties of moment-generating functions to show that the random variable

n i=1 Xi is a Poisson random variable with mean

n i=1

μi and variance

n i=1

μi .

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