Consider X1, X2,...,Xn independent Poisson random variables with parameters 1, 2,...,n. Use the properties of moment-generating functions to show that the random variable n i=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.