Let X and Y be two independent random variables with X ~ Poisson(ux) and Y ~ Poisson(uy). (a) Show that the moment generating function (mgf) of X is Mx(t) = exp{µx(e' – 1)} = etx(et –1). (b) Show that the mgf of X +Y is Mx+y(t) = exp{(µx+µy)(e' – 1)} %3D (c) Based on the result in (b), what distribution does X + Y follow?

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