The moment generating function (MGF) of a random variable XX is a function MX(s)MX(s) defined as MX(s)=E[esX].MX(s)=E[esX]. We say that MGF of XX exists, if there exists a positive constant aa such that MX(s)MX(s) is finite for all s∈[−a,a]s∈[−a,a]. ...