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If m(t) is the moment generating function of a random variable, then so is (1/2)+(1/3)m(t)+(1/6)m(t)^2. Explain why this is true.
10. If m(t) is the moment generating function of a random variable, then so is (1/2)+(1/3)m(t)+(1/6)m(t)^2. Explain why this is true.
So i went to my prof and he said finding m(0)=1 is not correct neither is finding the variance or mean. He said that i must find the random variable this m(t) corresponds to and that is the only way. This is a 200 level stats class so the solution can not contain any crazy proof. I say this only because the tas in the stats room at my uni are just as confused about this question as me and 1 gave me a solution but it involves concepts such as dirac measure which ive never even heard of. Any help is greatly appreciated.
