Question: Derive the moment generating function of the Poisson random variable Y. Write Then note that the quantity being summed is a Poisson probability with parameter

Derive the moment generating function of the Poisson random variable Y. Write

m(t) = E(e") = E nd'e %3! y=0 y! (Ae') (de')e- y=0

Then note that the quantity being summed is a Poisson probability with parameter λet.]

m(t) = E(e") = E nd'e %3! y=0 y! (Ae') (de')e- y=0 y! y! y-0

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