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    Find the moment generating function for a Poisson random variable.

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    Show that the moment-generating function for the Poisson random variable with mean λ is given by M(t)= e^ ( λ( e^(t) -1) )

    Ans: I started (seen below) but not sure if i'm doing it right.
    P(t)= E( t^(y) ) = ∑ t^(y) * ( (λ^(y)) / (y!) )* e^(-λ)
    = ∑ ( (tλ)^(y) ) / ( y! * e^(λ) )

    = I'm not sure where to go from there, or if I even
    started it off correctly.

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    Solution Summary

    The mgf for a Poisson random variable is investigated.