# 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.

https://brainmass.com/math/graphs-and-functions/moment-generating-function-poisson-random-variable-170472

#### Solution Summary

The mgf for a Poisson random variable is investigated.

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