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# Find the moment generating function for a Poisson random variable.

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3.86
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Show that the moment-generating function for the Poisson random variable with mean &#955; is given by M(t)= e^ ( &#955;( e^(t) -1) )

Ans: I started (seen below) but not sure if i'm doing it right.
P(t)= E( t^(y) ) = &#8721; t^(y) * ( (&#955;^(y)) / (y!) )* e^(-&#955;)
= &#8721; ( (t&#955;)^(y) ) / ( y! * e^(&#955;) )

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

##### Solution Summary

The mgf for a Poisson random variable is investigated.

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