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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