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.
The mgf for a Poisson random variable is investigated.