find pmf by using mgf

#1
hi!
I have problem to solve the question below..did i need to use Poisson distribution to solve this question or maybe not??

Find the probability mass function of Y if its moment generating function is M(t)=exp^(lamda(exp^(t)-1)+3t),for lamda>0.
 

BGM

TS Contributor
#2
Do you know to transform the Moment Generating Function to its corresponding Probability Generating function?

Hints: \( e^{\ln t} = t \)

Once you obtain the PGF then you can obtain the corresponding pmf.