In this link:
On the other hand, in this link:
So, how are these two equations same?
The first link gives the formula for moment generating function. $M_X(t)=E[e^{tX}]$
The second link gives the formula for probability generating function for discrete random variable. $G_X(s)=E[s^X]$
They are not the same.
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The first link gives the formula for moment generating function. $M_X(t)=E[e^{tX}]$
The second link gives the formula for probability generating function for discrete random variable. $G_X(s)=E[s^X]$
They are not the same.