Generating Functions, Taylor Series, Taylor Theorem, Central Limit Theorem, Deep Dives.
do we observe? We see that E(X^k] in Eq. (2) are the coefficients a_k in the EGF. Thus Eq. (2) is the generating function for the moments of X, and so the formula for the Moment Generating Function of X is the following: The formula for the Moment Generating Function of X (Image by Author) The MGF