Generating Functions, Taylor Series, Taylor Theorem, Central Limit Theorem, Deep Dives.
of Eq. (9): (Image by Author) By construction, Z_1/√n, Z_2/√n, …, Z_n/√n are independent random variables. So we can use property (7a) of MGFs which expresses the MGF of the sum of n independent random variables: MGF of sum of n independent random variables (Image by Author) By their definition,