Generating Functions, Taylor Series, Taylor Theorem, Central Limit Theorem, Deep Dives.
N(0, 1): The CDF of Z_bar_n becomes identical to the CDF of N(0,1) as n → ∞ (Image by Author) To prove this we realized that it was sufficient to prove that the MGF of Z_bar_n will converge to the MGF of N(0, 1) as n tends to infinity. (Image by Author) And that led us on a quest to find the MGF of