Generating Functions, Taylor Series, Taylor Theorem, Central Limit Theorem, Deep Dives.
to the power t²/2. In short, we’d want to prove the following identity: (Image by Author) Let’s define a random variable Z_k as follows: (Image by Author) We’ll now express the standardized mean Z_bar_n in terms of Z_k as shown below: (Image by Author) Next, we apply the MGF operator on both sides