Generating Functions, Taylor Series, Taylor Theorem, Central Limit Theorem, Deep Dives.
following (you may want to compute this as an exercise): MGF of a standard normal random variable (Image by Author) Speaking of the standard normal random variable, as shown in Eq. (4), the first, second, third, and fourth derivatives of the MGF of N(0, 1) when evaluated at t = 0 will give you the