Generating Functions, Taylor Series, Taylor Theorem, Central Limit Theorem, Deep Dives.
MGF. The zeroth derivative of the MGF of X evaluated at t = 0 is obtained by simply substituting t = 0 in Eq. (3). M⁰_X(t=0) evaluates to 1. The first, second, third, etc. derivatives of the MGF of X evaluated at t = 0 are denoted by M¹_X(t=0), M²_X(t=0), M³_X(t=0), etc. They evaluate respectively