Generating Functions, Taylor Series, Taylor Theorem, Central Limit Theorem, Deep Dives.
to the first, second, third etc. raw moments of X as shown below: The derivatives of M(X) evaluate to the moments of X (Image by Author) This gives us our first interesting and useful property of the MGF. The k-th derivative of the MGF evaluated at t = 0 is the k-th raw moment of X. The k-th