Uploaded July 2025 | Updated September 2026, 1 week ago

---

The moment generating function is an important advanced concept in probability. Much like functions can be expanded in a Taylor series, probability densities can be expanded in terms of the moment generating function. The MGF is the Laplace transform of the PDF. This concept is very useful to prove the central limit theorem.

This video was produced at the University of Washington, and we acknowledge funding support from the Boeing Company

%%% CHAPTERS %%%
00:00 Intro
00:46 Defining Moments
03:43 Defining the Moment Generating Function
07:12 Statement of Theorem relating MGF to Moment N
10:01 Example: Poisson Distribution
12:57 Example: Normal Distribution
18:00 Example: Exponential Distribution
20:53 Outro