MAT330/681 LECTURE 20 (4/19/2021): MOMENT GENERATING FUNCTIONS, CONDITIONAL EXPECTATION
• Announcements: Today's lecture has a few more videos than the last ones, but they are also shorter. Please remember that NEXT LECTURE WILL BE CONDUCTED LIVE, via the same Zoom link used throughout the semester, starting at 11:00am Eastern on Wednesday.
• Video 1: Definition of moment generating function: Download file or watch below
• Video 2: Moment generating function of a Binomial random variable Download file or watch below
• Video 3: Moment generating function of an exponential random variable Download file or watch below
• Video 4: Moment generating function of normal random variables: Download file or watch below
If you want a refresher on Calculus to remember why $\int_{-\infty}^{+\infty} e^{-s^2/2} ds=\sqrt{2\pi}$, watch this and then use $x=s/\sqrt2$.
• Video 5: The magic of moment generating functions: Download file or watch below
• Video 6: Conditional expectation for discrete and continuous random variables: Download file or watch below
• Video 7: Conditional expectation as a random variable, and its expectation: Download file or watch below
• Video 8: Trapped miner problem (exercise about conditional expectation): Download file or watch below