MAT330/681 LECTURE 20 (4/11/2022): MOMENT GENERATING FUNCTIONS, CONDITIONAL EXPECTATION
• Announcements: Please remember that next lecture (on Wednesday, April 13) will be held in-person, as per the day-by-day schedule. Please note that next week is Spring Break, so there will be no lectures.
• 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