MAT330 LECTURE 21 (4/20/2020): EXPONENTIAL RANDOM VARIABLE AND PDF OF FUNCTIONS OF A RANDOM VARIABLE





• Announcements: I hope everyone is doing well. This is the first lecture "after Spring Break", which is being posted a few days ahead of schedule, so feel free to watch it at your convenience.


• Video about exponential random variable (definition and expected value): Download file or watch below


• Video about variance of exponential random variable: Download file or watch below


• Video about the memorylessness of exponential random variables: Download file or watch below

Note: What I said about the wait time interpretation at the end of the video is written in details in the lecture notes (wrote it after recording to keep video shorter), see below.


• Video about exponential random variable (exercise): Download file or watch below


• Video about functions of a random variable (example): Download file or watch below


• Continuation of above video about functions of a random variable (example and general theory): Download file or watch below




• Lecture Notes (static file from above videos): PDF file


• External link 1: Theory visualization of exponential distribution. I highly recommend checking this out, select "Continuous", and then "Exponential" from the dropdown menu, and move around the sliders for the parameters, to see how the probability density function changes.


• External link 2: Recap/Summary of exponential random variables (video): Watch on YouTube


• External link 3: Recap/Summary of memorylessness of exponential random variables (video): Watch on YouTube


• External link 4: Example of finding PDF of monotonic function of a random variable (video): Watch on YouTube


• External link 5 (bonus): Intuition behind PDF of monotonic function of random variable (video): Watch on YouTube


• External link 6 (bonus): Example of PDF of a non-monotonic function of a random variable (video): Watch on YouTube





Last updated: April 14, 2020, 5:30pm EDT