Expected Values for Continuous Variables!!!

If you ever muck around in statistics, it's not long before you see E(x) = something. These are expected values. Expected Values for Continuous Variables are a little trickier than their discrete counterparts because we have to do some calculus. However, I'll walk you through it, one step at a time, so don't sweat it! BAM! NOTE: This one is, believe it or not, pretty near to my heart. When I was taking Statistical Theory in graduate school (from Rodger Berger of Casella and Berger, who wrote the standard textbook on statistical theory, "Statistical Inference") I remember having a lot of trouble with expected values. They intimidated me for two reasons 1) deriving them seemed like total luck and 2) I never understood, exactly, what the formula for continuous variables meant in a deep way. I could look at the equation and name the parts, but that was all I could do. Anyway, fast forward a few years and here I am, going back to these basics, this time determined to get that "deep understanding" I missed before, and, at least for myself, I succeeded. And I hope that means other people will also be able to get a deep understanding of expected values as well. NOTE: This StatQuest assumes that you are already familiar with the concept of an Expected Value. If not, check out the 'Quest: https://youtu.be/KLs_7b7SKi4 Also, if you want to learn more about Integration By Parts, here's a great resource: https://www.mathsisfun.com/calculus/integration-by-parts.html For a complete index of all the StatQuest videos, check out: https://statquest.org/video-index/ If you'd like to support StatQuest, please consider... Patreon: https://www.patreon.com/statquest ...or... YouTube Membership: https://www.youtube.com/channel/UCtYLUTtgS3k1Fg4y5tAhLbw/join ...buying one of my books, a study guide, a t-shirt or hoodie, or a song from the StatQuest store... https://statquest.org/statquest-store/ ...or just donating to StatQuest! https://www.paypal.me/statquest Lastly, if you want to keep up with me as I research and create new StatQuests, follow me on twitter: https://twitter.com/joshuastarmer 0:00 Awesome song and introduction 1:30 Discrete and continuous variables defined 3:42 The exponential distribution 7:03 Approximating expected values with discrete intervals 10:25 Deriving the expected value formula for continuous variables 12:18 Calculating the expected value of an exponential distribution 18:17 Summary #StatQuest