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Find more here: https://tbsom.de/s/pt Support the channel on Steady: https://steadyhq.com/en/brightsideofm... Or support me via PayPal: https://paypal.me/brightmaths Or via Ko-fi: https://ko-fi.com/thebrightsideofmath... Or via Patreon: / bsom Or via other methods: https://thebrightsideofmathematics.co... Watch the whole video series about Probability Theory and download PDF versions and quizzes: https://tbsom.de/s/pt There is also a dark mode version of this video: • Probability Theory 14 | Expectation a... There is also a bright mode version of this video: • Probability Theory 14 | Expectation a... To find the YouTube-Playlist, click here for the bright version: • Probability Theory And click here for the dark version of the playlist: • Probability Theory [dark version] Thanks to all supporters! They are mentioned in the credits of the video :) This is my video series about Probability Theory. I hope that it will help everyone who wants to learn about it. This video is about probability theory, also known as stochastics, stochastic processes or statistics. I keep the title in this general notion because I want cover a lot of topics with the upcoming videos. #ProbabilityTheory #Analysis #Calculus #Mathematics Here we talk about the concept of expectation for random variables. In this regard, we need to talk about abstract integrals and the change of variables formula. (This explanation fits to lectures for students in their first year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on) The Bright Side of Mathematics has whole video courses about different topics and you can find them here https://tbsom.de/s/start