Probability Theory 14 | Expectation and Change-of-Variables

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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.

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.

#ProbabilityTheory
#Analysis
#Calculus
#Mathematics

I hope that this helps students, pupils and others. Have fun!

(This explanation fits to lectures for students in their first and second year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)

[davidparker]

Your content is always an incredible mixture of concise and thorough explanation. Thank you for such wonderful content!

[rahulkrishnakumar]

Loving the connection between the Probability Theory and Measure Theory videos! Thanks for the amazing content

[DanielJanzon]

Great video! Glad to see measure-theoretic probability, there is a lot less of that than entry-level probability on YouTube.

[Ryokusei]

I love to see the formal definition of this stuff and how from that, we obtain our old and good expression for expected value.

[Hold_it]

Good to see the continuation of this series :)

[maconstantin]

Another excellent video! One thing I believe might be missing from the series is a discussion about the distinction between the pushforward measure and the probability density function. It might just be me, but I found it easy to confuse the two conceptually.

[evionlast]

Is the PDF graph axis on the left tail of the PDF?

[AlexSmith-jjul]

I love to see more videos on probability theory

[hn]

Hi, thank you for the great lecture! Can you explain why dP(x) = f(x) dx at 7:40?

[adilbhatti]

Hi richtig gute Arbeit. hast du das auch auf Deutsch, Danke

[alhasibsifat]

How can I know is this a discrete case or continuous?

[maciej]

​ @The Bright Side of Mathematics how you get from P(dw) to f(x) dx hmm with wave of hand? hmm ? How you get from P(dw) to dP(dw) yeah X^-1(x) = w but you don't explain details