Probability Theory 21 | Conditional Expectation (given events)

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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.
#ProbabilityTheory
#Analysis
#Calculus
#Mathematics
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[@chasekosborne2]

I just want to say thank you for your videos on these selected topics here, they are great for refreshing my knowledge thoroughly in these subjects. Your work is very much appreciated.

[@brightsideofmaths]

Thank you so much :) And thanks for the support!

[@_NickTech]

Thank you a lot for keeping it straightforward, simple, and formal! 💝

[@brightsideofmaths]

Thanks :) And thanks for your support!

[@aceofshade]

Yay! more probability theory!

[@ChainWasp]

amazing! I have a question. What about Expectation conditioned to a σ-algebra? E(X| F) ?

[@brightsideofmaths]

Yes, we discuss this (and similar notions) in the next video :)

[@aceofshade]

I have a question regarding E(XY|X) = E(Y|X)*X. I can understand this if X=3 or of x is a single value. But what if we can the expectation for a range of values of x. For example X can be {1,2,3} number of heads on 3 coin tosses. But we know the first coin is T and that leaves X to be {1,2}. We should still be able to have a conditional expectation on the information but I dont know how to solve that using X*E(Y|X).