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Abstract Bayes' Formula and Conditional Expectation

Table of contents: 08:28 - A gentle introduction of Bayes’ formula 10:17 - Interpreting the Abstract Bayes’ in terms of Conditioning on Events 13:45 - An intuitive introduction of Abstract conditional expectation 16:56 - Interpreting the Conditional Expectation in terms of Conditioning on Events 20:48 - Interpreting the Cond Expectation in terms of Conditioning on Random Variable 24:14 - Formal definition of Conditional Expectation 28:23 - Definition of abstract Conditional Probability 30:50 - Formal proof of Bayes’ Formula A correction: At 27:43 when it says \mu is absolutely continuous with respect to P, the reason should be: P[G]=0 means \mu[0]=0, and also at 26:11 please ignore the statement saying weaker/stronger!