L07.3 Conditional Expectation & the Total Expectation Theorem

MIT RES.6-012 Introduction to Probability, Spring 2018
View the complete course: ocw.mit.edu/RE...
Instructor: John Tsitsiklis
License: Creative Commons BY-NC-SA
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[@elonmusk4267]

learning from a legend

[@LeeiFJaw]

At the end of the lecture, the professor said the harder mathematical work is needed to show that the total expectation theorem also holds for the case when the discrete r.v. ranging over an infinite set.
My intuition about this is that the hardness originates from the absolute convergence or conditional convergence of infinite series. If you fix Y=y, the size of sub-universe can also be infinite. That means sometimes you can reorder the terms to make the summation to converge or to diverge. Hence the condition E[|x|]

[@starinsky2873]

also related: en.wikipedia.org/wiki/Law_of_total_expectation

[@tahacasablanca5276]

The infinite set of values of y can be uncountable?