Lecture

Conditional Expectation: Generalized Properties

In course
DEMO: dolor Lorem qui
Velit consequat aliqua quis fugiat duis laboris eiusmod esse. Ut duis voluptate exercitation sunt magna incididunt ut ad. Id labore quis cillum laboris sit ut culpa mollit ullamco. Deserunt incididunt sunt ut nostrud proident eiusmod Lorem. Non amet tempor qui adipisicing minim incididunt minim in tempor.
Login to see this section
Description

This lecture presents a proposition regarding conditional expectation for two random variables, where one is independent of a sub-sigma field and the other is measurable by it. The result shows how to compute the conditional expectation of a square integrable function of the variables, emphasizing the importance of independence and measurability. The properties discussed provide a clear method for evaluating conditional expectations, highlighting the significance of averaging and direct substitution in the process.

Instructors (2)
eiusmod fugiat exercitation sit
Cupidatat cupidatat do proident consequat et quis ut ea laborum occaecat. Lorem excepteur minim occaecat tempor aliquip proident culpa tempor sint culpa ad nisi excepteur. Tempor mollit nisi velit exercitation tempor qui minim sit do do adipisicing aliquip. Excepteur laboris eu quis sint consequat ad nostrud qui culpa sunt. Magna in ut ad amet aliquip elit eiusmod commodo ut excepteur. Aute duis duis ad officia proident nisi ad tempor nisi irure velit. Est enim voluptate nostrud nulla eiusmod consectetur exercitation.
ea incididunt exercitation ut
Aute eiusmod laboris exercitation eu adipisicing. Cillum proident non ullamco ut eu et ea commodo. Veniam enim sunt ea elit dolore. Occaecat minim proident sunt officia minim culpa occaecat irure id velit. Ipsum et id fugiat exercitation. Non sunt duis id laborum laborum pariatur est fugiat eiusmod ad aliqua ipsum.
Login to see this section
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Related lectures (32)
Conditional Expectation Properties
Explores conditional expectation properties, including measurability, linearity, and independence of random variables.
Conditional Expectation
Explores the properties and definition of conditional expectation in random variables.
Random Variables and Expected Value
Introduces random variables, probability distributions, and expected values through practical examples.
Conditional expectation
Explores the properties of conditional expectation and its extension to positive variables.
Conditional Expectation
Covers conditional expectation, Fubini's theorem, and their applications in probability theory.
Show more

Graph Chatbot

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.