Algebra of random variables

Related lectures (31)

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Explores the properties and definition of conditional expectation in random variables.

Explores the properties of conditional expectation and its extension to positive variables.

Discusses integrability, square-integrability, boundedness, centering, and linearity of random variables.

Explores conditional expectation properties, including measurability, linearity, and independence of random variables.

Discusses a proposition on conditional expectation for two random variables, emphasizing independence and measurability.

Covers the basics of Martingale theory and its applications in random variables.

Explores advanced probabilities, random variables, and expected values, with practical examples and quizzes to reinforce learning.

Covers the properties of expectation and examples of calculating expectations for random variables.

Explores the transformation of random variables, joint moments, covariance, and variance.

Covers independence between random variables and product measures in probability theory.