Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Concept

Algebra of random variables

Related lectures (30)

Conditional Expectation

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

Conditional expectation

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

Expectation: Basic Properties

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

Conditional Expectation Properties

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

Conditional Expectation: Generalized Properties

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

Advanced Probabilities: Random Variables & Expected Values

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

Independence and Products

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

Probability Review

Introduces subgaussian and subexponential random variables, conditional expectation, and Orlicz norms.

Estimating Deviations

Covers Markov's and Chebyshev's Inequalities for random variables and probability distributions.

Conditional Expectation

Covers conditional expectation, Fubini's theorem, and their applications in probability theory.

Von Neumann Extractor: Extensions

Covers the von Neumann Extractor, its extensions, extraction rules, uniformity proofs, and exchangeability of sequences.

Probabilities and Statistics: Key Theorems and Applications

Discusses key statistical concepts, including sampling dangers, inequalities, and the Central Limit Theorem, with practical examples and applications.

Martingale Convergence Theorem

Explores the proof of the martingale convergence theorem and the conditions for convergence to a random variable.

Transformations of Random Variables

Covers the pdf of the sum of continuous random variables, convolution, and transformations like Y=aX.

Statistical Modelling & Probability Basics

Covers statistical modelling basics, probability concepts, and random variables for data analysis.

Conditional Expectation: Basics

Introduces the basics of conditional expectation, covering definitions, properties, and examples in the context of random variables.

Probability Theory: Midterm Solutions

Covers the solutions to the midterm exam of a Probability Theory course, including calculations of probabilities and expectations.

Probabilities: Fundamentals and Independence

Covers the fundamentals of probabilities, including independence, conditional probabilities, and random variables.

Conditional Expectation: Grouping Lemma

Explores conditional expectation, the grouping lemma, and the law of large numbers.

Probability Theory: Conditional Expectation

Covers conditional expectation, convergence of random variables, and the strong law of large numbers.

Related lectures (30)

Conditional Expectation

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

Conditional expectation

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

Expectation: Basic Properties

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

Conditional Expectation Properties

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

Conditional Expectation: Generalized Properties

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

Advanced Probabilities: Random Variables & Expected Values

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

Independence and Products

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

Probability Review

Introduces subgaussian and subexponential random variables, conditional expectation, and Orlicz norms.

Estimating Deviations

Covers Markov's and Chebyshev's Inequalities for random variables and probability distributions.

Conditional Expectation

Covers conditional expectation, Fubini's theorem, and their applications in probability theory.

Von Neumann Extractor: Extensions

Covers the von Neumann Extractor, its extensions, extraction rules, uniformity proofs, and exchangeability of sequences.

Probabilities and Statistics: Key Theorems and Applications

Discusses key statistical concepts, including sampling dangers, inequalities, and the Central Limit Theorem, with practical examples and applications.

Martingale Convergence Theorem

Explores the proof of the martingale convergence theorem and the conditions for convergence to a random variable.

Transformations of Random Variables

Covers the pdf of the sum of continuous random variables, convolution, and transformations like Y=aX.

Statistical Modelling & Probability Basics

Covers statistical modelling basics, probability concepts, and random variables for data analysis.

Conditional Expectation: Basics

Introduces the basics of conditional expectation, covering definitions, properties, and examples in the context of random variables.

Probability Theory: Midterm Solutions

Covers the solutions to the midterm exam of a Probability Theory course, including calculations of probabilities and expectations.

Probabilities: Fundamentals and Independence

Covers the fundamentals of probabilities, including independence, conditional probabilities, and random variables.

Conditional Expectation: Grouping Lemma

Explores conditional expectation, the grouping lemma, and the law of large numbers.

Probability Theory: Conditional Expectation

Covers conditional expectation, convergence of random variables, and the strong law of large numbers.