Law of total variance

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

Explores conditional expectation properties, variance, and examples in practical applications.

Explores long memory in time series and ARCH models for financial volatility.

Covers the basics of discrete probability, including notations, axioms, pmf, examples, expectation, variance, and indicator variables.

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

Explores independence and conditional probability in probability and statistics, with examples illustrating the concepts and practical applications.

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

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

Explores the equidistribution of CM points and the implications of ergodicity in measure-preserving systems.

Covers common distributions, moment generating functions, and covariance matrices in statistics for data science.