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Sample mean and covariance
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All of Probability: Basic Bounds, LLN & CLT
Introduces basic bounds, LLN, and CLT in probability theory, emphasizing convergence to normal distribution.
Inverse Power Method: Introduction to ODEs
Explores the inverse power method for ODEs and the significance of Lipschitz continuity.
Multivariate Statistics: Normal Distribution
Introduces multivariate statistics, covering normal distribution properties and characteristic functions.
Optimality and Asymptotics
Explores the optimality of the Least Squares Estimator and its large sample distribution.
Normal Distribution: Characteristics and Z-scores
Explores normal distribution characteristics, Z-scores, probability in inferential statistics, sample effects, and binomial distribution approximation.
Estimating R: Moments and Covariance
Covers the estimation of R, focusing on moments and covariance.
Central Limit Theorem: Illustration and Applications
Explores the Central Limit Theorem and its statistical implications in random variables.
Causal Systems & Transforms: Delay Operator Interpretation
Covers z Variable as a Delay Operator, realizable systems, probability theory, stochastic processes, and Hilbert Spaces.
Principal Component Analysis: Understanding Data Structure
Explores Principal Component Analysis, dimensionality reduction, data quality assessment, and error rate control.
Multivariate Normal Distribution
Covers the multivariate normal distribution, moment-generating function, and combinatorics.