Optional Stopping Theorem

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Page 2 of 4

Covers random vectors, joint probability density, independent random variables, functions of two random variables, and Gaussian random variables.

Law of Large Numbers: Strong Convergence

Explores the strong convergence of random variables and the normal distribution approximation in probability and statistics.

Probability and Statistics: Fundamental Theorems

Explores fundamental theorems in probability and statistics, joint probability laws, and marginal distributions.

Causal Systems & Transforms: Delay Operator Interpretation

Covers z Variable as a Delay Operator, realizable systems, probability theory, stochastic processes, and Hilbert Spaces.

Modes of Convergence of Random Variables

Covers the modes of convergence of random variables and the Central Limit Theorem, discussing implications and approximations.

Quantifying Statistical Dependence: Covariance and Correlation

Explores covariance, correlation, and mutual information in quantifying statistical dependence between random variables.

Stochastic Processes: Review and Properties

Covers the review of random variables, probability density functions, variance, and Gaussian processes.

Probability and Statistics: Fundamentals

Covers the fundamental concepts of probability and statistics, including interesting results, standard model, image processing, probability spaces, and statistical testing.

Martingale Convergence Theorem

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

Stochastic Calculus: Lecture 1

Covers the essentials of probability, algebras, and conditional probability, including the Borel o-algebra and Poisson processes.