Martingale Transforms

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

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Discusses entropy, data compression, and Huffman coding techniques, emphasizing their applications in optimizing codeword lengths and understanding conditional entropy.

Uniform Integrability and Convergence

Explores uniform integrability, convergence theorems, and the importance of bounded sequences in understanding the convergence of random variables.

Advanced Probability: Summary

Covers random variables, sample spaces, probability distributions, functions, expected value, variance, and estimations.

Stochastic Models for Communications

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

Continuous Random Variables

Explores continuous random variables, density functions, joint variables, independence, and conditional densities.

Stable Laws: Lindeberg-Rafeller Theorem

Covers the Lindeberg-Rafeller theorem, discussing characteristic functions, moment problems, and the Central Limit Theorem.

Random Variables and Expected Value

Introduces random variables, probability distributions, and expected values through practical examples.

Central Limit Theorem: Proof and Applications

Explores the proof and applications of the Central Limit Theorem, emphasizing independence and random variable distributions.

Brownian Motion: Theory and Applications

Covers the theory of Brownian motion, diffusion, and random walks, with a focus on Einstein's theory for one-dimensional motion.