Optional Stopping Theorem

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Page 3 of 4

Covers stochastic models for communications, focusing on random variables, Markov chains, Poisson processes, and probability calculations.

Martingale Convergence Theorem: Version 1

Introduces the martingale convergence theorem and demonstrates its application with examples.

Martingale Convergence Theorem: Proof and Recap

Covers the proof and recap of the martingale convergence theorem, focusing on the conditions for the existence of a random variable.

Sub- and Supermartingales: Theory and Applications

Explores sub- and supermartingales, stopping times, and their applications in stochastic processes.

Central Limit Theorem

Covers the Central Limit Theorem and its application to random variables, proving convergence to a normal distribution.

Stochastic Models for Communications

Explores mean, variance, probability functions, inequalities, and various types of random variables, including Binomial, Geometric, Poisson, and Gaussian distributions.

Advanced Probability: Summary

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

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.

Introduction and Probability Spaces

Covers the basics of probability theory, including probability spaces and random variables.

Continuous Random Variables

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