Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Stochastic Models for Communications: Markov Chains and Random Variables

Related lectures (32)

Probability and Statistics: Fundamental Theorems

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

Probability and Statistics

Delves into probability, statistics, paradoxes, and random variables, showcasing their real-world applications and properties.

Markov Chains: Stopping Times

Explores stopping times in Markov Chains, illustrating their properties and the Strong Markov Property.

Continuous Random Variables

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

Convergence of Random Variables

Explores independent and identically distributed random variables, convergence, and distribution properties.

Central Limit Theorem

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

Generalized Linear Models

Covers probability, random variables, expectation, GLMs, hypothesis testing, and Bayesian statistics with practical examples.

Optimization and Simulation

Introduces the Metropolis-Hastings algorithm for efficient simulation of random variables with given probabilities.

Linear Combinations: Moment-Generating Functions

Explores moment-generating functions, linear combinations, and normality of random variables.

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.

Continuous Random Variables: Basics

Explores continuous random variables, cdf, pdf, convolution, and sum of dice.

Exponential random variables: theory and applications

Explores exponential random variables, memorylessness, and applications in stochastic processes and Markov chains.

Modes of Convergence of Random Variables

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

Statistical Inference: Random Variables

Covers random variables, probability functions, expectations, variances, and joint distributions.

Markov Chains: Transience & Recurrence

Explores the notions of transience and recurrence in Markov chains through various examples and calculations.

Probability Review

Introduces subgaussian and subexponential random variables, conditional expectation, and Orlicz norms.

Probabilities and Statistics: Key Theorems and Applications

Discusses key statistical concepts, including sampling dangers, inequalities, and the Central Limit Theorem, with practical examples and applications.

Random Variables and Expected Value

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

Conditional Expectation: Grouping Lemma

Explores conditional expectation, the grouping lemma, and the law of large numbers.

Poisson processes

Covers the properties and construction of Poisson processes from i.i.d. Exp(X) random variables, emphasizing the importance of the process rate and jump time distributions.