Lectures related to Stochastic Processes: Symmetric Random Walk

Probability and Statistics: Fundamental Theorems

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

Law of Large Numbers: Strong Convergence

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

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.

Estimating Deviations

Covers Markov's and Chebyshev's Inequalities for random variables and probability distributions.

Probability and Statistics

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

Stochastic Models for Communications

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

Advanced Probabilities: Random Variables & Expected Values

Explores advanced probabilities, random variables, and expected values, with practical examples and quizzes to reinforce learning.

Probability Distributions in Environmental Studies

Explores probability distributions for random variables in air pollution and climate change studies, covering descriptive and inferential statistics.

Probability and Statistics: Fundamentals

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

Elements of Statistics: Estimation & Distributions

Covers fundamental statistics concepts, including estimation theory, distributions, and the law of large numbers, with practical examples.

Conditional Expectation: Grouping Lemma

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

Estimating R: Moments of a Distribution

Explains the importance of moments in measuring distribution properties, such as expectation and variance.

Random Variables and Expected Value

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

Central Limit Theorem: Properties and Applications

Explores the Central Limit Theorem, covariance, correlation, joint random variables, quantiles, and the law of large numbers.

Probability Theory: Midterm Solutions

Covers the solutions to the midterm exam of a Probability Theory course, including calculations of probabilities and expectations.

Elements of Statistics: Probability and Random Variables

Introduces key concepts in probability and random variables, covering statistics, distributions, and covariance.

Common Distributions: Moments and MGFs

Covers common distributions, moment generating functions, and covariance matrices in statistics for data science.

Independence and Covariance

Explores independence and covariance between random variables, discussing their implications and calculation methods.

Probability Distributions: Basics and Properties

Covers the basics of probability distributions, including mean, variance, and properties of random variables.

Variance and Covariance: Properties and Examples

Explores variance, covariance, and practical applications in statistics and probability.