Lectures related to Inequalities: Cauchy-Schwarz, Jensen, Chebyshev

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.

Conditional expectation

Explores the properties of conditional expectation and its extension to positive variables.

Independence and Products

Covers independence between random variables and product measures in probability theory.

Sub-sigma-fields and Random Variables

Explores sub-sigma fields, random variables, and Borel measurable functions in probability theory.

Probability Theory: Basics

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

Conditional Expectation: Grouping Lemma

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

Probability and Statistics

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

Information Theory: Channel Capacity and Convex Functions

Explores channel capacity and convex functions in information theory, emphasizing the importance of convexity.

Law of Large Numbers: Statistics

Explains the Law of Large Numbers and its application to random variables.

Probability Distributions in Environmental Studies

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

Concentration Inequalities: Hoeffding's Inequality

Covers Hoeffding's inequality and concentration inequalities with a focus on sequences of random variables.

Central Limit Theorem

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

Probability and Statistics: Fundamental Theorems

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

Modes of Convergence of Random Variables

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

Large Deviations Principle

Explores the Large Deviations Principle, focusing on exponential tail decay and Laplace transform analysis.

Central Limit Theorem: Proof via Lindeberg's Principle

Explores the proof of the Central Limit Theorem through Lindeberg's principle and the convergence of random variables.

Advanced Probability: Quiz

Covers a quiz on advanced probability concepts and calculations.

Probability and Statistics: Fundamentals

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

Law of Large Numbers: Strong Convergence

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

Quantifying Statistical Dependence: Covariance and Correlation

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