Lectures related to Linearity of Expectation: First Moment Method

Probability and Statistics: Fundamentals

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

Quantum States and Operators

Covers the description of states in quantum mechanics and their relation to probability, expectation values, and the Schrödinger equation.

Law of Large Numbers: Strong Convergence

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

Dense Graphs: From Theory to Applications

Explores the transition from sparse to dense graphs and their real-world applications.

Probability and Statistics: Independence and Conditional Probability

Explores independence and conditional probability in probability and statistics, with examples illustrating the concepts and practical applications.

Fixed Points in Graph Theory

Focuses on fixed points in graph theory and their implications in algorithms and analysis.

Conditional Density and Expectation

Explores conditional density, expectations, and independence of random variables with practical examples.

Stein Algorithm: Polynomial Identity Testing

Explores the Stein algorithm for polynomial identity testing and the minimization of a cut problem.

Elements of Statistics: Probability and Random Variables

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

Probability and Statistics: Fundamental Theorems

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

Probability and Statistics

Explores joint random variables, conditional density, and independence in probability and statistics.

Conditional Probability: Prediction Decomposition

Explores conditional probability, Bayes' theorem, and prediction decomposition for informed decision-making.

Continuous Random Variables

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

Graphical Models: Representing Probabilistic Distributions

Covers graphical models for probabilistic distributions using graphs, nodes, and edges.

Elements of Statistics

Introduces key statistical concepts like probability, random variables, and correlation, with examples and explanations.

Random Variables and Covariance

Covers random variables, variances, and covariance, as well as the probability in random graphs.

Random Variables: Expectation and Independence

Explores random variables, expectation, and independence in probability theory.

Probability Theory: Midterm Solutions

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

Independence and Products

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

Central Limit Theorem: Properties and Applications

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