Lectures related to Gaussian Correlation Conjecture

Maximum Likelihood Theory & Applications

Covers maximum likelihood theory, applications, and hypothesis testing principles in econometrics.

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

Advanced Probabilities: Random Variables & Expected Values

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

Random Vectors and Stochastic Models for Communications

Covers random vectors, joint probability, and conditional probability in communication stochastic models.

Elements of Statistics: Probability and Random Variables

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

Probability and Statistics

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

Probability Models: Fundamentals

Introduces the basics of probability models, covering random variables, distributions, and statistical estimation.

Multivariate Statistics: Normal Distribution

Introduces multivariate statistics, covering normal distribution properties and characteristic functions.

Statistical Inference: Random Variables

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

Probability Theory: Random Variables and Covariance

Covers random variables, covariance, and joint probability distributions.

Stochastic Models for Communications

Covers random vectors, joint probability density, independent random variables, functions of two random variables, and Gaussian random variables.

Quantifying Statistical Dependence

Delves into quantifying statistical dependence through covariance, correlation, and mutual information.

Multivariate Statistics: Normal Distribution

Covers the multivariate normal distribution, properties, and sampling methods.

Probability Theory: Midterm Solutions

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

Linear Regression: Theory and Applications

Covers the theory and practical applications of linear regression.

Unsupervised Learning: PCA & K-means

Covers unsupervised learning with PCA and K-means for dimensionality reduction and data clustering.

Continuous Random Variables

Covers continuous random variables, probability density functions, and distributions, with practical examples.

Mutual Information in Biological Data

Explores mutual information in biological data, emphasizing its role in quantifying statistical dependence and analyzing protein sequences.

Conditional Density and Expectation

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

Multivariate Statistics: Wishart and Hotelling T²

Explores the Wishart distribution, properties of Wishart matrices, and the Hotelling T² distribution, including the two-sample Hotelling T² statistic.