Gaussian Correlation Conjecture

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

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

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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.