Gaussian Vectors: Properties and Distributions

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Explores stochastic models for communications, covering mean, variance, characteristic functions, inequalities, various discrete and continuous random variables, and properties of different distributions.

Extreme Value Models: Technical Derivation

Explores the technical derivation and properties of Multivariate Extreme Value models.

Linear Models: Least Squares

Explores linear models, least squares, Gaussian vectors, and model selection methods.

Generating Functions: Properties and Applications

Explores generating functions, Laplace transform, and their role in probability distributions.

Elementary Distributions Factsheet

Covers elementary distributions like Bernoulli, Binomial, Geometric, Negative Binomial, Poisson, and Multinomial.

Probability Distributions: Moments and Transformations

Explores the bijection between distribution functions and moment generating functions.

Dependence in Random Vectors

Explores dependence in random vectors, covering joint density, conditional independence, covariance, and moment generating functions.

Spherical Symmetry in Statistical Mechanics

Explores spherical symmetry in statistical mechanics and its role in phase transitions.

Elements of Statistics: Exercises

Covers exercises on Bayes' Theorem, moment generating functions, photon counts, disease probabilities, and distribution properties.

All of probability: generating functionals and cumulants

Covers moment generating function, cumulants, Laplace transform, and Fourier transform in probability theory.