Branching Processes: Networks, Genealogy, Avalanche

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Estimation and Confidence Intervals

Explores bias, variance, and confidence intervals in parameter estimation using examples and distributions.

Moment Generating Function and Multivariate Normal Distribution

Explores moment generating functions and multivariate normal distributions in probability and statistics.

Clustering Algorithms: K-Means vs Spectral Clustering

Compares K-Means and Spectral Clustering algorithms, highlighting their differences and practical applications in clustering student behaviors.

Stochastic Models for Communications

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

Probability and Statistics

Covers p-quantile, normal approximation, joint distributions, and exponential families in probability and statistics.

Probability and Statistics: Discrete Random Variables

Explores discrete random variables, mass functions, and distribution functions in probability and statistics.

Probability Distributions

Covers various probability distributions and their applications in real-world scenarios.

Gravitational Lensing Analysis

Covers the analysis of gravitational lensing in galaxy clusters, focusing on the mass distribution and precision achieved in the mass model of the galaxy cluster MACSJ0416.1-2403.

Introduction to Astrophysics: The Solar System

Covers astronomical units, light years, parallax, exoplanets, stars, nebulae, and galaxy clusters.

Brownian Motion: Theory and Applications

Covers the theory of Brownian motion, diffusion, and random walks, with a focus on Einstein's theory for one-dimensional motion.