Levy Flights & Brownian Motion

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Explores air pollution analysis using wind data, probability distributions, and trajectory models for air quality assessment.

Linear Regression: Theory and Applications

Covers the theory and practical applications of linear regression.

Probability and Statistics

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

Introduction to Continuous Random Variables: Probability Distributions

Introduces continuous random variables and their probability distributions, emphasizing their applications in statistics and data science.

Random Variables and Expected Value

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

Martingales and Brownian Motion Construction

Explores the construction of Brownian motion with continuous trajectories and the dimension of its zero set.

Probability and Statistics

Covers Simpson's paradox, probability distributions, and real-life examples in probability and statistics.

Common Distributions: Moment Generating Functions

Explores common probability distributions, special distributions, and entropy concepts.

Statistical Thermodynamics: Density of States

Explores density of states in statistical thermodynamics and the use of Heaviside functions for energy level probabilities.

Quantization of Probability Distributions

Covers quantization of probability distributions, statistical k-means clustering, mean estimation, robust clustering methods, and open research questions.