Cumulative distribution function

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Statistical Inference: Random Variables

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

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Explores Bayes' Theorem for defective parts detection, discrete random variables, and distribution functions, with practical examples and exercises.

Advanced Probabilities: Random Variables & Expected Values

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

Random Vectors & Distribution Functions

Covers random vectors, joint distribution, conditional density functions, independence, covariance, correlation, and conditional expectation.

Continuous Random Variables: Basics

Explores continuous random variables, cdf, pdf, convolution, and sum of dice.

Causal Systems & Transforms: Delay Operator Interpretation

Covers z Variable as a Delay Operator, realizable systems, probability theory, stochastic processes, and Hilbert Spaces.

Collisionless Boltzmann Equation

Explores the Collisionless Boltzmann Equation, Jeans theorems, and equilibria of collisionless systems, focusing on connections between barotropic fluids and ergodic stellar systems.

Fluid Quantities and Two-Fluid Model

Covers fluid quantities, moments of kinetic equation, two-fluid model, and plasma turbulence simulation.

Collisionless Boltzmann Equation

Explores the Collisionless Boltzmann equation, distribution functions, Jeans theorems, resonances, chaotic orbits, and equilibria in stellar systems.

ECDF and Quantiles

Covers ECDF, quantiles, mean, median, and box plots for dataset analysis.