Lectures related to Collisionless Boltzmann Equation

Explores continuous random variables, density functions, joint variables, independence, and conditional densities.

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

Normal Distribution: Properties and Calculations

Covers properties and calculations related to the normal distribution, including probabilities and quantiles.

Probability and Statistics: Discrete Random Variables

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

Discrete Random Variables

Covers properties and transformations of discrete random variables, focusing on PMF and expectation.

Statistics for Data Science: Basics and Modelling

Introduces statistical modelling basics, probability theory, and key concepts for data science applications.

Conditional Density and Expectation

Covers conditional density, independence of random variables, expectation, and variance calculation.

Brownian Motion: Fundamentals and Applications

Explores the fundamentals of Brownian motion, including particle positions and distribution functions.

Statistical Inference: Random Variables

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

Continuous Random Variables: Basic Ideas

Explores continuous random variables and their properties, including support and cumulative distribution functions.

Collisionless Systems Equilibrium

Explores collisionless systems equilibrium, anisotropic distribution functions, Jeans Equations, and models with finite potential.

Probability Models: Fundamentals

Introduces the basics of probability models, covering random variables, distributions, and statistical estimation.

Calculations of Expectation

Covers the calculation of expectation and variance for different types of random variables, including discrete and continuous ones.

Fundamental Limits of Gradient-Based Learning

Delves into the fundamental limits of gradient-based learning on neural networks, covering topics such as binomial theorem, exponential series, and moment-generating functions.

Distribution of Random Variables

Introduces the concept of the distribution of a random variable and explores specific cases of discrete and continuous random variables.

Families of Distributions: PDFs and CDFs

Explores PDFs and CDFs for discrete and continuous random variables, including Gaussian, uniform, and exponential distributions.

Probability and Statistics Log in to Mediaspace to watch this video

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

Martingales and Brownian Motion: Reflection Principle Log in to Mediaspace to watch this video

Explores the reflection principle in martingales and Brownian motion, simplifying probability calculations.

Probability Distributions: Central Limit Theorem and Applications Log in to Mediaspace to watch this video

Discusses probability distributions and the Central Limit Theorem, emphasizing their importance in data science and statistical analysis.

Radiative Exchange: Specular View Factors Log in to Mediaspace to watch this video

Covers specular view factors, radiative exchange, energy transfer, and numerical integration methods in thermal radiation.