Lectures related to Convergence in Distribution

Convergence of Random Variables

Explores different modes of convergence for random variables.

Continuous Random Variables: Basic Ideas

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

Continuous Random Variables

Covers continuous random variables, probability density functions, and distributions, with practical examples.

Continuous Random Variables

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

Linear Combinations: Moment-Generating Functions

Explores moment-generating functions, linear combinations, and normality of random variables.

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.

Kinetic Theory: Distribution Function Evolution

Explores the evolution of the distribution function describing particles in phase space.

Causal Systems & Transforms: Delay Operator Interpretation

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

Probability and Statistics

Covers probability distributions, moments, and continuous random variables.

Normal Distribution: Properties and Calculations

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

Generating Functions: Properties and Applications

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

Probability and Statistics

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

Probability Distributions: Central Limit Theorem and Applications

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

Introduction to Continuous Random Variables: Probability Distributions

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

Distributions and Derivatives

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Random Variables: Expectation and Independence

Explores random variables, expectation, and independence in probability theory.

Radiative Exchange: Specular View Factors

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

Discrete Random Variables

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

Calculations of Expectation

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

Modes of Convergence

Explores modes of convergence in probability and statistics, illustrating concepts with examples and discussing the continuity theorem.