Lectures related to Generating Functions: Moments and Cumulants

Linear Combinations: Moment-Generating Functions

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

Probability Distributions: Moments and Transformations

Explores the bijection between distribution functions and moment generating functions.

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.

Generating Functions: Properties and Applications

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

Moment Generating Function and Multivariate Normal Distribution

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

Continuous Random Variables

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

Continuous Random Variables

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

Random Vectors and Stochastic Models for Communications

Covers random vectors, joint probability, and conditional probability in communication stochastic models.

Probability and Statistics

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

Statistical Inference: Random Variables

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

Statistical Theory: Fundamentals

Covers the basics of statistical theory, including probability models, random variables, and sampling distributions.

Random Variables: Expectation and Independence

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

Probability Theory: Basics and Applications

Covers the fundamentals of probability theory, including conditional probability, Bayes' rule, and random variables.

Discrete Random Variables

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

Probability Theory: Basics and Applications

Covers the fundamentals of probability theory, including corollaries, conditional probability, total probability theorem, and random variables.

Causal Systems & Transforms: Delay Operator Interpretation

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

Calculations of Expectation

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

Families of Distributions: PDFs and CDFs

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

Properties of Distribution Functions

Covers the properties of distribution functions, discrete and continuous random variables, independence, and notation in probability theory.

Continuous Random Variables: Basics

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