Lectures related to Transformations of Variables

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

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

Introduction to Continuous Random Variables: Probability Distributions

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

Probability Distributions: Central Limit Theorem and Applications

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

Probability and Statistics

Covers p-quantile, normal approximation, joint distributions, and exponential families in probability and statistics.

Linear Combinations: Moment-Generating Functions

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

Normal Distribution: Properties and Calculations

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

Statistical Inference: Random Variables

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

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.

Normal Distribution: Properties and Calculations

Covers the normal distribution, including its properties and calculations.

Normal Distribution: Basics and Applications

Covers the basics of the normal distribution and its applications in probability calculations.

Probability and Statistics

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

Probability Distributions

Covers various probability distributions and their applications in real-world scenarios.

Families of Distributions: PDFs and CDFs

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

Random Vectors and Stochastic Models for Communications

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

Multivariate Statistics: Normal Distribution

Introduces multivariate statistics, covering normal distribution properties and characteristic functions.

Elements of Statistics

Introduces key statistical concepts like probability, random variables, and correlation, with examples and explanations.

Sampling Theory: Statistics for Mathematicians

Covers the theory of sampling, focusing on statistics for mathematicians.

Common Distributions: Moment Generating Functions

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

Probability Distributions in Environmental Studies

Explores probability distributions for random variables in air pollution and climate change studies, covering descriptive and inferential statistics.