Lectures related to Central Limit Theorem: Multivariate Delta Method

Probabilities and Statistics: Key Theorems and Applications

Discusses key statistical concepts, including sampling dangers, inequalities, and the Central Limit Theorem, with practical examples and applications.

Probability and Statistics: Fundamental Theorems

Explores fundamental theorems in probability and statistics, joint probability laws, and marginal distributions.

Central Limit Theorem: Properties and Applications

Explores the Central Limit Theorem, covariance, correlation, joint random variables, quantiles, and the law of large numbers.

Elements of Statistics: Estimation & Distributions

Covers fundamental statistics concepts, including estimation theory, distributions, and the law of large numbers, with practical examples.

Probability Distributions in Environmental Studies

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

Convergence of Random Variables

Explores the convergence of random variables, the law of large numbers, and the distribution of failure time.

Continuous Random Variables

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

Law of Large Numbers: Strong Convergence

Explores the strong convergence of random variables and the normal distribution approximation in probability and statistics.

Convergence of Random Variables

Explores independent and identically distributed random variables, convergence, and distribution properties.

Advanced Probabilities: Random Variables & Expected Values

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

Conditional Expectation: Grouping Lemma

Explores conditional expectation, the grouping lemma, and the law of large numbers.

Linear Combinations: Moment-Generating Functions

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

Families of Distributions: PDFs and CDFs

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

Stochastic Models for Communications

Explores stochastic models for communications, covering mean, variance, characteristic functions, inequalities, various discrete and continuous random variables, and properties of different distributions.

Elements of Statistics: Probability and Random Variables

Introduces key concepts in probability and random variables, covering statistics, distributions, and covariance.

Normal Distribution: Properties and Calculations

Covers the normal distribution, including its properties and calculations.

Multivariate Random Variables

Explores multivariate random variables, joint Gaussian variables, convergence, and the central limit theorem.

Multivariate Random Variables

Covers multivariate random variables, joint Gaussian variables, and convergence of random variables.

Central Limit Theorem: Lindeberg's Principle

Explores the Central Limit Theorem, emphasizing the convergence towards a Gaussian distribution.

Probability and Statistics

Delves into probability, statistics, paradoxes, and random variables, showcasing their real-world applications and properties.