Lectures related to Law of averages

Central Limit Theorem: Lindeberg's Principle

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

Probability and Statistics: Fundamental Theorems

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

Central Limit Theorem: Multivariate Delta Method

Explores the Central Limit Theorem, Slutsky's Theorem, and the Multivariate Delta Method in probability and distribution convergence.

Markov Chain Convergence

Explores Markov chain convergence, emphasizing invariant distribution, Law of Large Numbers, and mean rewards computation.

Law of Large Numbers: General Assumptions

Delves into the complexities of extending from finite variance to finite expectation assumptions.

The Law of Large Numbers: Proof and Applications

Explores the proof and applications of the law of large numbers, emphasizing convergence of the empirical distribution.

All of Probability: LLN, CLT, Chernoff and PAC bound

Covers the Law of Large Numbers, Central Limit Theorem, Chernoff bounds, and PAC bounds in probability theory.

Markov Chains: Convergence and Equilibrium

Explores the convergence properties of Markov chains and the computation of long-run mean rewards.

Monte Carlo Estimation: Error Analysis

Covers the Monte Carlo method for generating realizations and unbiased estimators.

Stochastic Processes: Symmetric Random Walk

Covers the properties of the symmetric random walk in stochastic processes.

All of Probability: Basic Bounds, LLN & CLT

Introduces basic bounds, LLN, and CLT in probability theory, emphasizing convergence to normal distribution.

Central Limit Theorem: Empirical Mean

Explores the convergence of empirical mean distributions towards Gaussian distributions, focusing on the Central Limit Theorem.

Central Limit Theorem: Properties and Applications

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

Message passing in networks

Explains message passing in networks, emphasizing probabilities and average edges between communities.

Law of Large Numbers: Statistics

Explains the Law of Large Numbers and its application to random variables.

Law of Large Numbers: Strong Convergence

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

Variance and Covariance: Properties and Examples

Explores variance, covariance, and practical applications in statistics and probability.

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 Theory: Conditional Expectation

Covers conditional expectation, convergence of random variables, and the strong 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.