Lectures related to Large numbers

Conditional Expectation: Grouping Lemma

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

Understanding Card Counting

Explores the misconceptions and strategies of card counting in a treasure hunt.

Law of Large Numbers: Statistics

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

Markov Chains: Convergence and Equilibrium

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

Probability and Statistics: Fundamental Theorems

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

Markov Chain Convergence

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

Central Limit Theorem: Multivariate Delta Method

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

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.

Probability Theory: Conditional Expectation

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

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.

Integers: Elementary Concepts

Covers fundamental concepts related to integers, including properties of well-ordered sets and the principle of induction.

Monte Carlo Estimation: Error Analysis

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

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.

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.

Kolmogorov's 0-1 Law: Convergence and Divergence

Explores Kolmogorov's 0-1 law, showcasing cases of convergence and divergence in random variables based on the finiteness of expectations.

Law of Large Numbers: Strong Convergence

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