Correlated and Uncorrelated Sampling

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Errors in Sampling: Correlation and Time Analysis

Explores errors in sampling, correlation functions, time analysis, and blocking techniques.

Conditional Density and Expectation

Explores conditional density, expectations, and independence of random variables with practical examples.

Independence and Covariance

Explores independence and covariance between random variables, discussing their implications and calculation methods.

Distribution Estimation

Covers the estimation of distributions using samples and probability models.

Efficiency of Sampling: Ergodicity and Autocorrelation Functions

Explores the efficiency of sampling in molecular dynamics, focusing on ergodicity and autocorrelation functions.

Ergodic Theory: Chaos

Explores elements from Ergodic Theory, transformations, invariant sets, and Lyapunov Exponents for 1-dimensional maps.

Normal Distribution: Characteristics and Z-scores

Explores normal distribution characteristics, Z-scores, probability in inferential statistics, sample effects, and binomial distribution approximation.

Advanced Probabilities: Random Variables & Expected Values

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

Law of Large Numbers: Strong Convergence

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