Statistical Theory: Inference and Sufficiency

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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.

Estimation Methods in Probability and Statistics

Discusses estimation methods in probability and statistics, focusing on maximum likelihood estimation and confidence intervals.

Distribution Estimation

Covers the estimation of distributions using samples and probability models.

Law of Large Numbers: Strong Convergence

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

Testing: t-tests

Covers t-tests, p-values calculation, and comparison of coefficients.

Probabilistic Models for Linear Regression

Covers the probabilistic model for linear regression and its applications in nuclear magnetic resonance and X-ray imaging.

Convergence of Random Variables

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

Sampling Distributions: Theory and Applications

Explores sampling distributions, estimators' properties, and statistical measures for data science applications.

Interval Estimation

Covers the construction of confidence intervals for a normal distribution with unknown mean and variance.

Linear Algebra in Data Science

Explores the application of linear algebra in data science, covering variance reduction, model distribution theory, and maximum likelihood estimates.