Concentration Inequalities: Hoeffding's Inequality

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Covers McDiarmid's inequality, providing concentration bounds for functions of independent random variables.

Explores uniform integrability, convergence theorems, and the importance of bounded sequences in understanding the convergence of random variables.

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

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

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

Explores convergence in law for random variables, including Kolmogorov's theorem and proofs based on probability lemmas.

Explores joint random variables, conditional density, and independence in probability and statistics.

Explores different modes of convergence for random variables.

Explores Hoeffding's inequality and its applications in probability theory and statistical analysis.

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