Variance: Definition, Examples, and Theorems

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Random Variables: Basics and Examples

Explains random variables, distributions, and Bernoulli trials with coin flip examples.

Elements of Statistics: Probability and Random Variables

Introduces key concepts in probability and random variables, covering statistics, distributions, and covariance.

Central Limit Theorem: Proof and Applications

Explores the proof and applications of the Central Limit Theorem, emphasizing independence and random variable distributions.

Probability Theory: Conditional Expectation

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

Conditional Expectation

Covers conditional expectation, Fubini's theorem, and their applications in probability theory.

Probability Spaces

Covers random variables, expectation, and distributions in probability spaces.

Variance: Independent Random Variables and Bernoulli Trials

Explores Bienaymé's Formula for independent random variables and variance in Bernoulli trials.

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.

Convergence in Law: Weak Convergence and Skorokhod's Representation Theorem

Explores convergence in law, weak convergence, and Skorokhod's representation theorem in probability theory.

Conditional Density and Expectation

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