Exponential random variables: theory and applications

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Probability and Statistics

Covers probability distributions, moments, and continuous random variables.

Normal Distribution: Properties and Calculations

Covers the normal distribution, including its properties and calculations.

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.

Calculations of Expectation

Covers the calculation of expectation and variance for different types of random variables, including discrete and continuous ones.

Convergence of Random Variables

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

Statistical Models: Families and Transformations

Explores statistical models, families of distributions, transformations, and their applications in probability theory.

Random Variables: Expectation and Independence

Explores random variables, expectation, and independence in probability theory.

Statistical Inference: Random Variables

Covers random variables, probability functions, expectations, variances, and joint distributions.

Entropy and Sampling Theory

Explores entropy, exponential family, sampling theory, and statistical inference from samples.

Statistical Theory: Fundamentals

Covers the basics of statistical theory, including probability models, random variables, and sampling distributions.