Studies axioms, counting formulas, conditional probability, independence, random variables, continuous and discrete distribution, expectation, moment generating functions, law of large numbers, ...

The central limit theorem (CLT) commonly presented in introductory probability and mathematical statistics courses is a simplification of the Lindeberg—Lévy CLT which uses moment generating functions ...

Mixture models are important in theoretical and applied statistics. Mathematical statistics courses for undergraduate senior or first-year graduate students should expose students to some properties ...

Addresses the topics of probability, random variables, discrete and continuous densities, expectation and variance, special distributions (binomial, Poisson, normal, etc.), moment generating functions ...