Read These Chapter 5. Discrete Probability Distributions in the textbook: 5.1 The Probability Distribution for a Discrete Variable (pp. 186-188) It may be a good idea to work on your own to calculate ...

Surprisingly, for a large class of such problems optimizing distributions turn out to be discrete. For example, in information theory, in his seminal paper (Smith’ 71), Smith has shown that an ...

Random variables: distribution functions, discrete and absolutely continuous distributions, examples. Expectation and the Lebesgue integral: convergence theorems and properties. Different modes of ...

This is a first course in measure-theoretic probability. It covers the following topics. Abstract probability spaces: sample spaces, sigma-algebras, probability measures, examples. Borel sigma-algebra ...

Description This is a graduate-level course focused on techniques and models in modern discrete probability. Topics include: the first and second moment methods, martingales, concentration ...