Discrete Probability Distributions Definitions Area of Opportunity: (for Poisson distribution) a continuous interval (time, length, area, volume, etc). Binomial Distribution has the following ...

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

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 ...

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 ...