Distributions
Bruno de Finetti, Antonio Machı̀, A. F. M. Smith · Wiley series in probability and statistics · 2017
This chapter introduces the notion of a probability distribution and the requisite mathematical tools, tying them in rigorously with the previous formulation and making any necessary modifications or limitations. From the viewpoint of the pure mathematician, who is not concerned with the question of how a given definition relates to the exigencies of the application, or to anything outside the mathematics, the choice is merely one of mathematical convenience and elegance. This chapter focuses on the application of the mathematical tools within the calculus of probability. It talks about three kinds of ideas and tools, namely descriptive properties, synthetic characteristics, and analytic characteristics. In the most natural interpretation, the notion of convergence deals with sequences of random quantities. It considers the notion of stochastic independence in the context of random quantities.