Metrics
6 Record Views
Journal article
On the continuity property of the probability function and its applications
Applied mathematical sciences, Vol.15(11), pp.519-543
2021
Abstract
In this paper, we study the ‘continuity’ property of probability functions and explore thoroughly its well-known “equivalence” to the axiom of ‘countable additivity’. Students in early university courses in Probability and Statistics are often quite fearful of dealing with topics involving ‘convergence’ of random variables - and their distributions - where the ‘continuity’ property plays a major role, namely, those involving notions of almost sure (a.s.) convergence, convergence in probability (pr.) or convergence in distribution (d) etc.. We illustrate this via simple well-structured proofs and multiple informative examples. A lack of adequate emphasis on the ‘continuity’ property in early courses creates a gap in students’ understanding of the role of convergence of distributions in large sample statistical analysis. This article aims to fill up this gap. The article is directed towards students and teachers of introductory courses in Probability and Statistics.
Files and links (1)
Related links
Details
- Title
- On the continuity property of the probability function and its applications
- Publication Details
- Applied mathematical sciences, Vol.15(11), pp.519-543
- Resource Type
- Journal article
- Publisher
- Hikari Ltd.
- Copyright
- © 2021 Hikari Ltd.
- Identifiers
- 99381378975906600
- Academic Unit
- Mathematics and Statistics; Hal Marcus College of Science and Engineering
- Language
- English