Geometric Probability Analysis of Meeting Probability and Intersection Duration for Triple Event Concurrency

Mohammad Al Bataineh (), Zouhair Al-qudah, Atef Abdrabou and Ayman N. Sandokah
Additional contact information
Mohammad Al Bataineh: Electrical and Communication Engineering Department, United Arab Emirates University, Al Ain P.O. Box 15551, United Arab Emirates
Zouhair Al-qudah: Department of Electrical and Communication Engineering, Al-Hussein bin Talal University, Ma’an 71111, Jordan
Atef Abdrabou: Electrical and Communication Engineering Department, United Arab Emirates University, Al Ain P.O. Box 15551, United Arab Emirates
Ayman N. Sandokah: Al-Faris School, Amman 11732, Jordan

Mathematics, 2023, vol. 11, issue 12, 1-18

Abstract: This study investigates the dynamics of three discrete independent events occurring randomly and repeatedly within the interval [ 0 , T ] . Each event spans a predetermined fraction γ of the total interval length T before concluding. Three independent continuous random variables represent the starting times of these events, uniformly distributed over the time interval [ 0 , T ] . By employing a geometric probability approach, we derive a rigorous closed-form expression for the probability of the joint occurrence of these three events, taking into account various values of the fraction γ. Additionally, we determine the expected value of the intersection duration of the three events within the time interval [ 0 , T ] . Furthermore, we provide a comprehensive solution for evaluating the expected number of trials required for the simultaneous occurrence of these events. Numerous numerical examples support the theoretical analysis presented in this paper, further validating our findings.

Keywords: geometric probability; joint event; meeting probability; expected value; random variables (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/12/2708/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/12/2708/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:12:p:2708-:d:1171599

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().