Cardinality of Joint and Disjoint Sets and a Related Discrete Distribution
Keywords:
Cardinality, Joint Sets, Disjoint Sets, Discrete Distribution, Probability Distribution, Factorial Moment StructureAbstract
The number of elements belonging to the intersection of some overlapped sets and that belonging precisely to the junction of some overlapped sets are related. We have demonstrated a more straightforward presentation with some examples for a broad spectrum of students and instructors. It shows an apparent relationship between the cardinality of joint and disjoint sets. There is a probability distribution associated with it, and it is unexplored. We have provided some examples to illustrate it. We have derived the factorial moment structure of the probability distribution for the first time, and they found it to be elegant. We have also derived raw and corrected moments of the distribution.
Downloads
References
Björklund, A., Husfeldt, T. and Koivisto, M. (2009). Set Partitioning via Inclusion-Exclusion, SIAM J. Comput., 39(2), 546–563. https://doi.org/10.1137/070683933
Eisen, M. (1969). Elementary Combinatorial Analysis. Gordon and Breach Science Publishers. New York.
Hines, W.W. & Montgomery, D.C. (1990). Probability and Statistics for Engineering and Management Science. John Wiley, New York.
Johnson, N.L., Kotz, S. and Kemp, A.W. (1993). Univariate Discrete Distributions. John Wiley and Sons Inc., New York.
Kolman, B., Anton, H. and Averbach, B. (1992). Mathematics with Applications for the Management, Life, and Social Sciences. Saunders College Publishing, New York.
Downloads
Published
Issue
Section
License
Copyright (c) 2022 American Observer PressEngineering International follows a hybrid access and licensing model.
Standard publisher-controlled articles may not be reproduced, redistributed, modified, or reused without prior written permission from American Observer Press.
Articles published under the journal’s Open Access option may be distributed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0), as indicated on the individual article page.
