Cardinality of Joint and Disjoint Sets and a Related Discrete Distribution

Authors

  • Anwar H. Joarder Department of Computer Science and Engineering, Northern University of Business & Technology Khulna, Khulna 9100, BANGLADESH
  • S. M. Shahidul Islam Department of Mathematics, Hajee Mohammad Danesh Science and Technology University, Dinajpur-5200, BANGLADESH

DOI:

https://doi.org/10.18034/ei.v10i2.681

Keywords:

Cardinality, Joint Sets, Disjoint Sets, Discrete Distribution, Probability Distribution, Factorial Moment Structure

Abstract

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.

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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.

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Published

2022-09-28

Issue

Vol. 10 No. 2 (2022): July - December Issue

Section

Peer Reviewed Articles

License

Copyright (c) 2022 Anwar H. Joarder, S. M. Shahidul Islam

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Engineering International is licensed under a Creative Commons Attribution-Noncommercial 4.0 International License (CC-BY-NC). Articles can be read and shared for noncommercial purposes under the following conditions:

  • BY: Attribution must be given to the original source (Attribution)
  • NC: Works may not be used for commercial purposes (Noncommercial)

 

How to Cite

Joarder, A. H., & Islam, S. M. S. (2022). Cardinality of Joint and Disjoint Sets and a Related Discrete Distribution. Engineering International, 10(2), 55-68. https://doi.org/10.18034/ei.v10i2.681

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