Representation with Index Matrices Discrete Random Variables

Stela Todorova

doi:doi:10.11648/j.ajam.20251301.14

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Representation with Index Matrices Discrete Random Variables

Stela Todorova^*

Published in American Journal of Applied Mathematics (Volume 13, Issue 1)

Received: 4 January 2025 Accepted: 18 January 2025 Published: 10 February 2025

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Abstract

With the Theory of probabilities it is made a mathematical description of a finite set of probability trials with random outcomes. Basically, the results from a given laboratory experiment are illustrated with tables, diagrams, ordinary matrices. Index matrices are a new approach of presenting and analyzing information of data. In this article the author will represent with Index Matrices, which elements are real numbers; function-type of elements, with which results of formulas with different parameters can be calculated and predicates, with which can be checked if a random outcome meets certain conditions according to a finite set of interval order. In order the data that we analyze to be more precisely verified, is not only ordered sequentially, but also a result of calculation of parameters from a given diapason at equal intervals. In this way the number of desired outcomes can be compared with not desired outcomes and with the data from different experiments, which can result in prediction of alternative values in the future. An illustration with Excel is described with an Index matrix, which elements are voltages between 0 and a value read by analog pin of Arduino Uno board, which is also presented with X and Y axis of a Chart diagram.

Published in	American Journal of Applied Mathematics (Volume 13, Issue 1)
DOI	10.11648/j.ajam.20251301.14
Page(s)	57-63
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2025. Published by Science Publishing Group

Keywords

Index Matrix, Theory of Probability, Random Variables, Algebra of Events, Probability of Trials, Arduino

References

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[2]	Димитров, М. Теория на вероятностите. Университетско издателство "Стопанство". София. 2002. [Dimitrov, M. Theory of probability. (2002) University Publishing House "Stopanstvo". Sofia]
[3]	Aksin, D., Al-Shyoukh, M. A., Maloberti, F. "An 11 Bit Sub Ranging SAR ADC with Input Signal Range of Twice Supply Voltage"; IEEE International Symposium on Circuits and Systems, ISCAS 2007, New Orleans, 27, 30 May 2007, pp. 1717-1720. https://doi.org/10.1109/ISCAS.2007.377925
[4]	Arduino. analogRead (). Available at https://www.arduino.cc/reference/tr/language/functions/analog-io/analogread/
[5]	Сотирова, Е. Димитрова, Л. Иновска, Г. Гордън, Г. Михайлова, Р. Илиева, П. Панайотов, Х. Мавров, Д. Ръководство за лабораторни упражнения по информатика. Бургас. 2013. [Sotirova, E. Dimitrova, L. Inovska, G. Gorden, G. Mihailova, R. Ilieva, P. Panayotov H. Mavrov, D. Guide to informatics laboratory exercises (2013) Burgas]
[6]	Todorova, S. Research of the index matrices and their applications. University "Prof. A. Zlatarov" (AU). Faculty of Technical Sciences. Academic degree: Doctor (PhD). 30.09.2024. Supervisor: Assoc. Prof. Veselina Kuncheva Bureva, PhD; Assoc. Prof. Nora Angelova Angelova, PhD. Reviewers: Acad. Prof. Krassimir Todorov Atanassov, DSc DSc Assoc. Prof. Velin Stoqanov Andonov, PhD. Burgas. 113 pages.
[7]	Smith W. A. C Programming with Arduino. Elektor International Media B. V. 2016.
[8]	Todorova, S. Proykov, M. Mathematical analysis of an electrical circuit. International Scientific Industry 4.0. Volume 6. Issue 1. pp. 25 26. 2021.
[9]	Riverglennapt, Nodes, branches and loops of a circuit, Available: https://riverglennapts.com/bg/circuit-and-network/172-nodes-branches-and-loops-of-a-circuit.html
[10]	Тодорова, С. Обзор върху публикациите по индексирани матрици. Годишник на секция "Инорматика". Съюз на учените в България. стр. 32 – стр. 62. Том XII. 2022-2023 [Todorova, S. Overview of publications on index matrices. (2022-2023) Yearbook of Section "Informatics". Union of Scientists in Bulgaria. pp. 32-62. Tom XII].
[11]	Platt, Ch. Make: Electronics: Learning by Discovery: A hands-on primer for the new electronics enthusiast. Third Edition. Published by Make Community, LLC. 2021.
[12]	Атанасов, К. Бурева В. Кратък курс по дискретни структури. Авангард Прима. гр. София. 2018 [Atanassov, K. Bureva V. Short course on discrete structures (2018). Avangard Prima. Sofia].
[13]	Birkhoff, G. Lattice Theory, Providence, RI: AMS, 1940.
[14]	Banzi, M. Shiloh M. Getting Started with Arduino: The Open Source Electronics Prototyping Platform. 4^th Edition. Published by Make Community, LLC. 2022.
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[16]	Todorova, S. Bureva, V. Angelova, N. Proykov M. Programme Product for Index Matrices. Book of Abstracts of International Symposium on Bioinformatics and Biomedicine 8-10 October 2020, Burgas, Bulgaria.

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APA Style

Todorova, S. (2025). Representation with Index Matrices Discrete Random Variables. American Journal of Applied Mathematics, 13(1), 57-63. https://doi.org/10.11648/j.ajam.20251301.14

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ACS Style

Todorova, S. Representation with Index Matrices Discrete Random Variables. Am. J. Appl. Math. 2025, 13(1), 57-63. doi: 10.11648/j.ajam.20251301.14

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AMA Style

Todorova S. Representation with Index Matrices Discrete Random Variables. Am J Appl Math. 2025;13(1):57-63. doi: 10.11648/j.ajam.20251301.14

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@article{10.11648/j.ajam.20251301.14,
  author = {Stela Todorova},
  title = {Representation with Index Matrices Discrete Random Variables},
  journal = {American Journal of Applied Mathematics},
  volume = {13},
  number = {1},
  pages = {57-63},
  doi = {10.11648/j.ajam.20251301.14},
  url = {https://doi.org/10.11648/j.ajam.20251301.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20251301.14},
  abstract = {With the Theory of probabilities it is made a mathematical description of a finite set of probability trials with random outcomes. Basically, the results from a given laboratory experiment are illustrated with tables, diagrams, ordinary matrices. Index matrices are a new approach of presenting and analyzing information of data. In this article the author will represent with Index Matrices, which elements are real numbers; function-type of elements, with which results of formulas with different parameters can be calculated and predicates, with which can be checked if a random outcome meets certain conditions according to a finite set of interval order. In order the data that we analyze to be more precisely verified, is not only ordered sequentially, but also a result of calculation of parameters from a given diapason at equal intervals. In this way the number of desired outcomes can be compared with not desired outcomes and with the data from different experiments, which can result in prediction of alternative values in the future. An illustration with Excel is described with an Index matrix, which elements are voltages between 0 and a value read by analog pin of Arduino Uno board, which is also presented with X and Y axis of a Chart diagram.},
 year = {2025}
}

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TY  - JOUR
T1  - Representation with Index Matrices Discrete Random Variables
AU  - Stela Todorova
Y1  - 2025/02/10
PY  - 2025
N1  - https://doi.org/10.11648/j.ajam.20251301.14
DO  - 10.11648/j.ajam.20251301.14
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 57
EP  - 63
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20251301.14
AB  - With the Theory of probabilities it is made a mathematical description of a finite set of probability trials with random outcomes. Basically, the results from a given laboratory experiment are illustrated with tables, diagrams, ordinary matrices. Index matrices are a new approach of presenting and analyzing information of data. In this article the author will represent with Index Matrices, which elements are real numbers; function-type of elements, with which results of formulas with different parameters can be calculated and predicates, with which can be checked if a random outcome meets certain conditions according to a finite set of interval order. In order the data that we analyze to be more precisely verified, is not only ordered sequentially, but also a result of calculation of parameters from a given diapason at equal intervals. In this way the number of desired outcomes can be compared with not desired outcomes and with the data from different experiments, which can result in prediction of alternative values in the future. An illustration with Excel is described with an Index matrix, which elements are voltages between 0 and a value read by analog pin of Arduino Uno board, which is also presented with X and Y axis of a Chart diagram.
VL  - 13
IS  - 1
ER  -

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Author Information

Stela Todorova

Department of Mathematics, Informatics and Physics, “Prof. Dr Assen Zlatarov” University, Burgas, Bulgaria

Contact Email

http://orcid.org/0000-0002-0418-5853

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Plain Text BibTeX RIS

APA Style

Todorova, S. (2025). Representation with Index Matrices Discrete Random Variables. American Journal of Applied Mathematics, 13(1), 57-63. https://doi.org/10.11648/j.ajam.20251301.14

Copy | Download

ACS Style

Todorova, S. Representation with Index Matrices Discrete Random Variables. Am. J. Appl. Math. 2025, 13(1), 57-63. doi: 10.11648/j.ajam.20251301.14

Copy | Download

AMA Style

Todorova S. Representation with Index Matrices Discrete Random Variables. Am J Appl Math. 2025;13(1):57-63. doi: 10.11648/j.ajam.20251301.14

Copy | Download

@article{10.11648/j.ajam.20251301.14,
  author = {Stela Todorova},
  title = {Representation with Index Matrices Discrete Random Variables},
  journal = {American Journal of Applied Mathematics},
  volume = {13},
  number = {1},
  pages = {57-63},
  doi = {10.11648/j.ajam.20251301.14},
  url = {https://doi.org/10.11648/j.ajam.20251301.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20251301.14},
  abstract = {With the Theory of probabilities it is made a mathematical description of a finite set of probability trials with random outcomes. Basically, the results from a given laboratory experiment are illustrated with tables, diagrams, ordinary matrices. Index matrices are a new approach of presenting and analyzing information of data. In this article the author will represent with Index Matrices, which elements are real numbers; function-type of elements, with which results of formulas with different parameters can be calculated and predicates, with which can be checked if a random outcome meets certain conditions according to a finite set of interval order. In order the data that we analyze to be more precisely verified, is not only ordered sequentially, but also a result of calculation of parameters from a given diapason at equal intervals. In this way the number of desired outcomes can be compared with not desired outcomes and with the data from different experiments, which can result in prediction of alternative values in the future. An illustration with Excel is described with an Index matrix, which elements are voltages between 0 and a value read by analog pin of Arduino Uno board, which is also presented with X and Y axis of a Chart diagram.},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - Representation with Index Matrices Discrete Random Variables
AU  - Stela Todorova
Y1  - 2025/02/10
PY  - 2025
N1  - https://doi.org/10.11648/j.ajam.20251301.14
DO  - 10.11648/j.ajam.20251301.14
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 57
EP  - 63
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20251301.14
AB  - With the Theory of probabilities it is made a mathematical description of a finite set of probability trials with random outcomes. Basically, the results from a given laboratory experiment are illustrated with tables, diagrams, ordinary matrices. Index matrices are a new approach of presenting and analyzing information of data. In this article the author will represent with Index Matrices, which elements are real numbers; function-type of elements, with which results of formulas with different parameters can be calculated and predicates, with which can be checked if a random outcome meets certain conditions according to a finite set of interval order. In order the data that we analyze to be more precisely verified, is not only ordered sequentially, but also a result of calculation of parameters from a given diapason at equal intervals. In this way the number of desired outcomes can be compared with not desired outcomes and with the data from different experiments, which can result in prediction of alternative values in the future. An illustration with Excel is described with an Index matrix, which elements are voltages between 0 and a value read by analog pin of Arduino Uno board, which is also presented with X and Y axis of a Chart diagram.
VL  - 13
IS  - 1
ER  -

Copy | Download