On the Philosophy of Probability Behaviour Composite Probability Ƥ(P) In the Case of Discrete Function
Keywords:
Compliment, Experiment, Sample Space, Sequence
Abstract
This paper is dealing with probability theory, starting from an objectivism philosophic approach, towards mathematical approach. This approach is aiming to study the probability behaviour as a function and as a fraction quantity. This aim, is requiring a discussion of the usage of the probability statement, the causes behind the existence of probabilistic phenomenon, and an explanation that admits to measure the causality by probability theory, through the concept of conditioning and the concept of compliment. This paper is using conceptual experiment with a design that addresses the shortcoming of traditional conceptual experiment. Also, it is using the relative frequency of event and the probability axioms. These, in turn will reflect some aspects of the probabilistic behaviour, in addition to some important consequences that follow from. As a result this will provide a sample space to include all possible events in the form of sequence of sub sequences. Also, this paper will provide some definitions that define some elements of the fractions probabilities and the sample space. These are beside, some proven corollaries that admit to calculate composite probability in the case of discrete function. In addition, to a briefly treatment to the continuous function.
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References
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38. Marczyk, Michał, and Leszek Wroński. “Completion of the Causal Completability Problem.” The British Journal for the Philosophy of Science, vol. 66, no. 2, 2015, pp. 307–26. JSTOR, http://www.jstor.org/stable/24562936. Accessed 23 Dec. 2022.
39. Blanché, Robert. (1972). L’épistémologie. Paris: P.U.F.
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42. Pierre, Guiraud. (1969). La Sémantique. Sixème Ééition. France: Presses Universitaires De France.
43. Pierre Simon Laplace. (1921). Essai Philosophique sur les Probabilitéé. Paris: Gauthier-Villars Et.
44. Parzen, E. (1960). Modern Probability Theory and Its Applications. New York, NY: John Wiley & Sons, Inc.
45. Bingham, N. H. “Studies in the History of Probability and Statistics XLVI. Measure into Probability: From Lebesgue to Kolmogorov.” Biometrika, vol. 87, no. 1, 2000, pp. 145–56. JSTOR, http://www.jstor.org/stable/2673568. Accessed 23 Dec. 2022.
46. Todhunter, I. (1949). A History of the Mathematical Theory of Probability from the Time of Pascal to Laplace. New York: Chelsea.
2. Popper, K. (2002). The Logic of Scientific Discovery. Second English Edition. London: Routledge.
3. Alexander, M. Mood., Franklin, A. Graybill., Duane, C. Boes. (1974). Introduction to the Theory of Statistics. Third Edition. USA : McGraw-Hill, Inc.
4. Tucker, Howard G. (1967). A Graduate Course in Probability. New York: Academic Press, Inc.
5. Dunker, T., W. V. Li and W. Linde. (2000). Small Ball Probabilityes of Integrals of Weighted Brownian Motion. Statistics & Probability Letters, Volume 46, Issue 3, ISSN 0167-7152, https://doi.org/10.1016/S0167-7152(99)00098-X.
6. K.B. Athreya, A.N. Vidyashankar, Branching processes, Handbook of Statistics, Elsevier, Volume 19, 2001, Pages 35-53, ISSN 0169-7161,
ISBN 9780444500144, https://doi.org/10.1016/S0169-7161(01)19004-8.
7. Athreya, K. B. And P. Jagers. (1997). Classical and Modern Branching Processes. Papers from IMA WOKSHOP HELD AT THE University of Minnesota. Minneapolis, MN, June 13-17m 1994. IMA Volumes im Mathematucs abd Aookucatuibm 84, Springer-Velag, New York.
8. W. V. Li, Q. M. Shao (2001). Gaussian Processes: Inequalities, Small Ball Probabilities and Applications. Volume 19, pages 533-597 Netherlands: Elsevier Science B.V.
9. Lebesgue, Henri. (1904). Leçons sur L’intégration et La Recherche des Fonctions Primitives. Paris: Gauthier-Villars, Imprimeurs-Libraires.
10. Feller, W. (1971). An Introduction to Probability Theory and Its Applications. USA: John Wiley & Sons, Inc.
11. Paul, G. Heol., Sidney, C. PORT., Charles, J. Stone.(1971). Introduction to Probability Theory. USA: Houghton Mifflin Company.
12. Howard, M. Taylor., Samuel, Karlin. (1998). An Introduction to Stochastic Modeling. Third Edition. USA: Academic Press.
13. Werner, Heisenberg. (1930). The Physical Principles of the Quantum Theory. New York: Dover Publications, Inc.
14. Rényi, alfred. (1970). Foundations of Probability. San Francisco: Holden-Day.
15. Parzen, E. (1962). Stochastic Processes. USA: Holden-Day, Inc.
16. Cantor, G. (1883). Sur Les Ensembles Infinis et Linéaires de Points. ACTA Mathematica 2 (361-371). Paris: A. Hermann.
17. Khinchin, A. Ya. (1997). Continued Fractions. New York : Dover Publication, Inc.
18. Borel, Émile. (1898). Leçons sur La Théorie des Fonctions. Paris: Gauthier-Villars et Fils, Imprimeurs-Libraires.
19. Edward, J. Dudewicz., & Satya, N. Mishra. (1988). Modern Mathematical Statistics. Canada: John Wiley & Sons, Inc.
20. Larson, Harold J. (1973). Introduction to the Theory of Statistics. USA: John Wiley & Sons, Inc.
21. Stoll, Manfred. (1997). Introduction to Real Analysis. Boston: Addison Wesley Longman Inc.
22. Bartle, R., & Sherbert, Donald. (2011). Introduction to Real Analysis. Fourth Edition. USA: John Wiley & Sons, Inc.
23. Feller, W. (1950). An Introduction to Probability Theory and Its Applications Volume I. New York, NY: John Wiley & Sons, Inc.
24. Knuth, D. (1998). The Art of Computer Programming, Volume II, Second Edition. USA: Addison Wesley.
25. Hines, W., & Montgomery, D. (1990). Probability and Statistics in Engineering and Management Science. USA: John Wiley & Sons, Inc.
26. Douglas, M. (1997). Design and Analysis of Experiments. New York, NY: John Wiley & Sons, Inc.
27. Edwards, William F., et al. “Dependent Probability Spaces.” The College Mathematics Journal, vol. 39, no. 3, 2008, pp. 221–26. JSTOR, http://www.jstor.org/stable/27646628. Accessed 4 Dec. 2022.
28. M. Loève. (1977). Probability theory, Volume I. 4th Edition. New York: Springer-Verlag.
29. M. Loève. (1978). Probability theory, Volume II. 4th Edition. New York: Springer-Verlag.
30. Meyer, Paul L. (1970). Introductory Probability and Statistical Applications. Second Edition. USA: Addison-Wesley Publishing Company, Inc.
31. Fred, S. Roberts. (1979). Measurement Theory. Canada: Addison Wesley Publishing Company, Inc.
32. Werner, Heisenberg. (1962). Physics and Philosophy. New York: Harper & Row, Publishers.
33. Eugen, Merzbacher. (1970). Quantum Mechanics. Second Edition. USA: John Wiley & Sons.
34. Bohr, N. (1958). Atomic Physics and Human Knowledge. New York: John Wiley and Sons.
35. Pruss, Alexander R. “Probability, Regularity, and Cardinality.” Philosophy of Science 80, no. 2 (2013): 231–40. https://doi.org/10.1086/670299.
36. Brown, Harvey R. “Curious and Sublime: The Connection between Uncertainty and Probability in Physics.” Philosophical Transactions: Mathematical, Physical and Engineering Sciences, vol. 369, no. 1956, 2011, pp. 4690–704. JSTOR, http://www.jstor.org/stable/23057214. Accessed 4 Dec. 2022.
37. Howson, Colin. “Theories of Probability.” The British Journal for the Philosophy of Science, vol. 46, no. 1, 1995, pp. 1–32. JSTOR, http://www.jstor.org/stable/687631. Accessed 4 Dec. 2022.
38. Marczyk, Michał, and Leszek Wroński. “Completion of the Causal Completability Problem.” The British Journal for the Philosophy of Science, vol. 66, no. 2, 2015, pp. 307–26. JSTOR, http://www.jstor.org/stable/24562936. Accessed 23 Dec. 2022.
39. Blanché, Robert. (1972). L’épistémologie. Paris: P.U.F.
40. Baruch Brody. (1970). Readings in the Philosophy of Science. New Jersey: Prentice Hall, Inc., Englewood Cliffs.
41. John, Maynard Keynes. (2004). A Treatise on Probability. USA: Dover Publication, Inc.
42. Pierre, Guiraud. (1969). La Sémantique. Sixème Ééition. France: Presses Universitaires De France.
43. Pierre Simon Laplace. (1921). Essai Philosophique sur les Probabilitéé. Paris: Gauthier-Villars Et.
44. Parzen, E. (1960). Modern Probability Theory and Its Applications. New York, NY: John Wiley & Sons, Inc.
45. Bingham, N. H. “Studies in the History of Probability and Statistics XLVI. Measure into Probability: From Lebesgue to Kolmogorov.” Biometrika, vol. 87, no. 1, 2000, pp. 145–56. JSTOR, http://www.jstor.org/stable/2673568. Accessed 23 Dec. 2022.
46. Todhunter, I. (1949). A History of the Mathematical Theory of Probability from the Time of Pascal to Laplace. New York: Chelsea.
Published
2023-05-14
How to Cite
Jughaiman, A. (2023). On the Philosophy of Probability Behaviour Composite Probability Ƥ(P) In the Case of Discrete Function. European Scientific Journal, ESJ, 17, 152. Retrieved from https://eujournal.org/index.php/esj/article/view/16751
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ESI Preprints
Copyright (c) 2023 Abdulaziz Jughaiman
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