DOI
10.34229/KCA2522-9664.25.3.12
UDC 519.212.2:681.51
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2 Vasyl Stefanyk Precarpathian National University, Ivano-Frankivsk, Ukraine
 slobodian_s@ukr.net
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JOINT DISTRIBUTION OF SOME EVENTS IN THE BERNOULLI SCHEME
WITH PARAMETERS (n, p )
Abstract. An explicit form of the joint distribution of an arbitrary fixed pair of events belonging to the same finite family of events
in the Bernoulli scheme with parameters (n, p ) is established.
The connection of the parameter n with the maximum value of each of the obtained joint distributions
under the condition p = 0.5 is indicated.
Examples of the use of the established distributions for the analysis of the (0,1)-sequence are given.
Keywords: joint distribution, Bernoulli scheme, 2-chain, digital steganography, econometrics.
full text
REFERENCES
- 1. Menezes А.J., van Oorschot Р.С., Vanstone А.S. Handbook of Applied Cryptography. CRC Press, 1996. 816 p.
- 2. Rukhin A., Soto J., Nechvatal J., Smid M., Barker E., Leigh., Levenson M., Vangel M., Banks D., Heckert A., Dray J., Vo S. A statistical test suit for random and pseudorandom number generators for cryptographic applications. National Institute of Standards and Technology. Special Publications 800–22 revision 1a, 2010. 131 p.
- 3. Zadiraka V.K., Sergienko I.V., Kovalenko I.M., Andon P.I. Computer steganography. In the book: Alekseev V.A., Alishov N.I., Andon P.I., Anisimov A.V., Baran L.B., Belov V.M., Boyun V.P., Bulavatsky V.M., Bunin S.G., Valakh V.Ya. State and prospects of development of computer science in Ukraine [in Ukrainian]. Kyiv: Naukova Dumka, 2010. P. 736–747.
- 4. Pope M.B., Warkentin M., Bekkering E., Schmidt M.B. Digital steganography — an introduction to techniques and tools. Communication of the Association for Information Systems. 2012. Vol. 30. P. 347–366. https://doi.org/10.17705/.
- 5. Gujaraty D.N., Porter D.C. Basic econometrics. NY: Published by McGraw-Hill Companies, 2009. 946 p.
- 6. Geary R.C. Relative efficiency of count sign changes for assessing residual autoregression in least squares regression. Biometrika. 1970. Vol. 57, Iss. 1. P.123–127. https://doi.org/10.1016/ .
- 7. Swed F.S., Eisenhart C. Tables for testing randomness of grouping in a sequence of alternatives. Annals of Mathematical Statistics. 1943. Vol. 14, N 1. P.66–87. https://doi.org/ 10.1214/.
- 8. Masol V.I. A distribution of the number of l-steps in a random binary sequence subject to same constraints. Ukrainian Mathematical Journal. 1991. Vol. 43, N 9. P. 1110–1116. https:// doi.org/10.1007/.
- 9. Masol V., Popereshnyak S. Joint distribution of some statistics of random bit sequences. Cybernetics and Systems Analysis. 2021. Vol. 57, N 1. P. 139–145. https://doi.org/10.1007/.
- 10. Kartashov M.V. Probability, processes, statistics. Annual course for mathematicians and statisticians [in Ukrainian]. Kyiv: TViMS , 2004. 307 p.
