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undergraduate thesis
Zakon velikih brojeva
2017. urn:nbn:hr:126:133697
Budetić, Mia
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Applied Mathematics and Computer Science
Computer Science and Machine Learning Research Group

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Budetić, M. (2017). Zakon velikih brojeva (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:133697

Budetić, Mia. "Zakon velikih brojeva." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2017. https://urn.nsk.hr/urn:nbn:hr:126:133697

Budetić, Mia. "Zakon velikih brojeva." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2017. https://urn.nsk.hr/urn:nbn:hr:126:133697

Budetić, M. (2017). 'Zakon velikih brojeva', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 13 April 2025, https://urn.nsk.hr/urn:nbn:hr:126:133697

Budetić M. Zakon velikih brojeva [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2017 [cited 2025 April 13] Available at: https://urn.nsk.hr/urn:nbn:hr:126:133697

M. Budetić, "Zakon velikih brojeva", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2017. Available at: https://urn.nsk.hr/urn:nbn:hr:126:133697

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Metadata
TitleZakon velikih brojeva
Title (english)Law of Large Numbers
AuthorMia Budetić
MentorSlobodan Jelić (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Applied Mathematics and Computer Science)
(Computer Science and Machine Learning Research Group)
Osijek
Defense date and country2017-09-27, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Probability Theory and Statistics
Abstract
U ovome radu bavit ćemo se uvjetima uz koje nizovi slučajnih varijabli konvergiraju, brzini i vjerojatnosti konvergencije. Najprije ćemo ponoviti osnovne pojmove iz vjerojatnosti, kao što su nezavisnost slučajnih varijabli, matematičko očekivanje i varijanca te Čebiševljeva nejednakost. Definirat ćemo nekoliko tipova konvergencije slučajnih varijabli, uvesti pojam mjere i integracije po mjeri, te u usporedbi s time, iskazati i dokazati metodom rezanja, Čebiševljev, Bernulijev i Hinčin teorem slabih zakona velikih brojeva. ˇ Analizirat ćemo nizove nezavisnih slučajnih varijabli koje imaju ” nula-jedan” svojstvo, Borelov i Kolmogorovljev teorem i uvesti pojmove repnih funkcija i repnih događaja. Zatim ćemo definirati empirijsku funkciju distribucije, proučavati konvergenciju redova slučajnih varijabli i dokazati Borelov, Kolmogorovljev, Chungov i Cantellijev jaki zakon velikih brojeva. Za kraj ćemo navesti osnovne teoreme potrebne za dokaz zakona ponovljenog logaritma.
Abstract (english)
In this paper we will talk about conditions in which sequence of random variables converge, convergence rate and convergence probability. At the beginning we will recall some of the basic terms of probability such as independence of random variables, mathematic expectation and variance and Cebısev inequality. We will define few types of convergence of random variables, introduce the term of measure and measure integration and, comparing with them, we will state and prove Cebısev, Bernoulli and Khinchin weak law theorem of large numbers by using cutting method. We will be analyzing sequence of independent random variables that have ”zero – one” characteristic, Borel and Kolmogorov theorem and introduce term of tail functions and tail events. Furthermore, we will define empirical function of distribution, study convergence of series of random variables and prove Borel, Kolmogorov, Chung and Cantelli strong law of large numbers. In the end, we will bring up basic theorems needed to prove the law of repeated logarithm.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:133697
Study programmeTitle: University undergraduate study programme in mathematics
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2017-10-27 10:49:19