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undergraduate thesis
Konvergencija nizova slučajnih varijabli
2020. urn:nbn:hr:126:281964
Nedić, Magdalena
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics
Probability and Mathematical Statistics Research Group

Cite this document

Nedić, M. (2020). Konvergencija nizova slučajnih varijabli (Undergraduate thesis). Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:281964

Nedić, Magdalena. "Konvergencija nizova slučajnih varijabli." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. https://urn.nsk.hr/urn:nbn:hr:126:281964

Nedić, Magdalena. "Konvergencija nizova slučajnih varijabli." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. https://urn.nsk.hr/urn:nbn:hr:126:281964

Nedić, M. (2020). 'Konvergencija nizova slučajnih varijabli', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 25 June 2022, https://urn.nsk.hr/urn:nbn:hr:126:281964

Nedić M. Konvergencija nizova slučajnih varijabli [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2020 [cited 2022 June 25] Available at: https://urn.nsk.hr/urn:nbn:hr:126:281964

M. Nedić, "Konvergencija nizova slučajnih varijabli", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:126:281964

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Metadata
TitleKonvergencija nizova slučajnih varijabli
Title (english)Convergence of Sequences of a Random Variables
AuthorMagdalena Nedić
MentorDragana Jankov Maširević (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Pure Mathematics)
(Probability and Mathematical Statistics Research Group)
Osijek
Defense date and country2020-09-25, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Probability Theory and Statistics
Abstract
U ovom radu obrađen je dio teorije vjerojatnosti vezan uz konvergenciju nizova slučajnih varijabli, poznat i kao stohastička konvergencija. Riječ je o četiri tipa konvergencije, a to su: konvergencija po distribuciji, konvergencija po vjerojatnosti, konvergencija u srednjem reda p i konvergencija gotovo sigurno. Svaki tip konvergencije detaljno je objašnjen i precizno definiran te su navedeni nužni i dovoljni uvjeti za određivanje konvergencije niza slučajnih varijabli. Također, navedeni rezultati su popraćeni ilustrativnim primjerima ili nekim praktičnim primjenama. Neki od tih primjena su važni rezultati u teoriji vjerojatnosti, kao što su: slabi zakon velikih brojeva, jaki zakon velikih brojeva, centralni granični teorem i slično. Naglasak je stavljen i na veze među pojedinim tipovima konvergencije te na konvergenciju transformirane neprekidne slučajne varijable. Za kraj je važno napomenuti i da je svaki tip konvergencije generaliziran i na primjeru slučajnog vektora.
Abstract (english)
In this paper we deal with a part of probability theory related to the convergence of sequences of random variables. There is four types of convergence, and they are: convergence in distribution, convergence in probability, convergence in mean and almost sure convergence. Each type of convergence is explained in detail and for each type the accompanying theorems and propositions necessary for determining convergence are attached. Also, everything is accompanied by illustrative examples or some practical applications. Some of these applications are important results in probability theory, such as: weak law of large numbers, strong law of large numbers, central limit theorem, etc. Emphasis is also placed on the relationships between individual types of convergence and on the convergence of the transformed continuous random variable. Finally, it is important to note that each type of convergence is generalized on the example of a random vector.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:281964
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 on2020-10-27 10:43:04