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master's thesis
Problem urni
Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. urn:nbn:hr:126:554909
Solić, Daria
Josip Juraj Strossmayer University of Osijek
Department of Mathematics

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Solić, D. (2020). Problem urni (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:554909

Solić, Daria. "Problem urni." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. https://urn.nsk.hr/urn:nbn:hr:126:554909

Solić, Daria. "Problem urni." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. https://urn.nsk.hr/urn:nbn:hr:126:554909

Solić, D. (2020). 'Problem urni', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 09 November 2024, https://urn.nsk.hr/urn:nbn:hr:126:554909

Solić D. Problem urni [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2020 [cited 2024 November 09] Available at: https://urn.nsk.hr/urn:nbn:hr:126:554909

D. Solić, "Problem urni", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:126:554909

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Metadata
TitleProblem urni
Title (english)Urn Problem
AuthorDaria Solić
MentorNenad Šuvak (mentor)
Committee memberMirta Benšić (predsjednik povjerenstva)
Committee memberNenad Šuvak (član povjerenstva)
Committee memberDragana Jankov Maširević (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
Osijek
Defense date and country2020-01-21, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu bavili smo se modelima urni koji su vrlo stari te se spominju još u Starom zavjetu židovskoj teologiji. Imaju bezbroj primjena u ekonomiji, industriji, tehnologiji, bioznanostima i zdravstvu. Kako je cilj rada bio modelirati određene modele urni Markovljevim lancima najprije smo naveli osnovne tvrdnje vezane za njih. Detaljno smo opisali Ehrenfestov i Bernoulli-Laplaceov model urni preko Markovljevih lanaca, naveli njihove primjene i dali povijesni pregled. Za kraj rekli smo nešto o urnama u bioznanosti, konkretno u evoluciji vrsta opisujući WrightFisherov model sa i bez selekcije, spola i mutacije preko Markovljevih lanaca.
Abstract (english)
In this diploma thesis we are dealing with urn models, very old models mentioned in Old Testament and Jewish theology. Urn models have countless ways of applications in economy, industry, technology, biosciences and various disciplines regarding health. The aim of the papper is to model some urn models via Markov chains so we first stated the basic results regarding the theory of Markov chains. Ehrenfest urn model and Bernoulli-Laplaces urn model are described in details in this paper through Markov chains, and also we have described their applications and historical overview. Finally, we introduced urn models in biosciences, specifically in the evolution of species by describing Wright-Fisher model with and without selection, sex and mutations through Markov chains.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:554909
Study programmeTitle: Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Course: Financial and Statistical Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
RepositoryRepository of School of Applied Mathematics and Informatics
Created on2020-01-29 08:05:31