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undergraduate thesis
Formula potpune vjerojatnosti i Bayesova formula
2016. urn:nbn:hr:126:538739
Klarić, Matea
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics and Mathematics Teaching
Probability, Mathematical Statistics and Data Science Research Group

Cite this document

Klarić, M. (2016). Formula potpune vjerojatnosti i Bayesova formula (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:538739

Klarić, Matea. "Formula potpune vjerojatnosti i Bayesova formula." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2016. https://urn.nsk.hr/urn:nbn:hr:126:538739

Klarić, Matea. "Formula potpune vjerojatnosti i Bayesova formula." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2016. https://urn.nsk.hr/urn:nbn:hr:126:538739

Klarić, M. (2016). 'Formula potpune vjerojatnosti i Bayesova formula', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 15 January 2025, https://urn.nsk.hr/urn:nbn:hr:126:538739

Klarić M. Formula potpune vjerojatnosti i Bayesova formula [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2016 [cited 2025 January 15] Available at: https://urn.nsk.hr/urn:nbn:hr:126:538739

M. Klarić, "Formula potpune vjerojatnosti i Bayesova formula", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2016. Available at: https://urn.nsk.hr/urn:nbn:hr:126:538739

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Metadata
TitleFormula potpune vjerojatnosti i Bayesova formula
AuthorMatea Klarić
MentorDragana Jankov Maširević (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Pure Mathematics and Mathematics Teaching)
(Probability, Mathematical Statistics and Data Science Research Group)
Osijek
Defense date and country2016-06, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Probability Theory and Statistics
Abstract
Uvjetna vjerojatnost je vjerojatnost u kojoj kao dodatnu informaciju imamo da se određeni događaj realizirao. Za takvu vrstu vjerojatnosti, odnosno vjerojatnost da se dogodio događaj A ako znamo da se realizirao događaj B, koristimo oznaku P(A\left | B) ili P_{B}(A). Nadalje, formula potpune vjerojatnosti se dobije: 1. podjelom prostora događaja na nekoliko disjunktnih događaja koji u uniji čine cijeli taj prostor, 2. računajući vjerojatnost događaja koji se realizirao uz opisane disjunktne događaje kao uvjete. Promatranje vjerojatnosti u drugom smjeru je moguće pomoću Bayesove formule. Ona služi za računanje vjerojatnosti realizacije događaja iz prethodno opisane podjele uz informaciju o tome koji se događaj dogodio nakon izvođenja pokusa. U razumijevanju suštine Bayesovog teorema bitno je prepoznati potrebnu podjelu (particiju) skupa svih događaja, pri čemu se dodatna informacija o ishodu pokusa odnosi na neki određeni događaj iz te podjele.
Abstract (english)
Conditional probability is a probability where the additional information is that certain event has been realized. For such kind of probability, i.e. the probability that event A happened if we know that event B has been realized, the symbol P(A\left | B) or P_{B}(A) is used. Furthermore, the formula of total probability is derived by: 1. dividing the space of events on several disjunct events that in union make up that whole space, 2. counting the probability of the event that has been realised with the described disjunct events as conditions. Counting probability in the opposite direction is possible by using of Bayes' formula. Such formula is used for probability of event realisation from the previously described partition, with information about which event happened after the experiment has been performed. In understanding the essence of Bayes' theorem it is important to recognize the required partition of the set of all events whereby the additional information refers to a certain event from that partition.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:538739
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
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Created on2016-06-09 11:03:41