Formula potpune vjerojatnosti i Bayesova formula

Klarić, Matea

undergraduate thesis

Formula potpune vjerojatnosti i Bayesova formula

Klarić, Matea (2016)

Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics
Probability and Mathematical Statistics Research Group

Cite this document

APA 6th Edition

Klarić, M. (2016). Formula potpune vjerojatnosti i Bayesova formula (Undergraduate thesis). Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:538739

MLA 8th Edition

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

Chicago 17th Edition

Harvard

Klarić, M. (2016). 'Formula potpune vjerojatnosti i Bayesova formula', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 14 July 2020, https://urn.nsk.hr/urn:nbn:hr:126:538739

Vancouver

Klarić M. Formula potpune vjerojatnosti i Bayesova formula [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2016 [cited 2020 July 14] Available at: https://urn.nsk.hr/urn:nbn:hr:126:538739

IEEE

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

Cite this item: https://urn.nsk.hr/urn:nbn:hr:126:538739

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Metadata

Title	Formula potpune vjerojatnosti i Bayesova formula
Author	Matea Klarić
Mentor	Dragana Jankov Maširević (mentor)
Granter	Josip Juraj Strossmayer University of Osijek Department of Mathematics (Chair of Pure Mathematics) (Probability and Mathematical Statistics Research Group) Osijek
Defense date and country	2016-06, 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)
Language	croatian
URN:NBN	urn:nbn:hr:126:538739
Study programme	Title: 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 resource	Text
File origin	Born digital
Access conditions	Open access
Terms of use
Created on	2016-06-09 11:03:41