undergraduate thesis
Formula potpune vjerojatnosti i Bayesova formula

Matea Klarić (2016)
Metadata
TitleFormula potpune vjerojatnosti i Bayesova formula
AuthorMatea Klarić
Mentor(s)Dragana Jankov Maširević (thesis advisor)
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.
Keywordscomplete sample space conditional probability independent events formula of total probability Bayes' theorem
GranterSveučilište Josipa Jurja Strossmayera u Osijeku
Odjel za matematiku
Lower level organizational unitsZavod za teorijsku matematiku
Katedra za teoriju vjerojatnosti i matematičku statistiku
PlaceOsijek
StateCroatia
Scientific field, discipline, subdisciplineNATURAL SCIENCES
Mathematics
Probability Theory and Statistics
Study programme typeuniversity
Study levelundergraduate
Study programmeUniversity undergraduate study programme in mathematics
Academic title abbreviationuniv.bacc.math.
Genreundergraduate thesis
Language Croatian
Defense date2016-06
Parallel 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.
Parallel keywords (Croatian)potpun sustav dogadaja uvjetna vjerojatnost nezavisni dogadaji formula potpune vjerojatnosti Bayesova formula
Resource typetext
Access conditionOpen access
Terms of usehttp://creativecommons.org/licenses/by-nc-nd/3.0/hr/
URN:NBNhttps://urn.nsk.hr/urn:nbn:hr:126:538739
CommitterMirna Šušak Lukačević