1. Bayes' theorem
- Author
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Peša, Valerija, Dražić, Ivan, and Sučić, Viktor
- Subjects
law of total probability ,Bayes' theorem ,classical definition of probability ,probability axioms ,simple events ,event space ,event ,hypotheses ,conditional probability ,sample space ,independent events - Abstract
U završnom radu definirane su osnove vjerojatnosti koje čine temelj Bayesovu teoremu. Pojašnjene su operacije na prostoru događaja i De Morganov zakon. Definirani su aksiomi vjerojatnosti, klasična definicija vjerojatnosti te svojstva vjerojatnosti. Uvjetna vjerojatnost i nezavisni događaji objašnjeni su matematičkom definicijom i svojstvima, te primjenom u primjerima. Pokazani su potpun sustav događaja i zakon potpune vjerojatnosti, te njihova primjena. Objašnjenje Bayesova teorema dano je matematičkom definicijom i raznim primjerima koji opisuju njegovu praktičnu primjenu., In final thesis there are defined basis of probability that are foundation of Bayes' theorem. There are explained operations on sample space and De Morgan's law. Probability axioms, probability space and classical definition of probability are defined. Conditional probability and indepedent events are clarified with its mathematical definition and properties, as well as its application in examples. Sample space, and law of total probability are illustrated and applied. Explenation of Bayes' theorem is given with mathematical defiinition and various examples that describe its practical application.
- Published
- 2022