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undergraduate thesis
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Central Limit Theorem
Daria Solić (2017)
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Applied Mathematics
Computer Science Research Group
Metadata
TitleCentralni granični teorem
AuthorDaria Solić
Mentor(s)Slobodan Jelić (thesis advisor)
Abstract
U ovom radu se analiziraju osnovni pojmovi iz teorije vjerojatnosti, kao što su vjerojatnosni prostor, slučajna varijabla i Bernoullijeva distribucija, a koji su potrebni za iskazivanje i dokazivanje centralnog graničnog teorema. Iskazat će se klasični centralni granični teoremi koji su se pojavljivali kroz povijest i kojima su znanstvenici postupno dolazili do općeg centralnog graničnog teorema. Nadalje, analizirati će se i uniformna konvergencija u centralnom graničnom teoremu, karakteristična funkcija, infinitezimalni sistem te još neki pojmovi. Konačno, iskazat će se i dokazati opći centralni granični teorem.
Keywordsprobability space random variable Bernoulli’s scheme convergence by distribution characteristic function infinitesimal system de Moivre Laplace’s theorem central limit theorem
Parallel title (English)Central Limit Theorem
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
Lower level organizational unitsChair of Applied Mathematics
Computer Science Research Group
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 date2017-09-27
Parallel abstract (English)
This paper will reiterate the basic concepts of the probability theory such as probability space, random variable and Bernoulli’s distribution that are needed to demonstrate and prove central limit theorem. It will analyze classical central limit theorems which scientists used throughout history that helped them to discover general theory of central limit theorem. It will also analyze characteristic function, infinitesimal system, uniform convergence in central limit theorem and other concepts. Finally, it will show and prove general central limit theorem.
Parallel keywords (Croatian)vjerojatnosni prostor slučajna varijabla Bernoullijeva shema konvergencija po distribuciji karakteristična funkcija infinitezimalni sistem de Moivre Laplaceov teorem centralni granični teorem
Resource typetext
Access conditionOpen access
Terms of usehttp://rightsstatements.org/vocab/InC/1.0/
URN:NBNhttps://urn.nsk.hr/urn:nbn:hr:126:585736