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undergraduate thesis
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Characteristic Function
Matea Spajić (2015)
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics
Probability and Mathematical Statistics Research Group
Metadata
TitleKarakteristične funkcije
AuthorMatea Spajić
Mentor(s)Dragana Jankov Maširević (thesis advisor)
Abstract
Karakteristične funkcije slučajnih varijabli su važno sredstvo teorije vjerojatnosti zbog svojih značajnih svojstava. Svojstva koja imaju karakteristične funkcije su uve- like olakšala neke probleme teorije vjerojatnosti te ćemo ih zbog toga u ovom radu pobliže upoznati. Za početak ćemo se podsjetiti nekih osnovnih definicija i važnijih teorema koji ce nam pomoći da shvatimo što su to karakteristične funkcije. Nakon osnovnih pojmova denirati ćemo karakterističnu funkciju i njezina osnovna svojstva, te navesti dva najznačajnija teorema koja su pomogla da se rad s funkcijama distribu- cije prelaskom na karakteristične funkcije znatno olakša. Naposljetku ćemo izračunati karakteristične funkcije nekih specifičnih distribucija diskretnih i neprekidnih slučajnih varijabli.
KeywordsCharacteristic function random variable probability density function distribution function mathematical expectation
Parallel title (English)Characteristic Function
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
Lower level organizational unitsChair of Pure Mathematics
Probability and Mathematical Statistics 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 date2015-09-29
Parallel abstract (English)
Characteristic functions of random variables are basic tools of probability theory because of it's signicant properties which make problems in probability theory a lot easier. Because of it's signicance we will explain them more thoroughly. First of all we will recall some of the base denitions and theorems, which will help us to understand what characteristic functions are. After basic terms we will dene charac- teristic function and it's main properties. Furthermore we will introduce two of the most signicant theorems - Inversion theorem and Uniqueness theorem. Lastly we will also calculate characteristic functions of some specic distributions of random variables.
Parallel keywords (Croatian)Karakteristična funkcija slučajna varijabla funkcija gustoće funkcija distribucije ma- tematičko očekivanje
Resource typetext
Access conditionOpen access
Terms of usehttp://rightsstatements.org/vocab/InC/1.0/
URN:NBNhttps://urn.nsk.hr/urn:nbn:hr:126:764310