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undergraduate thesis
Transformacije diskretnih i neprekidnih slučajnih varijabli
2017. urn:nbn:hr:126:085903
Krajnović, Maja
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics and Mathematics Teaching
Probability, Mathematical Statistics and Data Science Research Group

Cite this document

Krajnović, M. (2017). Transformacije diskretnih i neprekidnih slučajnih varijabli (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:085903

Krajnović, Maja. "Transformacije diskretnih i neprekidnih slučajnih varijabli." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2017. https://urn.nsk.hr/urn:nbn:hr:126:085903

Krajnović, Maja. "Transformacije diskretnih i neprekidnih slučajnih varijabli." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2017. https://urn.nsk.hr/urn:nbn:hr:126:085903

Krajnović, M. (2017). 'Transformacije diskretnih i neprekidnih slučajnih varijabli', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 08 April 2025, https://urn.nsk.hr/urn:nbn:hr:126:085903

Krajnović M. Transformacije diskretnih i neprekidnih slučajnih varijabli [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2017 [cited 2025 April 08] Available at: https://urn.nsk.hr/urn:nbn:hr:126:085903

M. Krajnović, "Transformacije diskretnih i neprekidnih slučajnih varijabli", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2017. Available at: https://urn.nsk.hr/urn:nbn:hr:126:085903

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Metadata
TitleTransformacije diskretnih i neprekidnih slučajnih varijabli
Title (english)Transformations of Discrete and Continuous Random Variables
AuthorMaja Krajnović
MentorNenad Šuvak (mentor)
MentorDragana Jankov Maširević (komentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Pure Mathematics and Mathematics Teaching)
(Probability, Mathematical Statistics and Data Science Research Group)
Osijek
Defense date and country2017-09-29, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Probability Theory and Statistics
Abstract
Transformacije slučajnih varijabli vrlo su bitne u teoriji vjerojatnosti jer nam omogućavaju lakše rješavanje različitih vjerojatnosnih problema. U ovom radu ćemo se prvo upoznati s nekim osnovnim pojmovima, definicijama i teoremima kako bismo mogli shvatiti što su i čemu služe transformacije slučajnih varijabli. Vidjet ćemo da sva vjerojatnosna svojstva slučajne varijable X možemo opisati pomoću njene funkcije distribucije F, odnosno pomoću njene tablice distribucije ako je X diskretna te pomoću funkcije gustoće ako je X neprekidna slučajna varijabla. Nadalje, zanimat će nas kako pronaći distribuciju nove slučajne varijable Y = g(X) ako poznajemo distribuciju slučajne varijable X i funkciju g. To je problem kojim ćemo se baviti u ovom radu. Takoder ćemo pokazati da čak i jednostavne transformacije slučajnih varijabli s jednostavnim distribucijama mogu dovesti do slučajnih varijabli sa složenim distribucijama pa ćemo probleme rješavati u raznim specijalnim slučajevima. Prvo ćemo proučiti transformacije koje možemo primijeniti i na diskretne i neprekidne slučajne varijable, a zatim ćemo razmotriti i one transformacije koje su karakteristične samo za jedan tip slučajnih varijabli.
Abstract (english)
Transformations of random variables are very important in probability theory because they allow us to solve various probability problems. First of all, we will recall some of the basic terms, definitions and theorems which will help us to understand what the transformations of random variables are. We will also see that all properties of a random variable X can be described by its distribution function F, i.e. using its distribution table if X is discrete and using its density function when X is a continuous random variable. Furthermore, we are interested in finding distribution of new random variable Y = g(X) if we know distribution of random variable X and function g. This is the problem that we are going to deal with in this paper. As we will see, even simple transformations of random variables, with simple distributions, can lead to a random variables with complex distributions so we will solve the problem in various special cases. First, we will examine the transformations that can be applied to the discrete and continuous random variables, then we will consider those transformations which can be applied only on one type of random variables.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:085903
Study programmeTitle: 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 resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2017-10-23 07:17:16