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undergraduate thesis
Slučajni vektor
2020. urn:nbn:hr:126:934262
Kopić, Katarina
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

Kopić, K. (2020). Slučajni vektor (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:934262

Kopić, Katarina. "Slučajni vektor." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. https://urn.nsk.hr/urn:nbn:hr:126:934262

Kopić, Katarina. "Slučajni vektor." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. https://urn.nsk.hr/urn:nbn:hr:126:934262

Kopić, K. (2020). 'Slučajni vektor', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 10 November 2024, https://urn.nsk.hr/urn:nbn:hr:126:934262

Kopić K. Slučajni vektor [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2020 [cited 2024 November 10] Available at: https://urn.nsk.hr/urn:nbn:hr:126:934262

K. Kopić, "Slučajni vektor", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:126:934262

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Metadata
TitleSlučajni vektor
Title (english)Random Vector
AuthorKatarina Kopić
MentorDragana Jankov Maširević (mentor)
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 country2020-09-25, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Probability Theory and Statistics
Abstract
U ovome radu ćemo generalizirati pojam slučajne varijable na n-dimenzionalan prostor, odnosno promatrat ćemo slučajni vektor. Poznato je da slučajnu varijablu možemo u potpunosti opisati pomoću njezine funkcije distribucije, a također ćemo pomoću odgovarajućeg oblika funkcije distribucije opisati i slučajni vektor te pokazati svojstva navedene funkcije. Definirat ćemo posebno diskretan te posebno neprekidan slučajni vektor i promotriti njihova svojstva. Pogledat ćemo kako zadati diskretan slučajni vektor pomoću tablice distribucije te kako definirati marginalne distribucije. Također ćemo se osvrnuti na zadavanje neprekidnog slučajnog vektora te ćemo definirati marginalne gustoće. Na kraju rada ćemo se baviti numeričkim karakteristikama slučajnog vektora, od kojih su među važnijima očekivanje i kovarijanca te ćemo definirati kovarijacijsku matricu i korelacijsku matricu koje se u praksi često koriste.
Abstract (english)
In the following paper we generalize the notion of a random variable to an n-dimensional space, observing a random vector. Based on the notion that a random variable can be fully described using its distribution function, we use a distribution function to describe a random vector and observe its properties. We separately define a discrete and a continuous random vector and focus on their properties. In addition, we consider the assignment of a discrete random vector using a distribution table and the definition of marginal distributions. Furthermore, we look at how continuous random vectors can be assigned, and how marginal densities can be defined. The paper concludes with numerical characteristics of a random vector, most importantly the expectation and covariance as well as definitions of a covariance matrix and a correlation matrix often used in practice.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:934262
Study programmeTitle: Bachelor of Mathematics and Computer Science
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike i računarstva (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike i računarstva)
Type of resourceText
File originBorn digital
Access conditionsOpen access
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Created on2020-10-27 10:35:46