Zajedničke razdiobe slučajnih varijabli i primjene

undergraduate thesis

• Title (english): Joint probability distributions and applications
• Author: Dora Hećimović
• Mentor: Erna Begović Kovač (mentor)
• Committee member: Erna Begović Kovač (predsjednik povjerenstva)
• Committee member: Anita Šalić (član povjerenstva)
• Committee member: Andrej Vidak (član povjerenstva)
• Granter: University of Zagreb; Faculty of Chemical Engineering and Technology; Zagreb
• Defense date and country: 2022-09-23, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Svaki provedeni pokus daje neki ishod. Svakome se ishodu pokusa može pridružiti određena numerička vrijednost. Pravilo koje svakom pojedinom ishodu promatranog pokusa pridruži neki realni broj naziva se slučajna varijabla. Slučajna varijabla može biti diskretna (čije vrijednost čine konačan ili prebrojiv skup) ili kontinuirana (čije vrijednosti čine beskonačan ili neprebrojiv skup). Svaka slučajna varijabla ima svoju razdiobu vjerojatnosti, distribuciju vjerojatnosti, očekivanje, varijancu, standardnu derivaciju te mnoge druge statističke veličine. U ovom radu proučavamo pokuse u kojima istovremeno sudjeluje više slučajnih varijabli. Promatramo zajedničku funkciju gustoće vjerojatnosti te iz nje izvedene marginalne funkcije gustoće vjerojatnosti.

Abstract (english)

Every experiment gives an outcome, and each outcome can be represented by a number. A rule that assigns a real number to each individual outcome of the observed experiment is called a random variable. A random variable can be discrete (whit values from a finite or a countable set) or continuous (whit values from an infinite uncountable set). Each random variable has its probability, expectation, variance, standard deviation, and many other statistical quantities. In this paper we study the cases where more random variables are involved. We discuss the joint probability distribution and the related marginal probability distributions.

• Keywords: slučajna varijabla; očekivanje; varijanca; kovarijanca; koeficijent korelacije; zajednička funkcija gustoće vjerojatnosti; marginalna funkcija gustoće vjerojatnosti; centralni granični teorem
• Keywords (english): random variable; expected value; variance; covariance; correlation coefficient; joint probability distribution; marginal probability distribution; central limit theorem
• Language: croatian
• URN:NBN: urn:nbn:hr:149:643200
• Study programme: Title: Environmental Engineering - Undergraduate study; Study programme type: university; Study level: undergraduate; Academic / professional title: sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka ekoinženjerstva (sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka ekoinženjerstva)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Access restricted to students and staff of home institution
• Created on: 2023-02-24 08:13:07