Grafičko prikazivanje matematičkih funkcija gustoće jedne varijable u programskom jeziku Python

undergraduate thesis

• Title (english): Graphical representation of mathematical density functions of one variable in the Python programming language
• Author: Mihael Grmovšek
• Mentor: Mervan Pašić (mentor)
• Committee member: Mervan Pašić (predsjednik povjerenstva)
• Committee member: Tomislav Burić (član povjerenstva)
• Committee member: Lenka Mihoković (član povjerenstva)
• Granter: University of Zagreb; Faculty of Electrical Engineering and Computing; Zagreb
• Defense date and country: 2020-09-01, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Computing

Abstract

U ovom radu se razrađuje teorija vjerojatnosti. Kreće se od definicije vjerojatnosti, a zatim se opisuju vjerojatnosni prostori, nezavisnost događaja, Silvesterova formula, uvjetne vjerojatnosti, Bayesova formula te slučajne varijable prije definicija funkcija gustoće i funkcija razdiobe. Detaljno se opisuju svojstva funkcija razdiobe i funkcija gustoće te se navode područja primjene takvih funkcija. Također se navodi nekoliko najpoznatijih funkcija gustoće. U nastavku rad prezentira mogućnosti popularnih matematičkih alata kao što su GeoGebra i Wolfram|Alpha. Opisuju se njihove mogućnosti kod crtanja funkcija jedne varijable, a posebno se opisuju mogućnosti kod crtanja matematičkih funkcija gustoće jedne realne varijable. Na kraju se navode mogućnosti vlastitog programa, napravljenog u Pythonu pomoću biblioteka tkinter i pyglet, koji predstavlja primitivni grafički kalkulator.

Abstract (english)

In this paper, probability theory is described. Paper starts from the probability definition, and then describes the probability spaces, event independence, Sylvester's formula, conditional probabilities, Bayesian formula, and random variables before defining density functions and distribution functions. The properties of distribution functions and density functions are described in detail and the areas of application of such functions are stated. Several of the most well-known density functions are also listed. Furthermore, the paper presents the possibilities of popular mathematical tools such as GeoGebra and Wolfram|Alpha. Their possibilities of drawing the functions of single variable are described, and in particular the possibilities of drawing mathematical functions of density of one real variable are described. Finally, the possibilities of our own program, made in Python using the libraries tkinter and pyglet, which is a primitive graphing calculator, are listed.

• Keywords: teorija vjerojatnosti; slučajne varijable; funkcija gustoće; funkcija razdiobe; Python; tkinter; pyglet
• Keywords (english): probability theory; random variables; density function; distribution function; Python; tkinter; pyglet
• Language: croatian
• URN:NBN: urn:nbn:hr:168:186031
• Study programme: Title: Computing; Study programme type: university; Study level: undergraduate; Academic / professional title: sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva (sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Closed access
• Created on: 2023-01-14 08:52:15