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Probability theory 1

Code: 61497
ECTS: 5.0
Lecturers in charge: prof. dr. sc. Hrvoje Šikić - Lectures
Lecturers: Ivan Biočić, mag. math. - Exercises
English level:

1,0,0

All teaching activities will be held in Croatian. However, foreign students in mixed groups will have the opportunity to attend additional office hours with the lecturer and teaching assistants in English to help master the course materials. Additionally, the lecturer will refer foreign students to the corresponding literature in English, as well as give them the possibility of taking the associated exams in English.
Load:

1. komponenta

Lecture typeTotal
Lectures 30
Exercises 15
* Load is given in academic hour (1 academic hour = 45 minutes)
Description:
COURSE AIMS AND OBJECTIVES: To prove the most important results of the classical probability theory using the approach of the measure theory.


COURSE DESCRIPTION AND SYLLABUS:
1. Random variables and their distribution functions.
2. Classification of random variables
3. Random vectors and their distribution functions. Classification of random vectors.
4. Probabilities on infinite dimensional spaces.
5. Mathematical expectation on the Lebesgue-Stieltjes integral.
6. Properties of mathematical expectation. The basic theorem about transformation of mathematical expectation.
7. Important inequalities in probability theory.
8. Convergence of random variables.
9. Integration on product spaces. Theorem Ionescu-Tulcea (without proof). Product of countably many probability spaces.
10. Independence of random variables; various characterizations.
11. Functions of random variables and random vectors. Applications in statistics.
12. Weak laws of large numbers.
13. Zero-one laws.
14. Convergence of series of random variables.
Literature:
  1. N. Sarapa: Teorija vjerojatnosti
  2. M. M. Rao: Probability Theory with Applications
  3. R. B. Ash: Real Analysis ad Probability
  4. R. Durret: Probability: Theory and Examples
3. semester
Mandatory course - Mandatory studij - Mathematical Statistics
Consultations schedule:

Content

Link to the course web page: https://web.math.pmf.unizg.hr/nastava/tv/index.php

Link to the notices web page: https://www.pmf.unizg.hr/math/predmet/teovje1