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Probability theory 2

Code: 61501
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. Strong laws of large numbers.
2. Definition and basic properties of characteristic functions.
3. Inversion theorem and its applications.
4. Characteristic functions of random vectors and applications.
5. Moments and characteristic functions.
6. Convolutions.
7. Weak convergence of probability measures.
8. Prokhorov theorem and applications.
9. Continuity theorem.
10. Bochner-Hintchin theorem.
11. Applications of characteristic functions in statistics.
12. Classical central limit theorem.
13. Lindeberg theorem.
14. Lindeberg-Feller theorem.
Literature:
  1. N. Sarapa: Teorija vjerojatnosti
  2. R. B. Ash: Real Analysis ad Probability
  3. M. M. Rao: Probability Theory with Applications
  4. R. Durret: Probability: Theory and Examples
Prerequisit for:
Enrollment :
Passed : Probability theory 1
4. semester
Mandatory course - Mandatory studij - Mathematical Statistics
Consultations schedule:

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