1. komponenta

Lecture type	Total
Lectures	45
Exercises	15

* Load is given in academic hour (1 academic hour = 45 minutes)

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.

1. Teorija vjerojatnosti, N. Sarapa, Školska knjiga, Zagreb, 2002.
2. Real Analysis ad Probability, R. B. Ash, Academic Press, New York, 1972.
3. Probability Theory with Applications, M. M. Rao, Academic Press, New York, 1984.
4. Probability: Theory and Examples, R. Durret, Wadsworth & Brooks, 1991.

Enrollment :
Attended : Probability theory 1

Examination :
Passed : Probability theory 1

Mandatory course - Regular study - Mathematical Statistics