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. 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.

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.

Mandatory course - Regular study - Mathematical Statistics