1. komponenta

Lecture type	Total
Lectures	45

COURSE AIMS AND OBJECTIVES: To acquaint students with the fundamental results and ideas of probability theory. To train students to be able to understand and follow contemporary literature in statistics and data science

COURSE DESCRIPTION AND SYLLABUS:
1. Introduction. Sigma algebra and rings
2. Measure and probability
3. Integrals and moments of random variables
4. Distribution of random variables and vectors.
5. Convergence of moments. Moment generating function
6. Borel-Cantelli lemma and Kolmogorov 0-1 law.
7. Weak law of large numbers
8. Strong law of large numbers.
9. Convergence in distribution. Coupling
10. Convergence towards Poisson distribution
11. Convergence towards normal distribution
12. Extensions and examples of central limit theorem
13. Cramer-Wold device
14. Introduction to large deviations theory
15. Examples and applications

1. Probability and measure, Billingsley, Patrick, John Wiley & Sons, 2008.
2. Teorija vjerojatnosti, Sarapa, Nikola, Školska knjiga, 2002.
3. Probability: an introduction, Grimmett, Geoffrey, and Dominic Welsh, Oxford University Press, 2014.
4. Probability: theory and examples. Vol. 49., Durrett, Rick, Cambridge university press, 2019.
5. Foundations of modern probability. 3rd edition, Kallenberg, Olav, Springer, 2021.

Izborni modul C - Znanost o podacima, 1. godina - Regular study - Computer Science and Mathematics
Ostali izborni predmeti - Regular study - Computer Science and Mathematics

Izborni modul C - Znanost o podacima, 1. godina - Regular study - Computer Science and Mathematics
Ostali izborni predmeti - Regular study - Computer Science and Mathematics

Ostali izborni predmeti - Regular study - Computer Science and Mathematics

Ostali izborni predmeti - Regular study - Computer Science and Mathematics