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### Probability

 Code: 36905 ECTS: 7.0 Lecturers in charge: doc. dr. sc. Snježana Lubura Strunjak doc. dr. sc. Hrvoje Planinić Lecturers: Adrian Beker - Exercises Nikola Grubišić , 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.

### 1. komponenta

Lecture typeTotal
Lectures 45
Exercises 30
Description:
COURSE AIMS AND OBJECTIVES: To introduce students to the basic notions of probability theory.

COURSE DESCRIPTION AND SYLLABUS:
1. Basic probability notions. Events, sample space, probability, etc. (3 hours)
2. Discrete probability space. Finite case. Laplace model. Countable case. Elements of combinatorics. (2 hours)
3. Geometric probability. (2 hours)
4. Conditional probability. Independence. Bayes formula. Borel 0-1 law. (2 hours)
5. Repeated trials. Product space. Independent case and conditioned case. (3 hours)
6. Bernoulli trials. Binomial distribution. Discrete distributions. Poisson and Moivre-Laplace theorems. (6 hours)
7. Discrete random variables. Distribution functions, density. Multidimensional case. Independent variables. Basic formulas. Expectation, variance, Čebišev inequality, and related concepts. Convergence. Weak and strong laws of large numbers. (9 hours)
8. Continuous random variables. Examples, density functions, expectations, and other basic concepts. Multidimensional case. Emphasis is on basic examples: Gaussian (normal), gamma, Chi-square distribution, Fisher, etc. Central limit theorem (no proofs) with applications. Conditional density. (12 hours)
9. Poisson process. (3 hours)
Literature:
1. J. Pitman: Probability
2. N. Sarapa: Teorija vjerojatnosti
3. W. Feller: An Introduction to Probability Theory and its Applications I
Prerequisit for:
Enrollment :
Passed : Mathematical analysis 2
 3. semester Mandatory course - Regular study - Mathematics
Consultations schedule:

### Content

Link to the course former web page: https://web.math.pmf.unizg.hr/nastava/vjer/

Student demonstrators: Borna Šimić (e-mail: bornsimi@student.math.hr )

Tea Arvaj (e-mail: teaarva@student.math.hr )