### Probability and Statistics

#### Course Description

#### General Competencies

Students are trained to calculate the probabilities of events, characteristics of events related to concrete examples and defined random variables. For given samples of empiric data student are capable to estimate the different parameters of various distributions and test different kind of hypotheses. Students are introduced to basics of stochastic processes.

#### Learning Outcomes

- compute the probability of given event and the characteristic related to concrete example.
- recognize a characteristic distribution.
- manipulate with discrete and continuous random variables.
- manipulate with discrete and continuous random vectors.
- estimate the parameters of various distributions.
- apply testing hypotheses using the learned statistical tests.

#### Forms of Teaching

**Lectures**Lectures are organized through two cycles. The first cycle consists of 7 weeks of classes and mid-term exam, a second cycle of 6 weeks of classes and final exam. Classes are conducted through a total of 15 weeks with a weekly load of 4 hours.

**Exams**Mid-term exam in the 8th week of classes and final exam in the 15th week of classes.

**Exercises**The brief assessments will be held during the auditory exercises (up to 1 hour per week).

**Consultations**Consultations are held one hour weekly according to arrangement with students.

#### Grading Method

Continuous Assessment | Exam | |||||
---|---|---|---|---|---|---|

Type | Threshold | Percent of Grade | Threshold | Percent of Grade | ||

Quizzes | 0 % | 20 % | 0 % | 20 % | ||

Mid Term Exam: Written | 0 % | 40 % | 0 % | |||

Final Exam: Written | 0 % | 40 % | ||||

Exam: Written | 0 % | 80 % |

##### Comment:

The scores achieved on short tests will be transferred to the score of the exam only in the case when it is in the interest of the student.

#### Week by Week Schedule

- Sample space and events. Probability. Finite probability spaces. Finite equiprobable spaces.
- Infinite sample spaces. Uncountable uniform spaces.
- Conditional probability and independance. Bayes formula.
- Discrete random variables. Functions of discrete random variables. Expectation, moments and generating function. Discrete random vectors. Marginal distributions.
- Correlation coeficient. Covariance. Geometric distribution. Binomial distribution.
- Poisson distribution. Continuous random variables. Density and distribution functions.
- Functions of continuous random variable. Exponential distribution.
- Mid-term exam.
- Normal distribution.
- Continuous random vectors. Marginal distributions. Functions of random vectors. Conditional density and expectation.
- Law of large numbers. Central limit theorem. Gamma and beta functions. Gamma distribution. T-distribution. F-distribution.
- Basics of sample theory. Mean and median. Random sample of normal random variable. Point estimations. Maximum likelihood criterion. Interval estimations. Estimation of parametars of binomial distribution.
- Interval estimation of expectation. Interval estimation of variance. Confidance interval of binomial random variable. Kind of errors and test power. U-test. T-test. Theoretical and empirical distribution. Hi2 test.
- Stochastic processes. Finite-dimensional distributions. Classification of processes. Stationarity. Independence. Correlation functions. Poisson process. Construction of Poisson process. Sum and decomposition of Poissonovih processes. Birth and death process.
- Final exam.

#### Study Programmes

##### University undergraduate

#### Literature

*VJEROJATNOST I STATISTIKA, Diskretna vjerojatnost*, Element, Zagreb

*VJEROJATNOST I STATISTIKA, Slučajne varijable*, Element, Zagreb

*VJEROJATNOST I STATISTIKA, Matematička statistika, Stohastički procesi*, Element, Zagreb

*Uvod u matematičku statistiku*, Šk. knjiga, Zagreb

*Riješeni primjeri i zadaci iz teorije vjerojatnosti i statistike*, Šk. knjiga, Zagreb

#### Associate Lecturers

#### Exercises

#### General

**ID**86539

**5**ECTS

**L0**English Level

**L1**e-Learning

**60**Lectures

**15**Exercises

**0**Laboratory exercises

**0**Project laboratory

#### Grading System

**85**Excellent

**70**Very Good

**55**Good

**45**Acceptable