Courses – Fakultet tehničkih nauka u Novom Sadu

Subject: Probability and mathematical statistics (17.GI303B)

Native organizations units: Department of Fundamentals Sciences

Type of studies	Title

General information:

Category	Academic-general educative
Scientific or art field	Teorijska i primenjena matematika
Interdisciplinary	Yes
ECTS	4

Educational goal:

Enabling students in abstract thinking and acquiring basic knowledge in the field of probability and mathematical statistics. The objective is to develop a special form of thinking with students when researching mass phenomena in the field of civil engineering – hydraulics. Course character is applicative; hence the significance is on the knowledge that can explain the quantitative approach to problems in this field of studies. Also, students will be able to use a statistic programme. The objective is to enable students to be able to select adequate statistic methods, to elaborate a statistic analysis and to explain it with understanding. This knowledge is the foundation for better understanding of the professional literature and for successful improvements in their studies.

Educational outcome:

Acquired knowledge should be used by students in further education, and in professional courses, to create and solve mathematical models using the knowledge acquired in this course. Mastering theoretical knowledge in the field of probability and mathematical statistics learnt at this course, as well as mastering the skill of calculating and explaining the obtained statistic indicators.

Course content:

Theoretical classes: Probability: Probability axioms. Conditional probabilities. Bayes` formula. Random variable of discrete and continual type. Random vector of discrete and continual type and common classification. Conditional divisions. Transformation of random variables. Mathematical expectations. Variance and standard deviation. Moments. Covariance, correlation coefficient. Conditional expectations. Laws on great numbers. Central limit theorems. Correlation and regression, linear regression. Sample distribution, mean value and dispersion. Statistics: basic notions. Population, sample. Statistics. Descriptive statistic analysis (basic notions, data arrangement, table and graphic data presentation, data analysis using descriptive statistic methods, programme support for statistic analysis). Evaluation of unknown parameters (Dot evaluation: momentum method and maximal credibility method. Interval evaluation). Parameter and non-parameter hypotheses and tests. Practical classes (practice): At practice, adequate examples from theoretical classes are presented in order to practice the course content and hence contribute to better understanding.

Teaching methods:

Lectures. Numerical /computing and computer practice. Consultations. Lectures are held in a combined manner. At lectures, theoretical part of the course content is presented, and supplemented by characteristic examples for easier understanding. At practice that follow the lectures, characteristic exercises are solved and the course content is explained in more detail. At computer practice, the obtained data processing is performed using a statistic programme. Apart from lectures and practice, consultations are held regularly. A part of the course content that makes a logical unit can be taken during the teaching process in the form of two modules (First module: Probability, second module: Statistics).

Literature:

Authors	Title	Year	Publisher	Language
Stojaković, M.	Matematička statistika	2000	Fakultet tehničkih nauka, Novi Sad	Serbian language
Grupa autora	Zbirka rešenih zadataka iz verovatnoće i statistike	2009	Fakultet tehničkih nauka, Novi Sad	Serbian language
Grbić, T., Nedović, Lj.	Zbirka odabranih rešenih ispitnih zadataka iz verovatnoće, statistike i slučajnih procesa	2016	Fakultet tehničkih nauka, Novi Sad	Serbian language