Courses – Fakultet tehničkih nauka u Novom Sadu

Subject: Theory of Probability and Statistics (17.IM1012)

Native organizations units: Department of Fundamentals Sciences, Chair of Mathematics

Type of studies	Title
Undergraduate Academic Studies	Production Engineering (Year: 4, Semester: Winter)

General information:

Category	Academic-general educative
Scientific or art field	Teorijska i primenjena matematika
ECTS	5

Enabling students for abstract thinking and acquisition of basic knowledge in the field of Probability and Mathematical Statistics. The course objective is to develop special way of thinking in students while studying massive phenomena in the field of environmental engineering. The course character is applicational and the importance is given to the knowledge which can explain quantitative approach to the issues from the field of study. Students are also able to use statistical programs. The objective is to enable students to choose adequate statistical methods, to do statistical analysis and to essentially elaborate it. This knowledge is the foundation for better understanding of the professional literature and for successful advancement in studies.

The student should use acquired knowledge in further education and in professional courses. He/she can make and solve mathematical models using the knowledge acquired in this course. Mastering theoretical knowledge in the field of probability and mathematical statistics studied in this course and skills of calculating and analyzing calculated statistical indicators.

Theoretical lectures: Probability: Axioms of probability. Conditional probability. Bayes formula. Random variable of discrete and continuous type. Random vector of discrete type and common distribution. Conditional distribution. Transformation of random variables. Mathematical expectation. The variance and standard deviation. Moments. Covariance, correlation coefficient. Conditional expectations. Large numbers law. Central limit and linear theorem. Correlation and linear regression. Sample distribution, the mean value and dispersion. Statistics: basic concepts. Population, sample. Statistics. Descriptive statistical analysis (basic concepts, data editing, table and graphic presentation of data, data analysis using methods of descriptive statistics, software support to statistical analysis). Assessment of unknown parameters (point assessment: The method of moments and maximum likelihood method. Interval rates). Parametric and nonparametric hypothesis and tests. Practical lecture (practice): During the lectures adequate examples from theoretical lectures are done, thus practicing the knowledge and contributing to the better understanding of the lectured knowledge.

Lectures: Numerical computing practice, computer practice. Consultations. Lectures are combined. During the lectures theoretical part of the course followed by characteristic examples are presented for better understanding of the lectured material. During the practice, which accompanies lectures, typical problems are solved and the knowledge from the lectures is deepened. During the computer practice processing of obtained data is done using the statistical software. Besides lectures and practice, consultations are held on a regular basis. A part of the course, which represents a logical whole, can be taken during the teaching process in the form of the next two modules (the first module: Probability; the second module: Statistics. In order to take the final examination, the student has to complete computer practice.

Authors	Title	Year	Publisher	Language
Ash R. B.	Basic probability theory	1970	John Wiley & Sons, New York	English
Faber M. H.	Statistics and Probability Theory	2012	Springer, Dordrecht	English

Course activity	Pre-examination	Obligations	Number of points
Coloquium exam	No	No	20.00
Lecture attendance	Yes	Yes	5.00
Theoretical part of the exam	No	Yes	30.00
Practical part of the exam - tasks	No	Yes	40.00
Test	Yes	Yes	20.00
Exercise attendance	Yes	Yes	5.00
Coloquium exam	No	No	20.00