Courses – Fakultet tehničkih nauka u Novom Sadu

Subject: Mathematical Statistics (17.GI404)

Type of studies	Title
Undergraduate Academic Studies	Civil Engineering (Year: 2, Semester: Winter)

General information:

Category	Theoretical-methodological
Scientific or art field	Teorijska i primenjena matematika
ECTS	4

Enabling students for abstract thinking and acquiring fundamental knowledge in the field of probability and mathematical statistics. Course objective is to develop a special manner of students` thinking in studying mass phenomena in the field of construction – hydraulics. Course character is applicative, hence the significance is placed on the knowledge that can explain the quantitative approach to problems in the field of study. Furthermore, students are becoming capable of using a statistics programme. The aim is to enable students to know how to select adequate statistic methods, elaborate a statistic analysis and explain its essence. This knowledge is the foundation for better understanding of professional literature and successful improvement in the studies.

Acquired knowledge should be used by students in further education and in professional courses to make and solve mathematical models using the knowledge from this course by adopting theoretical knowledge in the field of probability and mathematical statistics presented in this course, as well as skills for calculating and interpreting final statistic indicators.

Theoretical course: Probability: Probability axioms. Conditional probability. Bayes` theorem. Random variable of discrete and continual type. Random vector of discrete and continual type and common distribution. Conditional distributions. Transformation of random variables. Mathematical expectations. Variation and standard deviation. Moments. Co-variation, correlation coefficient. Conditional expectations. Laws on large numbers. Central border theorems. Correlation and regression; linear regression. Sample distribution, mean value and dispersion. Statistics: basic notions. Population, sample. Statistics. Descriptive statistic analysis (basic notions, data acquisition, table and graphic data presentation, data analysis by descriptive statistic methods, programme support for static analysis). Evaluation of unknown parameters (Dot evaluations: moment methods and maximal reliability method. Interval evaluation.). Parameter and non-parameter hypothesis and tests. Practice classes: At practice, student do adequate examples from the theoretical classes to practice the presented course content, so that practice help the understanding of the presented content.

Lectures. Numerical calculation and computer practice. Tutorials. Lectures are performed in a combined manner. At lectures, students are presented with the theoretical part of the course content followed by characteristic examples for easier understanding. At practice, that follow the lectures, students do characteristic exercises and widen the course content from the lectures. At computer practice, using the statistic programme, students do the processing of the obtained results. Apart from lectures and practice, there are regular tutorials. A part of the content that makes a logical unit can be taken during the teaching process in the form of 2 modules (first module: Probability, second module: Statistics).

Authors	Title	Year	Publisher	Language

Course activity	Pre-examination	Obligations	Number of points
Lecture attendance	Yes	Yes	2.00
Final exam - part two	No	No	50.00
Exercise attendance	Yes	Yes	3.00
Test	Yes	Yes	10.00
Test	Yes	Yes	10.00
Complex exercises	Yes	Yes	15.00
Test	Yes	Yes	10.00
Written part of the exam - tasks and theory	No	Yes	50.00
Final exam - part one	No	No	50.00