Infopaket

Probability theory and mathematics statistics

ОК 16.

Обов’язкова дисципліна для ОП

First

2022/2023

3 Semester

3

1. Classical, statistical and geometric definition of probability. Repeated trials, random variables and distribution functions. Statistical estimates of distribution parameters, possibilities of testing statistical hypotheses. Elements of correlation and regression analysis PR02 PR07. Basic theorems of probability theory. Numerical characteristics of random variables, law of large numbers. Statistical sample distributions. Numerical characteristics of statistical material PR02 PR07 PR09 2. Formulate the subject and tasks of probability theory and mathematical statistics. Define and prove the main theorems of the theory of probabilities PR02 PR07. Conduct statistical distributions of samples. Develop numerical characteristics of statistical material. Carry out statistical evaluations of distribution parameters. Apply elements of correlation and regression analysis when solving applied tasks in the field of cartography and GIS PR02 PR07 PR09. 3. and 4. PR02 PR09

Full-time form

Knowledge of school mathematics at the secondary school level, successful study of the discipline "Higher Mathematics".

The program of this educational discipline is aimed at studying the basic concepts of combinatorics, the basics of probability theories, the theory of estimating unknown parameters, statistical hypothesis testing, elements of correlation-regression analysis, methods, theorems and formulas of probability theory and mathematical statistics. The functional block of the discipline involves mastering such components as the ability to apply knowledge of probability theory and mathematical statistics in the field of cartographic research, geographic information systems, and remote sensing of the Earth. The content of the academic discipline consists in studying the basics of probability theory and mathematical statistics for the possibility of applying the acquired knowledge, abilities and skills in solving applied problems in the field of geodesy, cartography and land management.

1. Voloshyn O. R., Galayko N. V. Mathematical statistics: a course of lectures. Lviv: LvDUVS, 2010. 88 p. 2. Voloshchenko A.B., Jalladova I.B. Theory of probabilities and mathematical statistics: educational and methodical manual for self. studied disciplines K.: KNEU, 2003. 356 p. 3. Donchenko V. S., Sidorov M. V., Sharapov M. M. Probability theory and mathematical statistics: a textbook. K.: Academy, 2009. 288 p. 4. Yu. V. Zhernovy. A collection of problems on probability theory and mathematical statistics for students of non-mathematical specialties. Lviv, 2009. 18 p. 5. Pushak Y. S., Lozovy B. L. Probability theory and elements of mathematical statistics: textbook. Lviv: UAD, 2006. 428 p. 6. Asrorov, F.; Sobchuk, V.; Kurylko, O. Finding bounded solutions to linear impulsive systems. Eastern-European Journal of Enterprise Technologies. 2019. DOI: 10.15587/1729-4061.2019.178635

Lecture classes, practical classes with the use of mathematical packages, written modular tests, assessment of work in practical classes, assessment of tasks for independent work, credit.

The level of achievement of all planned learning outcomes is determined by the results of written test papers and the results of work in practical classes. The contribution of learning results to the final grade, provided they are mastered at the appropriate level and all assignments are successfully completed, is as follows: 1. learning outcomes 1.1 – 1.8 [knowledge] up to 55%; 2. learning result 2.1 – 2.6 [skill] – up to 30%; 3. learning outcome 3 [communication] – up to 5%; 4. learning outcome 4 [autonomy and responsibility] – up to 10%. Discipline control is carried out according to the modular rating system. The results of students' educational activities for the semester are evaluated on a 100-point scale. The system of evaluating students' knowledge of the discipline includes the following forms: semester and final knowledge evaluation.

Ukrainian