Probability and Statistics

Објавено: June 28, 2022
1. Course Title Probability and Statistics
2. Code 4ФЕИТ08Л001
3. Study program КТИ
4. Organizer of the study program (unit, institute, department) Faculty of Electrical Engineering and Information Technologies
5. Degree (first, second, third cycle) First cycle
6. Academic year/semester II/4 7. Number of ECTS credits 6
8. Lecturer
9. Course Prerequisites Passed: Mathematics 1, Mathematics 2
10. Course Goals (acquired competencies): This course aims to provide an understanding of the basic concepts of probability theory and statistical analysis. Upon completion of the course, the student is able to:
• calculate the probability of random events,
• use Bayes’ theorem,
• understand and use the concept of a random variable,
• interpret and apply the central limit theorem,
• understand the basic statistical concepts and tools,
• use techniques for determining point estimates and confidence intervals;
• choose appropriate statistical tests and perform hypotheses testing,
• use software for visualization and statistical data processing,
• draw conclusions and present the obtained results from statistical analysis,
• solve problems from computer technologies and engineering using probabilistic and statistical methods.
11. Course Syllabus: Combinatorics, probability axioms, geometric and conditional probability. Independent events, total probability and Bayes’ formula. Random variable, numerous characteristics of a random variable, some more important distributions. Transformation of a random variable. Random vector, numerous characteristics of random vector. Transformation of a random vector. Limit theorems.
Introduction to statistics. Population and sample. Descriptive statistics. Point estimates of the unknown parameters. Methods for point estimation. Confidence intervals. Testing of parametric and nonparametric hypotheses. Using software for statistical data processing.
12. Learning methods: Lectures, classroom exercises, self-learning.
13. Total number of course hours 3 + 3 + 0 + 0
14. Distribution of course hours 180
15. Forms of teaching 15.1. Lectures-theoretical teaching 45
15.2. Exercises (laboratory, practice classes), seminars, teamwork 45
16. Other course activities 16.1. Projects, seminar papers 0
16.2. Individual tasks 30
16.3. Homework and self-learning 60
17. Grading 17.1. Exams 30
17.2. Seminar work/project (presentation: written and oral) 10
17.3. Activity and participation 0
17.4. Final exam 60
18. Grading criteria (points) up to 50 points 5 (five) (F)
from 51to 60 points 6 (six) (E)
from 61to 70 points 7 (seven) (D)
from 71to 80 points 8 (eight) (C)
from 81to 90 points 9 (nine) (B)
from 91to 100 points 10 (ten) (A)
19. Conditions for acquiring teacher’s signature and for taking final exam Аttend classes regularly and take tests
20. Forms of assessment

During the semester, two partial written exams are provided (in the 8th and 15th week of the semester, duration up to 90 minutes), and tests can be conducted during the classes. In the scheduled exam sessions, a written exam is taken (duration up to 135 minutes).
For students who have passed the partial exams, i.e. the written exam, a final oral exam can be conducted (duration up to 60 minutes). The final grade includes the points from the partial exams, i.e. the written exam, the points from the individual student work (homeworks), the points from the tests and the final oral exam.
21. Language Macedonian and English
22. Method of monitoring of teaching quality Self-evaluation and surveys
23. Literature
23.1. Required Literature
No. Author Title Publisher Year
1 А. Бучковска, К. Хаџи-Велкова Санева, С. Атанасова Вовед во веројатност за инженери ФЕИТ/УКИМ 2018
2 К. Хаџи-Велкова Санева, С. Атанасова, А. Бучковска Збирка решени задачи од веројатност УКИМ 2016
3 Douglas C. Montgomery, George C. Runger Applied Statistics and Probability for Engineers John Wiley & Sons, Inc. 2003
23.2. Additional Literature
No. Author Title Publisher Year
1 Д. П. Берцекас, Џ. Н. Цициклис Вовед во веројатност АРС Ламина 2012
2 Џ. А. Рајс Математичка статистика и анализа на податоци Арс Ламина 2014