Subject

Probability and statistics

Course Title

Probability and statistics
Probability and statistics

Code

F23L2W006

Study Programme

Computer Science, Computer Engineering

Organizer of the study programme (unit, institute, department or division)

Faculty of Computer Science and Engineering

Degree level (first, second, third cycle)

First Cycle

Academic year / semester

3 / Winter

Number of ECTS credits

Teacher

Alexandra Popovska Mitrović, Biljana Toytovska Ribarski, Natasa Ilievska, Verica Bakeva

Prerequisites for enrolling in the course

Calculus 1 or Mathematics 1

10.

Objectives of the course programme (competences)

To introduce the basic concepts of probability and statistical analysis, with a discussion of their applications in computer science. To enable students to successfully pursue specialized courses in which elements of probability theory and statistics are applied.

11.

Course content

Elements of combinatorics. Probability of random events. Properties of probabilities. Discrete probability space. Classical definition. Conditional probability. Bayes' theorem. Independence of random events. Bernoulli scheme. Discrete and continuous distributions. Random vectors: marginal and conditional distributions. Functions of random variables. Numerical characteristics of random variables: mathematical expectation, variance of a random variable, correlation coefficient between two random variables.
Law of large numbers. Central limit theorem. Elements of statistics: population and sample, parameters and statistics. Basic data processing and descriptive statistics. Mathematical model of a random sample. Distributions of sample statistics: normal, t-distribution, Chi-square and F-distribution. Parameter estimates of a characteristic: moments method, maximum likelihood method, confidence intervals. Parametric tests. Nonparametric tests. Linear regression, least squares estimation.

12.

Learning methods

Lectures using presentations, interactive lectures, exercises (using equipment and software packages), teamwork, case studies, guest lecturers, independent preparation and defense of a project assignment and a seminar paper.

13.

Total available time

6 ECTS x 30 hours = 180 hours

14.

Distribution of available time

45 + 45 + 45 + 0 + 45 = 180 hours

15.

Forms of teaching activities

15.1.	Lectures - theoretical instruction	45 hours
15.2.	Exercises (laboratory, auditory), seminars, teamwork	45 hours

16.

Other forms of activities

16.1.	Project assignments	0 hours
16.2.	Independent assignments	45 hours
16.3.	Home study	45 hours

17.

Assessment method

17.1.	Tests	0 points
17.2.	Seminar paper / project (presentation: written and oral)	0 points
17.3.	Activities and learning	0 points
17.4.	Final exam	100 points

18.

Grading criteria (points / grade)

up to 50 points	5 (five) (F)
from 51 to 60 points	6 (six) (E)
from 61 to 70 points	7 (seven) (D)
from 71 to 80 points	8 (eight) (C)
from 81 to 90 points	9 (nine) (B)
from 91 to 100 points	10 (ten) (A)

19.

Requirement for obtaining a signature and taking the final exam

Activities 15.2 and 16.1 have been completed.

20.

Language of instruction

Macedonian and English

21.

Method for monitoring the quality of teaching

internal evaluation and survey mechanism

22.

Literature

22.1.	Required literature 1. Veritsa Bakeva \| Probability \| UKIМ \| 2015 2. D. C. Montgomery, G.C. Runger \| Applied Statistics and Probability for Engineers \| John Wiley & Sons, Inc. \| 2003 3. Geza Schay \| Introduction to probability with statistical applications \| Birkhäuser \| 2007 4. Michael Baron \| Probability and statistics for computer scientists \| Chapman & Hall/CRC \| 2007
22.2.	Additional literature No. Author Title Publisher Year