Subject

Introduction to Random Processes

Course Title

Introduction to Random Processes
Introduction to random processes

Code

F23L2S090

Study Programme

—

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

4 / Summer

Number of ECTS credits

Teacher

Veritsa Bakeva

Prerequisites for enrolling in the course

A minimum of 36 ECTS credits earned

10.

Objectives of the course programme (competences)

To enable students to model random processes for real-life situations.

11.

Course content

Lectures:
1. Definition of a random process. Mathematical expectation, initial moment of order 1-1, correlation function.
2. Special random processes: with independent, uncorrelated, orthogonal values. Stationary random processes.
3. Markov chains: definition, homogeneous chains. Transition probabilities for a single and n-step transition. Real-world examples.
4. Stationarity of Markov chains: strict and asymptotic.
5. Classification of Markov chains. Application in PageRank.
6. Conditional Mathematical Expectation. Branching Processes: Mathematical Expectation and Dispersion.
7. Generating function of a discrete random variable. Extinction probability in Markov chains.
8. Poisson processes: definition and properties.
9. Markov processes: definition, homogeneity. Transition probabilities over time t. State probabilities.
10. Transition rate in Markov chains. Chapman-Kolmogorov equations. Birth and death processes.
11. Mass service systems: definition and basic concepts. Simple mass service systems.
12. Brownian motion (Wiener process): definition and basic properties.

Practical Classes:
1. Definition of a random process. Mathematical expectation, initial moment of order 1-1, correlation function.
2. Special random processes: with independent, uncorrelated, orthogonal values. Stationary random processes.
3. Markov chains: definition, homogeneous chains. Transition probabilities for a single and n-step transition. Real-world examples.
4. Stationarity of Markov chains: strict and asymptotic.
5. Classification of Markov chains. Application in PageRank.
6. Conditional Mathematical Expectation. Branching Processes: Mathematical Expectation and Dispersion.
7. Generating function of a discrete random variable. Extinction probability in Markov chains.
8. Poisson processes: definition and properties.
9. Markov processes: definition, homogeneity. Transition probabilities over time t. State probabilities.
10. Transition rate in Markov chains. Chapman-Kolmogorov equations. Birth and death processes.
11. Mass service systems: definition and basic concepts. Simple mass service systems.
12. Brownian motion (Wiener process): definition and basic properties.

12.

Learning methods

Mastering concepts, properties, and techniques through independent work; solving assigned tasks and practice problems; completing a project assignment.

13.

Total available time

6 ECTS x 30 hours = 180 hours

14.

Distribution of available time

30 + 30 + 25 + 15 + 80 = 180 hours

15.

Forms of teaching activities

15.1.	Lectures - theoretical instruction	30 hours
15.2.	Exercises (laboratory, auditory), seminars, teamwork	30 hours

16.

Other forms of activities

16.1.	Project assignments	15 hours
16.2.	Independent assignments	25 hours
16.3.	Home study	80 hours

17.

Assessment method

17.1.	Tests	0 points
17.2.	Seminar paper / project (presentation: written and oral)	15 points
17.3.	Activities and learning	0 points
17.4.	Final exam	Seventy-five 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

15.1 and 15.2

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. Howard M. Taylor, Samuel Karlin \| An Introduction to Stochastic Modeling \| Academic Press \| 1998 2. Veritsa Bakeva, Magdalena Georgieva \| Random Processes \| Internal Script
22.2.	Additional literature No. Author Title Publisher Year