Information Package / Course Catalogue
Probabilistic Methods in Computer Engineering
Course Code: MCS535
Course Type: Area Elective
Couse Group: Second Cycle (Master's Degree)
Education Language: English
Work Placement: N/A
Theory: 3
Prt.: 0
Credit: 3
Lab: 0
ECTS: 6
Objectives of the Course

The aim of the course is to study basic methods of probability theory and mathematical statistics and to demonstrate the possible applications. Examples related to service systems, reliability, algorithms, and other subjects are given throughout the course. The course is constructed for students of engineering departments, using mathematics for its applications.

Course Content

Basic notions of probability theory, reliability theory, notion of a stochastic process, Poisson processes, Markov chains, statistical inference

Name of Lecturer(s)
Learning Outcomes
1.At the end of the course the students are expected to: Find reliability functions and mean times to failure for systems of different types.
2.Understand the notion of stochastic process and analyze different types of stochastic processes.
3.Understand basic facts concerning Markov chains.
4.Know special probability distributions such as Poisson, exponential, Erlang.
5.Apply the methods of statistical inference.
Recommended or Required Reading
1.K. S. Trivedi, Probability and Statistics with Reliability, Queueing, and Computer Science Applications, 2nd Edition, Wiley, 2002.
2.Sheldon Ross, Introduction to Probability Models. Academic Press, 1994
3.T. Aven, U. Jensen, Stochastic models in reliability, Springer, 1999
Weekly Detailed Course Contents
Week 1 - Theoretical
Sample space, random events, probability. Conditional probability. Independence.
Week 2 - Theoretical
Random variables and probability distributions. Random vectors.
Week 3 - Theoretical
Reliability theory. Finding reliabilities of different systems. Redundancy.
Week 4 - Theoretical
Failure rate and hazard function. IFR/DFR distributions.
Week 5 - Theoretical
Definition and examples of stochastic processes, their types.
Week 6 - Theoretical
The Poisson process and its generalizations
Week 7 - Theoretical
Random incidence
Week 8 - Theoretical
Markov chains: Markov property, transition probabilities, transition graph.
Week 9 - Theoretical
Classification of states and limiting probabilities. Regular chains and equilibrium.
Week 10 - Theoretical
Absorbing Markov chains. Fundamental matrix.
Week 11 - Theoretical
Random samples. Estimators, their characteristics.
Week 12 - Theoretical
Point and interval estimation.
Week 13 - Theoretical
Hypothesis testing. The null and alternative hypotheses, type I and type II errors. One-sided and two-sided tests. Tests on the population mean.
Week 14 - Theoretical
Hypothesis testing. The null and alternative hypotheses, type I and type II errors. One-sided and two-sided tests. Tests on the population mean.
Assessment Methods and Criteria
Type of AssessmentCountPercent
Attending Lectures1%5
Assignment2%10
Midterm Examination1%15
Final Examination1%70
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory142370
Assignment28220
Individual Work140114
Midterm Examination120323
Final Examination120323
TOTAL WORKLOAD (hours)150
Contribution of Learning Outcomes to Programme Outcomes
PÇ-1
PÇ-2
PÇ-3
PÇ-4
PÇ-5
PÇ-6
PÇ-7
PÇ-8
PÇ-9
OÇ-1
4
5
3
2
2
3
3
2
4
OÇ-2
2
3
2
2
2
2
2
2
4
OÇ-3
5
3
4
4
3
4
3
1
3
OÇ-4
3
3
3
4
2
3
3
2
3
OÇ-5
2
4
2
2
1
2
2
2
4
Adnan Menderes University - Information Package / Course Catalogue
2026