COURSE SYLLABUS

STOCHASTIC PROCESSES

1	Course Title:	STOCHASTIC PROCESSES
2	Course Code:	END5155
3	Type of Course:	Optional
4	Level of Course:	Second Cycle
5	Year of Study:	1
6	Semester:	1
7	ECTS Credits Allocated:	7,5
8	Theoretical (hour/week):	3
9	Practice (hour/week) :	0
10	Laboratory (hour/week) :	0
11	Prerequisites:	Undergraduate Level Probability and Statistics
12	Recommended optional programme components:	None
13	Language:	Turkish
14	Mode of Delivery:	Face to face
15	Course Coordinator:	Doç. Dr. Fatih ÇAVDUR
16	Course Lecturers:
17	Contactinformation of the Course Coordinator:	e-posta: fatihcavdur@uludag.edu.tr, Telefon: + 90 (224) 294 20 77 Adres: Uludağ Üniversitesi, Mühendislik-Mimarlık Fakültesi, Endüstri Mühendisliği Bölümü, Görükle Kampüsü, 16059 Nilüfer, Bursa
18	Website:
19	Objective of the Course:	Learning basic concepts of stochastic processes.
20	Contribution of the Course to Professional Development

Learning Outcomes:

1	Being able to understand the basics of stochastic processes.;
2	Having knowledge of basic probability concepts.;
3	Being able to analyze real-life systems using stochastic processes.;

22	Course Content:

Week	Theoretical	Practical
1	Basic Probability Concepts -Sample Space, Events, Probabilities of Events -Basic Definitions and Theorems -Conditional Probability
2	Random Variables -Introduction to Random Variables, Definitions -Mean and Variance of Random Variables -Discrete Random Variables -Continuous Random Variables
3	Expectation and Conditional Expectation -Definition of Expectation -Conditional Expectation -Computing Probabilities and Expectations using Conditioning
4	Discrete Probability Distributions -Bernoulli Process and Binomial Distribution -Negative Binomial, Geometric, Hyper-Geometric Distributions -Poisson Distribution
5	Continuous Probability Distributions -Uniform Distribution -Exponential Distribution -Normal Distribution -Gamma Distribution -Beta Distribution
6	Discrete Markov Chains -Markov Chains, Definitions and Basic Concepts
7	Discrete Markov Chains (cont.) -States, Classes and Some Properties
8	Continuous Time Markov Chains -Continuous Time Markov Chains, Definitions and Basic Concepts -Some Properties of Continuous Time Markov Chains
9	Continuous Time Markov Chains (cont.) -Birth and Death Processes -Applications
10	Exponential Distribution and Poisson Process -Exponential Distribution, Definitions and Basic Concepts, Memoryless Property
11	Exponential Distribution and Poisson Process (cont.) -Counting Process and Poisson Process -Some Properties of Poisson Process
12	Queuing Theory -Basic Concepts, Notation -Long-Run or Steady-State Parameters -Basic Queuing Systems, M/M/1, M/M/c etc.
13	Applications
14	Student Project Presentations

23	Textbooks, References and/or Other Materials:	1. Introduction to Probability Models; 10th Edition; Sheldon Ross; Academic Press 2. Stochastic Processes, Sheldon Ross, 2nd Edition; Wiley
24	Assesment

TERM LEARNING ACTIVITIES	NUMBER	PERCENT
Midterm Exam	1	25
Quiz	0	0
Homeworks, Performances	1	25
Final Exam	1	50
Total	3	100
Contribution of Term (Year) Learning Activities to Success Grade		50
Contribution of Final Exam to Success Grade		50
Total		100
Measurement and Evaluation Techniques Used in the Course
Information

ECTS / WORK LOAD TABLE

Activites	NUMBER	TIME [Hour]	Total WorkLoad [Hour]
Theoretical	14	3	42
Practicals/Labs	0	0	0
Self Study and Preparation	14	10	140
Homeworks, Performances	1	30	30
Projects	0	0	0
Field Studies	0	0	0
Midtermexams	1	5	5
Others	0	0	0
Final Exams	1	8	8
Total WorkLoad			225
Total workload/ 30 hr			7,5
ECTS Credit of the Course			7,5

CONTRIBUTION OF LEARNING OUTCOMES TO PROGRAMME QUALIFICATIONS

	PQ1	PQ2	PQ3	PQ4	PQ5	PQ6	PQ7	PQ8	PQ9	PQ10	PQ11	PQ12	PQ13
LO1	1	5	3	1	1	1	1	1	5	4	4	1	1
LO2	1	5	3	1	1	1	1	1	5	4	4	1	1
LO3	1	5	3	1	1	1	1	1	5	4	4	1	1

LO: Learning Objectives

PQ: Program Qualifications

Contribution Level:

1 Very Low

2 Low

3 Medium

4 High

5 Very High