PROBABILITY AND STATISTICS PROGRAMME COURSE DESCRIPTION

Code	Name of the Course Unit	Semester	In-Class Hours (T+P)	Credit	ECTS Credit
MAT207	PROBABILITY AND STATISTICS	3	3	3	5

GENERAL INFORMATION
Language of Instruction :	Turkish
Level of the Course Unit :	BACHELOR'S DEGREE, TYY: + 6.Level, EQF-LLL: 6.Level, QF-EHEA: First Cycle
Type of the Course :	Compulsory
Mode of Delivery of the Course Unit	-
Coordinator of the Course Unit	Prof. TARIK ÇAKAR
Instructor(s) of the Course Unit	Assist.Prof. MELİS BOLAT
Course Prerequisite	No

OBJECTIVES AND CONTENTS
Objectives of the Course Unit:	To introduce the basic concepts of probability theory To have the students acquire the skills to analyze nondeterministic signals by modelling them as random processes.
Contents of the Course Unit:	Introduction and definitions (Set Theory, Experiment, Sample Space, Events) Mathematical model of probability, Joint and conditional probability, Bayes theorem Independent events and Bernoulli trials The random variable concept Probability distribution and density functions Conditional distributions and densities Expected values, moments and characteristic functions Transformations of a single random variable. Multiple random variables, joint distribution and density functions Limit theorems Operations on multiple random variables Definition of a random process Independence and stationarity Time averages, statistical averages and ergodicity Autocorrelation and cross-correlation functions Gauss and Poisson processes

KEY LEARNING OUTCOMES OF THE COURSE UNIT (On successful completion of this course unit, students/learners will or will be able to)
Know the basic concepts of probability theory.
Use common probability distributions and analyse their properties.
Compute conditional probability distributions and conditional expectations.
Compute distributions by use of transformation techniques and solve problems.
Define and use the properties of Stochastic processes, especially Gaussian and Poisson Processes.

WEEKLY COURSE CONTENTS AND STUDY MATERIALS FOR PRELIMINARY & FURTHER STUDY
Week	Preparatory	Topics(Subjects)	Method
1	-	Introduction and definitions (Set Theory, Experiment, Sample Space, Events)	-
2	-	Mathematical model of probability, Joint and conditional probability, Bayes theorem	-
3	-	Independent events and Bernoulli trials	-
4	-	The random variable concept	-
5	-	Probability distribution and density functions, Conditional distributions and densities	-
6	-	Expected values, moments and characteristic functions	-
7	-	Transformations of a single random variable	-
8	-	MID-TERM EXAM	-
9	-	Multiple random variables, joint distribution and density functions	-
10	-	Limit theorems, Operations on multiple random variables	-
11	-	Random processes and their properties	-
12	-	Independence and stationarity of random processes	-
13	-	Time averages, statistical averages and ergodicity, Autocorrelation and cross-correlation functions	-
14	-	Gauss and Poisson processes	-
15	-	Preparation for Final exam	-
16	-	FINAL EXAM	-
17	-	FINAL EXAM	-

SOURCE MATERIALS & RECOMMENDED READING
Mühendislik İstatistiği;Montgomery,Runger,Hubele;Çeviri:Coşkun ÖZKAN,Palme Yayıncılık2017
Matemetiksel İstatistik,Mustafa Aytaç, Ezgi yayınları,Ankara Üniv.yayını,1999
Örnekleme Teorisi ve işletme yönetiminde uygulaması,Orhan İdil,İ.Ü. Yayını,1980
Matemetiksel İstatistiğe giriş,Uğur Korum,Ankara üniversitesi,1971
Yönetimde istatistik teknikler ve örnek olaylar, Orhan İdil,İst. Gelişim Üniv. ,1979

ASSESSMENT
Assessment & Grading of In-Term Activities	Number of Activities	Degree of Contribution (%)	Description

Level of Contribution
0	1	2	3	4	5

KNOWLEDGE
Theoretical
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Gain sufficient knowledge in Mathematics, Science and Industrial Engineering.				3

KNOWLEDGE
Factual
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Analyzes and evaluates existing application areas in the field of Industrial Engineering and develops applications for their solutions.				3

SKILLS
Cognitive
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Analyzes a system, the components of that system, the process of that system, and designs the system by examining it in line with realistic constraints and goals.						5
2	Gains the ability to model and solve engineering problems.				3

SKILLS
Practical
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Identifies the problems that may be encountered in the field of industrial engineering and acquires the ability to choose and apply the appropriate method to be used in problem solving.				3
2	Selects and uses technical tools necessary for industrial engineering applications; uses information technologies effectively.				3
3	Designs experiments, conducts experiments, collects data, analyzes and interprets the results to examine problems in the field of industrial engineering.					4

OCCUPATIONAL
Autonomy & Responsibility
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Gains the ability to work effectively within a team.					4
2	Works effectively individually and takes responsibility.				3

OCCUPATIONAL
Learning to Learn
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Accesses the necessary information for a determined problem and searches for resources for this purpose.					4
2	Has the ability to follow all developments in the field of industrial engineering and constantly renew itself.				3

OCCUPATIONAL
Communication & Social
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Gains oral and written communication skills and speaks at least one foreign language.		1

OCCUPATIONAL
Occupational and/or Vocational
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Has awareness of professional and ethical responsibility.		1
2	Has knowledge about the universal and social effects of industrial engineering applications and reaches solutions by being aware of the importance of an innovative approach in solving engineering problems.				3

WORKLOAD & ECTS CREDITS OF THE COURSE UNIT
Workload for Learning & Teaching Activities
Type of the Learning Activites	Learning Activities (# of week)	Duration (hours, h)	Workload (h)
Lecture & In-Class Activities	14	3	42
Preliminary & Further Study	14	3	42
Land Surveying	0	0	0
Group Work	0	0	0
Laboratory	0	0	0
Reading	0	0	0
Assignment (Homework)	3	5	15
Project Work	0	0	0
Seminar	0	0	0
Internship	0	0	0
Technical Visit	0	0	0
Web Based Learning	0	0	0
Implementation/Application/Practice	0	0	0
Practice at a workplace	0	0	0
Occupational Activity	0	0	0
Social Activity	0	0	0
Thesis Work	0	0	0
Field Study	0	0	0
Report Writing	0	0	0
Final Exam	1	1	1
Preparation for the Final Exam	5	3	15
Mid-Term Exam	1	1	1
Preparation for the Mid-Term Exam	5	2	10
Short Exam	1	2	2
Preparation for the Short Exam	1	3	3
TOTAL	45	0	131