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. OSMAN KOPMAZ
Instructor(s) of the Course Unit	Assist.Prof. BAHADIR KOPÇASIZ-Assist.Prof. FERHAT KÜRÜZ-Assist.Prof. ZEHRA CİVAN
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	Ability to apply mathematics, science and engineering knowledge.						5
2	Ability to apply mathematics, science and engineering knowledge.						5

KNOWLEDGE
Factual
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Ability to apply mathematics, science and engineering knowledge.						5
2	Ability to apply mathematics, science and engineering knowledge.						5

SKILLS
Cognitive
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Ability to design experiments, conduct experiments, collect data, analyze and interpret results.						5
2	Ability to design experiments, conduct experiments, collect data, analyze and interpret results.						5

SKILLS
Practical
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	A system, product or process has economic, environmental, social, political, ethical, health and safety, under realistic constraints and conditions such as feasibility and sustainability, Ability to design to meet requirements.				3
2	A system, product or process has economic, environmental, social, political, ethical, health and safety, under realistic constraints and conditions such as feasibility and sustainability, Ability to design to meet requirements.				3

OCCUPATIONAL
Autonomy & Responsibility
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Ability to work in teams with different disciplines					4
2	Ability to work in teams with different disciplines					4

OCCUPATIONAL
Learning to Learn
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Ability to identify, formulate and solve engineering problems						5
2	Ability to identify, formulate and solve engineering problems						5

OCCUPATIONAL
Communication & Social
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Awareness of having professional and ethical responsibilities.		1
2	Awareness of having professional and ethical responsibilities.		1
3	Ability to communicate effectively verbally and in writing.		1
4	Ability to communicate effectively verbally and in writing.		1

OCCUPATIONAL
Occupational and/or Vocational
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	The ability to have a comprehensive education to understand the impact of engineering solutions on global and social dimensions.				3
2	The ability to have a comprehensive education to understand the impact of engineering solutions on global and social dimensions.				3
3	Awareness of the necessity of lifelong learning and the ability to do so.		1
4	Awareness of the necessity of lifelong learning and the ability to do so.		1
5	The ability to have knowledge about current/contemporary issues.			2
6	The ability to have knowledge about current/contemporary issues.			2
7	Ability to use the techniques required for engineering applications and modern engineering and calculation equipment.				3
8	Ability to use the techniques required for engineering applications and modern engineering and calculation equipment.				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