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. ABDULSAMET HAŞILOĞLU
Instructor(s) of the Course Unit	Assist.Prof. FERHAT KÜRÜZ-Assist.Prof. SEMANUR SARIÇAM
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	Explains the fundamental engineering concepts of computer science and relates them to the groundwork of computer science.

KNOWLEDGE
Factual
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Uses theoretical and practical knowledge coming from mathematics, probability, statistics and various other branches of life sciences, to find solutions to engineering problems.

SKILLS
Cognitive
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Determines the components and the underlying process of a system and designs an appropriate computational model under reasonable constraints.
2	Designs a computer-aided conceptual model with modern techniques.

SKILLS
Practical
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Determines, detects and analyzes the areas of computer science applications and develops appropriate solutions.
2	Identifies, models and solves computer engineering problems by applying appropriate analytical methods.
3	Determines and uses the necessary information technologies in an efficient way for engineering applications.

OCCUPATIONAL
Autonomy & Responsibility
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Possess the responsibility and ability to design and conduct experiments for engineering problems by collecting, analyzing and interpreting data.
2	Possess the ability to conduct effective individual study.
3	Takes responsibility as a team work and contributes in an effective way.

OCCUPATIONAL
Learning to Learn
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Monitors the developments in the field of information technologies by means of internet and related journals and possess the required knowledge for the management, control, development and security of information technologies.
2	Develops positive attitude towards lifelong learning.

OCCUPATIONAL
Communication & Social
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Communicates effectively by oral and/or written form and uses at least one foreign language.
2	Possess sufficient consciousness about the issues of project management, practical applications and also environmental protection, worker's health and security.

OCCUPATIONAL
Occupational and/or Vocational
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Possess professional and ethical responsibility and willingness to share it.
2	Possess sufficient consciousness about the universality of engineering solutions and applications and be well aware of the importance of innovation.

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