Course Information


Course Information
Course Title Code Semester L+U Hour Credits ECTS
PROBABILITY THEORY 801000715010 3 + 0 3.0 8.0

Prerequisites None

Language of Instruction Turkish
Course Level Graduate Degree
Course Type Compulsory
Mode of delivery Oral presentation
Course Coordinator
Instructors Halil AYDOĞDU
Assistants
Goals Introducing basic concepts of the probability theory
Course Content Measure and probability spaces, product spaces, extension theorem, measurable functions and random variables, expectation, characteristic functions, independence, convergence, Fourier Theory and Convergence in Distribution, Central Limit Theorem and Stable Limit Theorem, Radon-Nikodym Theorem, Conditional probability and Martingales.
Learning Outcomes 1) Recognizes the concept of measure and probability measure
2) Comprehends product spaces and extension theorems
3) Creates a link between measurable functions and random variables
4) Recognizes expected value and characteristic function
5) Comprehends independence and convergence topics

Weekly Topics (Content)
Week Topics Teaching and Learning Methods and Techniques Study Materials
1. Week Introducing measure spaces Lecture; Question Answer
Opinion Pool
Brain Based Learning 		Homework Practice (Teaching Practice, Music/Musical Instrument Practice, Statistics, Laboratory, Field Work, Clinic and Polyclinic Practice)
2. Week Probability Space Lecture; Question Answer
Opinion Pool
Brain Based Learning 		Practice (Teaching Practice, Music/Musical Instrument Practice, Statistics, Laboratory, Field Work, Clinic and Polyclinic Practice)
3. Week Extension of probability space concept Lecture; Question Answer
Opinion Pool
Brain Based Learning 		Homework Practice (Teaching Practice, Music/Musical Instrument Practice, Statistics, Laboratory, Field Work, Clinic and Polyclinic Practice)
4. Week Product Spaces Lecture; Question Answer
Opinion Pool
Brain Based Learning 		Practice (Teaching Practice, Music/Musical Instrument Practice, Statistics, Laboratory, Field Work, Clinic and Polyclinic Practice)
5. Week Extension theorem Lecture; Question Answer
Opinion Pool
Brain Based Learning 		Practice (Teaching Practice, Music/Musical Instrument Practice, Statistics, Laboratory, Field Work, Clinic and Polyclinic Practice)
6. Week Measureable Functions Lecture; Question Answer
Opinion Pool
Brain Based Learning 		Practice (Teaching Practice, Music/Musical Instrument Practice, Statistics, Laboratory, Field Work, Clinic and Polyclinic Practice)
7. Week Extension of the concept of the measurable function Lecture; Question Answer
Opinion Pool
Brain Based Learning 		Practice (Teaching Practice, Music/Musical Instrument Practice, Statistics, Laboratory, Field Work, Clinic and Polyclinic Practice)
8. Week Random Variables Lecture; Question Answer
Opinion Pool
Scenario Based Learning; Brain Based Learning 		Homework Practice (Teaching Practice, Music/Musical Instrument Practice, Statistics, Laboratory, Field Work, Clinic and Polyclinic Practice)
9. Week Expected Value Lecture; Question Answer
Opinion Pool
Brain Based Learning 		Practice (Teaching Practice, Music/Musical Instrument Practice, Statistics, Laboratory, Field Work, Clinic and Polyclinic Practice)
10. Week Extension of Expectation Lecture; Question Answer
Opinion Pool
Brain Based Learning 		Practice (Teaching Practice, Music/Musical Instrument Practice, Statistics, Laboratory, Field Work, Clinic and Polyclinic Practice)
11. Week characteristic functions Lecture; Question Answer
Opinion Pool
Brain Based Learning 		Practice (Teaching Practice, Music/Musical Instrument Practice, Statistics, Laboratory, Field Work, Clinic and Polyclinic Practice)
12. Week Independence between two random variables Lecture; Question Answer
Opinion Pool
Brain Based Learning 		Homework Practice (Teaching Practice, Music/Musical Instrument Practice, Statistics, Laboratory, Field Work, Clinic and Polyclinic Practice)
13. Week Fourier Theory, Convergence in Law, Central Limit Theorems Lecture; Question Answer
Opinion Pool
Brain Based Learning 		Practice (Teaching Practice, Music/Musical Instrument Practice, Statistics, Laboratory, Field Work, Clinic and Polyclinic Practice)
14. Week Radon-Nikodym Theorem, Conditional probability and Martingales Lecture; Question Answer
Opinion Pool
Brain Based Learning 		Practice (Teaching Practice, Music/Musical Instrument Practice, Statistics, Laboratory, Field Work, Clinic and Polyclinic Practice)

Sources Used in This Course
Recommended Sources
Billingsley, P. (1995). Probability and Measure. John Wiley&Sons.
Durret, R. (1995). Probability Theory and Examples, Cambridge
Resnick, S.I. (2005). A.Probability Path. Birkhauser.
Rudin, W. (1976). Principles of Mathematical Analysis, McGraw-Hill Science/Engineering/Math; 3rd edition

Relations with Education Attainment Program Course Competencies
Program RequirementsContribution LevelDK1DK2DK3DK4DK5
PY11444444

*DK = Course's Contrubution.
0 1 2 3 4 5
Level of contribution None Very Low Low Fair High Very High
.

ECTS credits and course workload
Event Quantity Duration (Hour) Total Workload (Hour)
Course Duration (Total weeks*Hours per week) 14 9
Work Hour outside Classroom (Preparation, strengthening) 14 5
Homework 5 6
Midterm Exam 1 3
Time to prepare for Midterm Exam 1 8
Final Exam 1 3
Time to prepare for Final Exam 1 8
Total Workload
Total Workload / 30 (s)
ECTS Credit of the Course
Quick Access Hızlı Erişim Genişlet
Course Information
  • Course Information
  • Weekly Topics (Content)
  • Sources Used in This Course
  • Relations with Education Attainment Program Course Competencies
  • ECTS credits and course workload