Course Information

Course Title	Code	Semester	L+U Hour	Credits	ECTS
MATHEMATICAL STATISTICS	801000725560		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
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
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

Week	Topics	Teaching and Learning Methods and Techniques	Study Materials
1. Week	Introducing measure spaces	Lecture; Question Answer	Presentation (Including Preparation Time)
2. Week	Probability Space	Lecture; Question Answer	Presentation (Including Preparation Time)
3. Week	Extension of probability space concept	Lecture; Question Answer	Presentation (Including Preparation Time)
4. Week	Product spaces	Lecture; Question Answer	Presentation (Including Preparation Time)
5. Week	Extension theorem	Lecture; Question Answer	Presentation (Including Preparation Time)
6. Week	Measureable Functions	Lecture; Question Answer	Presentation (Including Preparation Time)
7. Week	Extension of the concept of the measurable function	Lecture; Question Answer	Presentation (Including Preparation Time)
8. Week	Random Variables	Lecture; Question Answer	Presentation (Including Preparation Time)
9. Week	Expected Value	Lecture; Question Answer	Presentation (Including Preparation Time)
10. Week	Extension of Expectation	Lecture; Question Answer	Presentation (Including Preparation Time)
11. Week	characteristic functions	Lecture; Question Answer	Presentation (Including Preparation Time)
12. Week	Independence between two random variables	Lecture; Question Answer	Presentation (Including Preparation Time)
13. Week	Extended definition of independence of amongst random variables	Lecture; Question Answer	Presentation (Including Preparation Time)
14. Week	Convergence	Lecture; Question Answer	Presentation (Including Preparation Time)

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

Event	Quantity	Duration (Hour)	Total Workload (Hour)
.	14	3	42
Course Duration (Total weeks*Hours per week)	14	4	56
Work Hour outside Classroom (Preparation, strengthening)	14	5	70
Homework	5	9	45
Midterm Exam	1	9	9
Time to prepare for Midterm Exam	1	12	12
Final Exam	1	3	3
Time to prepare for Final Exam	1	8	8
Total Workload
Total Workload / 30 (s)
ECTS Credit of the Course			30