GAZI UNIVERSITY INFORMATION PACKAGE - 2019 ACADEMIC YEAR

COURSE DESCRIPTION
PROBABİLİTY THEORY/5161303
Course Title: PROBABİLİTY THEORY
Credits 3 ECTS 7.5
Semester 1 Compulsory/Elective Elective
COURSE INFO
 -- LANGUAGE OF INSTRUCTION
  Turkish
 -- NAME OF LECTURER(S)
  Prof. Dr. Salih ÇELEBİOĞLU
 -- WEB SITE(S) OF LECTURER(S)
  http://websitem.gazi.edu.tr/site/scelebi
 -- EMAIL(S) OF LECTURER(S)
  scelebi@gazi.edu.tr
 -- LEARNING OUTCOMES OF THE COURSE UNIT
To learn and apply the independence concepts for sequences and families of events and random variables
To learn the convergence types of sequences of random variables and the relations among them
To learn the specific meaning of weak and strong law of large numbers and apply them
To be aware of using the characteristic functions as a tool of examining the convergence types
To learn the concepts related to infinetely divisible and stable distributions
To learn the concepts of conditional expected values and kernels in detail



 -- MODE OF DELIVERY
  The mode of delivery of this course is face to face.
 -- PREREQUISITES AND CO-REQUISITES
  There is no prerequisite or co-requisite for this course.
 -- RECOMMENDED OPTIONAL PROGRAMME COMPONENTS
  1. Clarke L.E., 1975, Random Variables, Longman, London. 2. Moran P.A.P., 1984, An Introduction to Probability Theory, Clarendon Press, Oxford. 3.
 --COURSE CONTENT
1. Week  Independence; independence for sequences and families of events and random variables
2. Week  Zero-one laws
3. Week  Convergence, almost everywhere convergence
4. Week  Convergence in the mean and convergence in distribution
5. Week  Relations among convergence types, law of large numbers
6. Week  Characteristic functions, inversion theorem
7. Week  Midterm
8. Week  Weak law of large numbers, central limit theorem
9. Week  Infinitely divisible distributions, Raikov's theorem
10. Week  The canonical representation of characteristic function of an infinitely divisible distribution
11. Week  Stable distributions
12. Week  Conditional expected values and condfitional probabilities
13. Week  Decomposition of conditional expected values
14. Week  Kernels
15. Week  Expected values of kernels and conditional distributions
16. Week  Final examination
 -- RECOMMENDED OR REQUIRED READING
  1. Clarke L.E., 1975, Random Variables, Longman, London. 2. Moran P.A.P., 1984, An Introduction to Probability Theory, Clarendon Press, Oxford. 3.
 -- PLANNED LEARNING ACTIVITIES AND TEACHING METHODS
  Lecture
 -- WORK PLACEMENT(S)
  Not Applicable
 -- ASSESSMENT METHODS AND CRITERIA
 
Quantity
Percentage
 Mid-terms
1
40
 Assignment
2
10
 Exercises
0
0
 Projects
0
0
 Practice
0
0
 Quiz
0
0
 Contribution of In-term Studies to Overall Grade  
40
 Contribution of Final Examination to Overall Grade  
60
 -- WORKLOAD
 Efficiency  Total Week Count  Weekly Duration (in hour)  Total Workload in Semester
 Theoretical Study Hours of Course Per Week
3
14
42
 Practising Hours of Course Per Week
0
 Reading
10
5
50
 Searching in Internet and Library
10
2
20
 Designing and Applying Materials
0
 Preparing Reports
4
7
28
 Preparing Presentation
0
 Presentation
0
 Mid-Term and Studying for Mid-Term
3
5
15
 Final and Studying for Final
3
10
30
 Other
0
 TOTAL WORKLOAD: 
185
 TOTAL WORKLOAD / 25: 
7.4
 ECTS: 
7.5
 -- COURSE'S CONTRIBUTION TO PROGRAM
NO
 PROGRAM LEARNING OUTCOMES
1
2
3
4
5
11. Based on the capabilities of undergraduate level, the students enrolled to the program can develop and deepen their knowledge and skill at the level of expertise on the same field of the undergradute study or a different field.X
22. The students use their theoretical and practical knowledge at the level of expertise in the area of statistics.X
33. The students should evaluate their acquired knowledge and skills in a critical perspective and the critical point of view guides their learning process.X
44. Theoretical and practical knowledge gained in graduate level in the field of Statistics should be applied and transfer to the current problems.X
55. By performing the process from the identification of the scientific research problem to reporting and the process should be transferred in oral, written and visual ways.X
66. The students should use computer software and information technologies on the level required by the field of Statistics.X
77. The students should have the ability to use Statistics in interdisciplinary studies.X
88. The students should have enough foreign language level to pursue statistical literature.X
99. At the required level of field of statistics, he/she should use statistical software and information technology efficiently in a such a way that helps solving problems in his/her research.X
1010. In the process of applying knowledge in a professional sense, social, scientific, and ethical values should be regarded.X