GRADUATE SCHOOL

PH.D. In Applied Mathematics and Statistics

STAT 559 | Course Introduction and Application Information

Course Name
Advanced Probability Theory
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
STAT 559
Fall/Spring
3
0
3
7.5

Prerequisites
None
Course Language
English
Course Type
Elective
Course Level
Second Cycle
Mode of Delivery -
Teaching Methods and Techniques of the Course -
Course Coordinator -
Course Lecturer(s)
Assistant(s) -
Course Objectives This course aims to make the students familiar with the basics of Probability Theory, its applications and Statistics.
Learning Outcomes The students who succeeded in this course;
  • will be able to find probabilities of different events.
  • will be able to work with discrete distribiutions, being able to compute important characteristis for them.
  • will be able to work with continuous distributions and find basic charactheristics for them.
  • will be able to analyze bivariate distributions, compute various characteristics for them.
  • will be able to derive the law, srtong law of large numbers and the central limit theorem for the sums of independent random variables.
Course Description The axioms of probability theory and historical probability backgrood are discussed. Random events, random variables as well as their basic characteristics are studied. Limit theorems for sums of independent random variables are also considered. Dependent random variables are studied. Bivariate random variables are discussed.

 



Course Category

Core Courses
Major Area Courses
X
Supportive Courses
Media and Management Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Related Preparation
1 Events. The axioms of  probability. Probability space. “ Probability theory” by A.A. Borovkov:7:27.
2 Random variables and distribution functions. “ Probability theory” by A.A. Borovkov:38:57.
3 Numerical characteristics of random variables. “ Probability theory” by A.A. Borovkov:60:92.
4 Bivariate random variables “A First Course in Probability” by Sheldon Ross, Prentics Hall : 239:269.
5 Bivariate distribution functions. “A First Course in Probability” by Sheldon Ross, Prentics Hall :270:303.
6 Inequalities. “A First Course in Probability” by Sheldon Ross, Prentics Hall :400:427.
7 Properties of conditional expectation. Martingales. “ Probability theory” by A.A. Borovkov:217:246.
8 Midterm Exam
9 Moment generating function and characteristic function. “ Probability theory” by A.A. Borovkov:92:107.
10 Summation and multiplication of random variables. “ Probability theory” by A.A. Borovkov:110:115,Pakes, A. G. and Navarro, J. (2007).Distributional characterizations through scaling relations, Australian Journal of Statistics, 49 (2), 115:135.
11 On convergence of random variables and distributions. “ Probability theory” by A.A. Borovkov:121:134.
12 The central limit theorem and the law of large numbers. “ Probability theory” by A.A. Borovkov:135:170
13 Limit theorems for dependent random variables. “Time Series Analysis” by J.D.Hamilton, Princeton, NJ: 180:201.
14 Limit theorems for dependent random variables. “Time Series Analysis” by J.D.Hamilton, Princeton, NJ: 202:234.
15 Review for Final Exam
16 Review of the Semester  

 

Course Notes/Textbooks 1. “ Probability theory” by A.A. Borovkov
Suggested Readings/Materials “A First Course in Probability” by Sheldon Ross, Prentice Hall “Time Series Analysis” by J.D.Hamilton, Princeton, NJ.

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
1
15
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exams
Midterm
1
40
Final Exam
1
45
Total

Weighting of Semester Activities on the Final Grade
2
55
Weighting of End-of-Semester Activities on the Final Grade
1
45
Total

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Theoretical Course Hours
(Including exam week: 16 x total hours)
16
3
48
Laboratory / Application Hours
(Including exam week: '.16.' x total hours)
16
0
Study Hours Out of Class
15
6
90
Field Work
0
Quizzes / Studio Critiques
0
Portfolio
0
Homework / Assignments
0
Presentation / Jury
0
Project
0
Seminar / Workshop
0
Oral Exam
0
Midterms
1
40
40
Final Exam
1
47
47
    Total
225

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1

To develop and deepen his/her knowledge on theories of mathematics and statistics and their applications in level of expertise, and to obtain unique definitions which bring innovations to the area, based on master level competencies,

X
2

To have the ability of original, independent and critical thinking in Mathematics and Statistics and to be able to develop theoretical concepts,

X
3

To have the ability of defining and verifying problems in Mathematics and Statistics,

X
4

With an interdisciplinary approach, to be able to apply theoretical and applied methods of mathematics and statistics in analyzing and solving new problems and to be able to discover his/her own potentials with respect to the application,

X
5

In nearly every fields that mathematics and statistics are used, to be able to execute, conclude and report a research, which requires expertise, independently,

X
6

To be able to evaluate and renew his/her abilities and knowledge acquired in the field of Applied Mathematics and Statistics with critical approach, and to be able to analyze, synthesize and evaluate complex thoughts in a critical way,

X
7

To be able to convey his/her analyses and methods in the field of Applied Mathematics and Statistics to the experts in a scientific way,

X
8

To be able to use national and international academic resources (English) efficiently, to update his/her knowledge, to communicate with his/her native and foreign colleagues easily, to follow the literature periodically, to contribute scientific meetings held in his/her own field and other fields systematically as written, oral and visual.

X
9

To be familiar with computer software commonly used in the fields of Applied Mathematics and Statistics and to be able to use at least two of them efficiently,

X
10

To contribute the transformation process of his/her own society into an information society and the sustainability of this process by introducing scientific, technological, social and cultural advances in the fields of Applied Mathematics and Statistics,

X
11

As having rich cultural background and social sensitivity with a global perspective, to be able to evaluate all processes efficiently, to be able to contribute the solutions of social, scientific, cultural and ethical problems and to support the development of these values,

X
12

As being competent in abstract thinking, to be able to connect abstract events to concrete events and to transfer solutions, to analyze results with scientific methods by designing experiment and collecting data and to interpret them,

X
13

To be able to produce strategies, policies and plans about systems and topics in which mathematics and statistics are used and to be able to interpret and develop results,

X
14

To be able to evaluate, argue and analyze prominent persons, events and phenomena, which play an important role in the development and combination of the fields of Mathematics and Statistics, within the perspective of the development of other fields of science,

X
15

In Applied Mathematics and Statistics, to be able to sustain scientific work as an individual or a group, to be effective in all phases of an independent work, to participate decision-making process and to make and execute necessary planning within an effective time schedule.

X

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

 


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