Skip to main content

Course Description

CourseCodeSemesterT+P (Hour)CreditECTS
ADVANCED PROBABILITY and APLICATIONS-Fall Semester3+038
Course Program
Prerequisites Courses
Recommended Elective Courses
Language of CourseEnglish
Course LevelThird Cycle (Doctorate Degree)
Course TypeElective
Course CoordinatorProf.Dr. Mehmet Kemal ÖZDEMİR
Name of Lecturer(s)Prof.Dr. Adnan KAVAK
Assistant(s)
AimThis is a graduate level course on advanced topics in probability and random variables. It aims to develop the ability to construct and analyze probabilistic models in a manner that combines intuitive understanding and mathematical precision. Different from the intrductory probability course, the course starts with digging the foundations in probability theory, random variables, expectation, and then it covers advanced topics such as transforms of distribution, further topics in random variables, limit theorems, statistical inference. This course also intends to provide students with the selected topics in stochastics processes such as Poisson process, Renewal process, Galton-Watson process, Gaussian process and discrete Markov Chains.
Course ContentThis course contains; Review of Basic Concepts (Probability Triple, Classical Probability Spaces, Concept of Sigma Field, Probability Measure, Conditional Probability, Limits of Events),Measurable Functions, Random Variables, Distribution Function,Random Vector, Joint Distribution, Independence,Expectation, Integral, and Weak and Strong Convergence,Chapter 3 of Textbook 1,Common Families of Distributions,Derived distributions,Midterm,Covariance and correlation, conditional expectation and variance, sums of random variables,Limit theorems,Statsitical inference,Topics in theory of stochastic processes,Discrete Markov Chains,Discrete Markov Chains.
Dersin Öğrenme KazanımlarıTeaching MethodsAssessment Methods
1. Understand the foundations in probability theory and random variables .21, 9A, E, F
2. Learn the concept of expectation, integral and convergence from different perspective. 21, 9A, E, F
3. Learn how to derive distributions of function of a random variable, and how to obtain transforms of random variables. 21, 9A, E, F
4. Learn how to obtain statistical inference 21, 9A, E, F
5. Analyze the stochastic processes and performance of systems using Markov Chains21, 9A, E, F
Teaching Methods:21: Simulation Technique, 9: Lecture Method
Assessment Methods:A: Traditional Written Exam, E: Homework, F: Project Task

Course Outline

OrderSubjectsPreliminary Work
1Review of Basic Concepts (Probability Triple, Classical Probability Spaces, Concept of Sigma Field, Probability Measure, Conditional Probability, Limits of Events)Lecture Notes, Chapter 1 of Textbook 1
2Measurable Functions, Random Variables, Distribution FunctionChapter 1 of Textbook 1
3Random Vector, Joint Distribution, IndependenceChapter 1 of Textbook 1
4Expectation, Integral, and Weak and Strong ConvergenceChapter 2 of Textbook 1
5Chapter 3 of Textbook 1Bölüm 3 Textbook 1
6Common Families of DistributionsChapter 3 of Textbook 1
7Derived distributionsChapter 4 of Textbook 2
8MidtermAll the topics till Week 8.
9Covariance and correlation, conditional expectation and variance, sums of random variablesChapter 4 of Textbook 2
10Limit theoremsChapter 5 of Textbook 2
11Statsitical inferenceChapter 9 of Textbook 2
12Topics in theory of stochastic processesChapter 8 of Textbook 1, Chapter 6 of Textbook 2
13Discrete Markov ChainsChapter 8 of Textbook 1, Chapter 7 of Textbook 2
14Discrete Markov ChainsChapter 8 of Textbook 1, Chapter 7 of Textbook 2
Resources
1. Advanced Probability Theory (Probability: Pure and Applied) , Janos Galambos, ISBN-13:978-9052016580
2. Introduction to Probability, 2nd Ed., Dimitri P. Bertsekas and John N. Tsitsiklis, ISBN-13: 978-1886529236

Course Contribution to Program Qualifications

Course Contribution to Program Qualifications
NoProgram QualificationContribution Level
12345
1
Develop and deepen the current and advanced knowledge in the field with original thought and/or research and come up with innovative definitions based on Master's degree qualifications.
X
2
Conceive the interdisciplinary interaction which the field is related with ; come up with original solutions by using knowledge requiring proficiency on analysis, synthesis and assessment of new and complex ideas.
X
3
Evaluate and use new information within the field in a systematic approach and gain advanced level skills in the use of research methods in the field.
X
4
Develop an innovative knowledge, method, design and/or practice or adapt an already known knowledge, method, design and/or practice to another field.
X
5
Broaden the borders of the knowledge in the field by producing or interpreting an original work or publishing at least one scientific paper in the field in national and/or international refereed journals.
X
6
Contribute to the transition of the community to an information society and its sustainability process by introducing scientific, technological, social or cultural improvements.
7
Independently perceive, design, apply, finalize and conduct a novel research process.
X
8
Ability to communicate and discuss orally, in written and visually with peers by using a foreign language at least at a level of European Language Portfolio C1 General Level.
X
9
Critical analysis, synthesis and evaluation of new and complex ideas in the field.
X
10
Recognizes the scientific, technological, social or cultural improvements of the field and contribute to the solution finding process regarding social, scientific, cultural and ethical problems in the field and support the development of these values.

Assessment Methods

Contribution LevelAbsolute Evaluation
Rate of Midterm Exam to Success 50
Rate of Final Exam to Success 50
Total 100
ECTS / Workload Table
ActivitiesNumber ofDuration(Hour)Total Workload(Hour)
Course Hours14342
Guided Problem Solving000
Resolution of Homework Problems and Submission as a Report14684
Term Project14456
Presentation of Project / Seminar000
Quiz000
Midterm Exam12424
General Exam13030
Performance Task, Maintenance Plan000
Total Workload(Hour)236
Dersin AKTS Kredisi = Toplam İş Yükü (Saat)/30*=(236/30)8
ECTS of the course: 30 hours of work is counted as 1 ECTS credit.

Detail Informations of the Course

Course Description

CourseCodeSemesterT+P (Hour)CreditECTS
ADVANCED PROBABILITY and APLICATIONS-Fall Semester3+038
Course Program
Prerequisites Courses
Recommended Elective Courses
Language of CourseEnglish
Course LevelThird Cycle (Doctorate Degree)
Course TypeElective
Course CoordinatorProf.Dr. Mehmet Kemal ÖZDEMİR
Name of Lecturer(s)Prof.Dr. Adnan KAVAK
Assistant(s)
AimThis is a graduate level course on advanced topics in probability and random variables. It aims to develop the ability to construct and analyze probabilistic models in a manner that combines intuitive understanding and mathematical precision. Different from the intrductory probability course, the course starts with digging the foundations in probability theory, random variables, expectation, and then it covers advanced topics such as transforms of distribution, further topics in random variables, limit theorems, statistical inference. This course also intends to provide students with the selected topics in stochastics processes such as Poisson process, Renewal process, Galton-Watson process, Gaussian process and discrete Markov Chains.
Course ContentThis course contains; Review of Basic Concepts (Probability Triple, Classical Probability Spaces, Concept of Sigma Field, Probability Measure, Conditional Probability, Limits of Events),Measurable Functions, Random Variables, Distribution Function,Random Vector, Joint Distribution, Independence,Expectation, Integral, and Weak and Strong Convergence,Chapter 3 of Textbook 1,Common Families of Distributions,Derived distributions,Midterm,Covariance and correlation, conditional expectation and variance, sums of random variables,Limit theorems,Statsitical inference,Topics in theory of stochastic processes,Discrete Markov Chains,Discrete Markov Chains.
Dersin Öğrenme KazanımlarıTeaching MethodsAssessment Methods
1. Understand the foundations in probability theory and random variables .21, 9A, E, F
2. Learn the concept of expectation, integral and convergence from different perspective. 21, 9A, E, F
3. Learn how to derive distributions of function of a random variable, and how to obtain transforms of random variables. 21, 9A, E, F
4. Learn how to obtain statistical inference 21, 9A, E, F
5. Analyze the stochastic processes and performance of systems using Markov Chains21, 9A, E, F
Teaching Methods:21: Simulation Technique, 9: Lecture Method
Assessment Methods:A: Traditional Written Exam, E: Homework, F: Project Task

Course Outline

OrderSubjectsPreliminary Work
1Review of Basic Concepts (Probability Triple, Classical Probability Spaces, Concept of Sigma Field, Probability Measure, Conditional Probability, Limits of Events)Lecture Notes, Chapter 1 of Textbook 1
2Measurable Functions, Random Variables, Distribution FunctionChapter 1 of Textbook 1
3Random Vector, Joint Distribution, IndependenceChapter 1 of Textbook 1
4Expectation, Integral, and Weak and Strong ConvergenceChapter 2 of Textbook 1
5Chapter 3 of Textbook 1Bölüm 3 Textbook 1
6Common Families of DistributionsChapter 3 of Textbook 1
7Derived distributionsChapter 4 of Textbook 2
8MidtermAll the topics till Week 8.
9Covariance and correlation, conditional expectation and variance, sums of random variablesChapter 4 of Textbook 2
10Limit theoremsChapter 5 of Textbook 2
11Statsitical inferenceChapter 9 of Textbook 2
12Topics in theory of stochastic processesChapter 8 of Textbook 1, Chapter 6 of Textbook 2
13Discrete Markov ChainsChapter 8 of Textbook 1, Chapter 7 of Textbook 2
14Discrete Markov ChainsChapter 8 of Textbook 1, Chapter 7 of Textbook 2
Resources
1. Advanced Probability Theory (Probability: Pure and Applied) , Janos Galambos, ISBN-13:978-9052016580
2. Introduction to Probability, 2nd Ed., Dimitri P. Bertsekas and John N. Tsitsiklis, ISBN-13: 978-1886529236

Course Contribution to Program Qualifications

Course Contribution to Program Qualifications
NoProgram QualificationContribution Level
12345
1
Develop and deepen the current and advanced knowledge in the field with original thought and/or research and come up with innovative definitions based on Master's degree qualifications.
X
2
Conceive the interdisciplinary interaction which the field is related with ; come up with original solutions by using knowledge requiring proficiency on analysis, synthesis and assessment of new and complex ideas.
X
3
Evaluate and use new information within the field in a systematic approach and gain advanced level skills in the use of research methods in the field.
X
4
Develop an innovative knowledge, method, design and/or practice or adapt an already known knowledge, method, design and/or practice to another field.
X
5
Broaden the borders of the knowledge in the field by producing or interpreting an original work or publishing at least one scientific paper in the field in national and/or international refereed journals.
X
6
Contribute to the transition of the community to an information society and its sustainability process by introducing scientific, technological, social or cultural improvements.
7
Independently perceive, design, apply, finalize and conduct a novel research process.
X
8
Ability to communicate and discuss orally, in written and visually with peers by using a foreign language at least at a level of European Language Portfolio C1 General Level.
X
9
Critical analysis, synthesis and evaluation of new and complex ideas in the field.
X
10
Recognizes the scientific, technological, social or cultural improvements of the field and contribute to the solution finding process regarding social, scientific, cultural and ethical problems in the field and support the development of these values.

Assessment Methods

Contribution LevelAbsolute Evaluation
Rate of Midterm Exam to Success 50
Rate of Final Exam to Success 50
Total 100

Numerical Data

Student Success

Ekleme Tarihi: 24/12/2023 - 02:16Son Güncelleme Tarihi: 24/12/2023 - 02:16