Course Description
| Course | Code | Semester | T+P (Hour) | Credit | ECTS |
|---|---|---|---|---|---|
| ADVANCED PROBABILITY and APLICATIONS | EECD1112899 | Fall Semester | 3+0 | 3 | 8 |
| Course Program |
| Prerequisites Courses | |
| Recommended Elective Courses |
| Language of Course | English |
| Course Level | Third Cycle (Doctorate Degree) |
| Course Type | Elective |
| Course Coordinator | Prof.Dr. Mehmet Kemal ÖZDEMİR |
| Name of Lecturer(s) | Prof.Dr. Mehmet Kemal ÖZDEMİR |
| Assistant(s) | None. |
| Aim | This 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 Content | This 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,Transforms of Distribution (Characteristic Functions, Moment Generating Functions),Common Families of Distributions,Derived distributions,Midterm preparation overview,Covariance and correlation, conditional expectation and variance, sums of random variables,Limit theorems,Statistical inference,Topics in theory of stochastic processes,Discrete Markov Chains-1,Discrete Markov Chains-2. |
| Dersin Öğrenme Kazanımları | Teaching Methods | Assessment Methods |
| Uses the foundations of probability theory and random variables in mathematical problems. | 21, 9 | A, F |
| Applies the concept of expectation, integral and convergence from different perspectives to engineering problems. | 21, 9 | A, F |
| Applies distributions of functions of random variables and their transforms into engineering problems. | 21, 9 | A, F |
| Obtain statistical inference from a given data set. | 21, 9 | A, F |
| It analyzes the performance of the system with Markov chains. | 21, 9 | A, F |
| Analyzes statistical images. | 21, 9 | A, F |
| Teaching Methods: | 21: Simulation Technique, 9: Lecture Method |
| Assessment Methods: | A: Traditional Written Exam, F: Project Task |
Course Outline
| Order | Subjects | Preliminary Work |
|---|---|---|
| 1 | Review 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 |
| 2 | Measurable Functions, Random Variables, Distribution Function | Chapter 1 of Textbook 1 |
| 3 | Random Vector, Joint Distribution, Independence | Chapter 1 of Textbook 1 |
| 4 | Expectation, Integral, and Weak and Strong Convergence | Chapter 2 of Textbook 1 |
| 5 | Transforms of Distribution (Characteristic Functions, Moment Generating Functions) | Bölüm 3 Textbook 1 |
| 6 | Common Families of Distributions | Chapter 3 of Textbook 1 |
| 7 | Derived distributions | Chapter 4 of Textbook 2 |
| 8 | Midterm preparation overview | All the topics till Week 8. |
| 9 | Covariance and correlation, conditional expectation and variance, sums of random variables | Chapter 4 of Textbook 2 |
| 10 | Limit theorems | Chapter 5 of Textbook 2 |
| 11 | Statistical inference | Chapter 9 of Textbook 2 |
| 12 | Topics in theory of stochastic processes | Chapter 8 of Textbook 1, Chapter 6 of Textbook 2 |
| 13 | Discrete Markov Chains-1 | Chapter 8 of Textbook 1, Chapter 7 of Textbook 2 |
| 14 | Discrete Markov Chains-2 | Chapter 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 | |||||||
| No | Program Qualification | Contribution Level | |||||
| 1 | 2 | 3 | 4 | 5 | |||
| 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 Level | Absolute Evaluation | |
| Rate of Midterm Exam to Success | 50 | |
| Rate of Final Exam to Success | 50 | |
| Total | 100 | |
| ECTS / Workload Table | ||||||
| Activities | Number of | Duration(Hour) | Total Workload(Hour) | |||
| Course Hours | 14 | 3 | 42 | |||
| Guided Problem Solving | 0 | 0 | 0 | |||
| Resolution of Homework Problems and Submission as a Report | 6 | 24 | 144 | |||
| Term Project | 0 | 0 | 0 | |||
| Presentation of Project / Seminar | 0 | 0 | 0 | |||
| Quiz | 0 | 0 | 0 | |||
| Midterm Exam | 1 | 15 | 15 | |||
| General Exam | 1 | 24 | 24 | |||
| Performance Task, Maintenance Plan | 0 | 0 | 0 | |||
| Total Workload(Hour) | 225 | |||||
| Dersin AKTS Kredisi = Toplam İş Yükü (Saat)/30*=(225/30) | 8 | |||||
| ECTS of the course: 30 hours of work is counted as 1 ECTS credit. | ||||||
Detail Informations of the Course
Course Description
| Course | Code | Semester | T+P (Hour) | Credit | ECTS |
|---|---|---|---|---|---|
| ADVANCED PROBABILITY and APLICATIONS | EECD1112899 | Fall Semester | 3+0 | 3 | 8 |
| Course Program |
| Prerequisites Courses | |
| Recommended Elective Courses |
| Language of Course | English |
| Course Level | Third Cycle (Doctorate Degree) |
| Course Type | Elective |
| Course Coordinator | Prof.Dr. Mehmet Kemal ÖZDEMİR |
| Name of Lecturer(s) | Prof.Dr. Mehmet Kemal ÖZDEMİR |
| Assistant(s) | None. |
| Aim | This 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 Content | This 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,Transforms of Distribution (Characteristic Functions, Moment Generating Functions),Common Families of Distributions,Derived distributions,Midterm preparation overview,Covariance and correlation, conditional expectation and variance, sums of random variables,Limit theorems,Statistical inference,Topics in theory of stochastic processes,Discrete Markov Chains-1,Discrete Markov Chains-2. |
| Dersin Öğrenme Kazanımları | Teaching Methods | Assessment Methods |
| Uses the foundations of probability theory and random variables in mathematical problems. | 21, 9 | A, F |
| Applies the concept of expectation, integral and convergence from different perspectives to engineering problems. | 21, 9 | A, F |
| Applies distributions of functions of random variables and their transforms into engineering problems. | 21, 9 | A, F |
| Obtain statistical inference from a given data set. | 21, 9 | A, F |
| It analyzes the performance of the system with Markov chains. | 21, 9 | A, F |
| Analyzes statistical images. | 21, 9 | A, F |
| Teaching Methods: | 21: Simulation Technique, 9: Lecture Method |
| Assessment Methods: | A: Traditional Written Exam, F: Project Task |
Course Outline
| Order | Subjects | Preliminary Work |
|---|---|---|
| 1 | Review 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 |
| 2 | Measurable Functions, Random Variables, Distribution Function | Chapter 1 of Textbook 1 |
| 3 | Random Vector, Joint Distribution, Independence | Chapter 1 of Textbook 1 |
| 4 | Expectation, Integral, and Weak and Strong Convergence | Chapter 2 of Textbook 1 |
| 5 | Transforms of Distribution (Characteristic Functions, Moment Generating Functions) | Bölüm 3 Textbook 1 |
| 6 | Common Families of Distributions | Chapter 3 of Textbook 1 |
| 7 | Derived distributions | Chapter 4 of Textbook 2 |
| 8 | Midterm preparation overview | All the topics till Week 8. |
| 9 | Covariance and correlation, conditional expectation and variance, sums of random variables | Chapter 4 of Textbook 2 |
| 10 | Limit theorems | Chapter 5 of Textbook 2 |
| 11 | Statistical inference | Chapter 9 of Textbook 2 |
| 12 | Topics in theory of stochastic processes | Chapter 8 of Textbook 1, Chapter 6 of Textbook 2 |
| 13 | Discrete Markov Chains-1 | Chapter 8 of Textbook 1, Chapter 7 of Textbook 2 |
| 14 | Discrete Markov Chains-2 | Chapter 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 | |||||||
| No | Program Qualification | Contribution Level | |||||
| 1 | 2 | 3 | 4 | 5 | |||
| 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 Level | Absolute Evaluation | |
| Rate of Midterm Exam to Success | 50 | |
| Rate of Final Exam to Success | 50 | |
| Total | 100 | |