Course Description
| Course | Code | Semester | T+P (Hour) | Credit | ECTS |
|---|---|---|---|---|---|
| STOCHASTIC PROCESSES | - | Spring Semester | 3+0 | 3 | 8 |
| Course Program |
| Prerequisites Courses | |
| Recommended Elective Courses |
| Language of Course | English |
| Course Level | Second Cycle (Master's Degree) |
| Course Type | Elective |
| Course Coordinator | Assist.Prof. Tunçer BAYKAŞ |
| Name of Lecturer(s) | Assist.Prof. Tunçer BAYKAŞ |
| Assistant(s) | |
| Aim | To improve the knowledge of students on random processes and related properties, and to provide tools for solving of the engineering problems with stochastic nature. |
| Course Content | This course contains; 1 Introduction, random variables and classification,2 Distribution functions, probability mass and density functions,3 Multivariate random variables and joint distributions,4 Functions of random variables, conditional distributions,5 Expected value and moments, moment generating function, characteristic function, conditional expected value and moments,,6 Discrete probability distributions,7 Continuous probability distributions,8 Law of large numbers and central limit theorem,9 Random processes and related functions (Distribution, correlation, variance, covariance functions),10 Stationary processes, independent processes, processes with independent stationary increments, ergodicity,11 Poisson process, Wiener process,12 Gaussian process , Markov process,13 Concepts of stochastic continuity, derivative and integral,14 Concept of power spectrum. |
| Dersin Öğrenme Kazanımları | Teaching Methods | Assessment Methods |
| Students will gain knowledge, skill and competency in the following subjects; Random variables, distribution functions, expected value, variance, moments, continuous and discrete random distributions, random processes, stationary and independent processes and ergocity, different types of random processes, power spectrum. | ||
| Teaching Methods: | |
| Assessment Methods: |
Course Outline
| Order | Subjects | Preliminary Work |
|---|---|---|
| 1 | 1 Introduction, random variables and classification | |
| 2 | 2 Distribution functions, probability mass and density functions | |
| 3 | 3 Multivariate random variables and joint distributions | |
| 4 | 4 Functions of random variables, conditional distributions | |
| 5 | 5 Expected value and moments, moment generating function, characteristic function, conditional expected value and moments, | |
| 6 | 6 Discrete probability distributions | |
| 7 | 7 Continuous probability distributions | |
| 8 | 8 Law of large numbers and central limit theorem | |
| 9 | 9 Random processes and related functions (Distribution, correlation, variance, covariance functions) | |
| 10 | 10 Stationary processes, independent processes, processes with independent stationary increments, ergodicity | |
| 11 | 11 Poisson process, Wiener process | |
| 12 | 12 Gaussian process , Markov process | |
| 13 | 13 Concepts of stochastic continuity, derivative and integral | |
| 14 | 14 Concept of power spectrum |
| Resources |
| R. D. Yates, D. Goodman, Probability and Stochastic Processes: A Friendly Introduction for Electrical and Computer Engineers , John Wiley and Sons, 2005. |
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. | ||||||
| 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. | ||||||
| 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. | ||||||
| 4 | Develop an innovative knowledge, method, design and/or practice or adapt an already known knowledge, method, design and/or practice to another field. | ||||||
| 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. | ||||||
| 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. | ||||||
| 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. | ||||||
| 9 | Critical analysis, synthesis and evaluation of new and complex ideas in the field. | ||||||
| 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 | 13 | 2 | 26 | |||
| Resolution of Homework Problems and Submission as a Report | 0 | 0 | 0 | |||
| Term Project | 0 | 0 | 0 | |||
| Presentation of Project / Seminar | 0 | 0 | 0 | |||
| Quiz | 0 | 0 | 0 | |||
| Midterm Exam | 0 | 0 | 0 | |||
| General Exam | 0 | 0 | 0 | |||
| Performance Task, Maintenance Plan | 1 | 20 | 20 | |||
| Total Workload(Hour) | 88 | |||||
| Dersin AKTS Kredisi = Toplam İş Yükü (Saat)/30*=(88/30) | 3 | |||||
| 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 |
|---|---|---|---|---|---|
| STOCHASTIC PROCESSES | - | Spring Semester | 3+0 | 3 | 8 |
| Course Program |
| Prerequisites Courses | |
| Recommended Elective Courses |
| Language of Course | English |
| Course Level | Second Cycle (Master's Degree) |
| Course Type | Elective |
| Course Coordinator | Assist.Prof. Tunçer BAYKAŞ |
| Name of Lecturer(s) | Assist.Prof. Tunçer BAYKAŞ |
| Assistant(s) | |
| Aim | To improve the knowledge of students on random processes and related properties, and to provide tools for solving of the engineering problems with stochastic nature. |
| Course Content | This course contains; 1 Introduction, random variables and classification,2 Distribution functions, probability mass and density functions,3 Multivariate random variables and joint distributions,4 Functions of random variables, conditional distributions,5 Expected value and moments, moment generating function, characteristic function, conditional expected value and moments,,6 Discrete probability distributions,7 Continuous probability distributions,8 Law of large numbers and central limit theorem,9 Random processes and related functions (Distribution, correlation, variance, covariance functions),10 Stationary processes, independent processes, processes with independent stationary increments, ergodicity,11 Poisson process, Wiener process,12 Gaussian process , Markov process,13 Concepts of stochastic continuity, derivative and integral,14 Concept of power spectrum. |
| Dersin Öğrenme Kazanımları | Teaching Methods | Assessment Methods |
| Students will gain knowledge, skill and competency in the following subjects; Random variables, distribution functions, expected value, variance, moments, continuous and discrete random distributions, random processes, stationary and independent processes and ergocity, different types of random processes, power spectrum. | ||
| Teaching Methods: | |
| Assessment Methods: |
Course Outline
| Order | Subjects | Preliminary Work |
|---|---|---|
| 1 | 1 Introduction, random variables and classification | |
| 2 | 2 Distribution functions, probability mass and density functions | |
| 3 | 3 Multivariate random variables and joint distributions | |
| 4 | 4 Functions of random variables, conditional distributions | |
| 5 | 5 Expected value and moments, moment generating function, characteristic function, conditional expected value and moments, | |
| 6 | 6 Discrete probability distributions | |
| 7 | 7 Continuous probability distributions | |
| 8 | 8 Law of large numbers and central limit theorem | |
| 9 | 9 Random processes and related functions (Distribution, correlation, variance, covariance functions) | |
| 10 | 10 Stationary processes, independent processes, processes with independent stationary increments, ergodicity | |
| 11 | 11 Poisson process, Wiener process | |
| 12 | 12 Gaussian process , Markov process | |
| 13 | 13 Concepts of stochastic continuity, derivative and integral | |
| 14 | 14 Concept of power spectrum |
| Resources |
| R. D. Yates, D. Goodman, Probability and Stochastic Processes: A Friendly Introduction for Electrical and Computer Engineers , John Wiley and Sons, 2005. |
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. | ||||||
| 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. | ||||||
| 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. | ||||||
| 4 | Develop an innovative knowledge, method, design and/or practice or adapt an already known knowledge, method, design and/or practice to another field. | ||||||
| 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. | ||||||
| 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. | ||||||
| 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. | ||||||
| 9 | Critical analysis, synthesis and evaluation of new and complex ideas in the field. | ||||||
| 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 | |