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| MATL5031 | Probability theory and Applications | 3+0+0 | ECTS:7.5 | | Year / Semester | Fall Semester | | Level of Course | Second Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | -- | | Co-Lecturer | -- | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The aim of this course is the introduction of the methodology and the basic concepts of probability, teaching knowledge on probability, review and discussions of the distributions and fundamental methods and the applications of these methods. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | Knows the theory of probability with its different definitions and historical development | | | | PO - 2 : | Learns the characteristics of probability | | | | PO - 3 : | Learns the distributions of probability | | | | PO - 4 : | Connects these distributions to the real life examples | | | | PO - 5 : | Grasps the theoretical basis of probability with applications | | | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), PO : Learning Outcome | | |
| Basic concepts of probability theory, short history, definition and properties of probability, concept and classification of random variables, probabilistic and numerical characteristics of distributions. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Stochastic experiment, random event, operations on events, examples | | | Week 2 | Formal, classical and experimantal definitions of probability | | | Week 3 | Algebra and sigma-algebra concepts and examples | | | Week 4 | Probability measure, probability space and examples | | | Week 5 | Kolmogrov axioms and their results | | | Week 6 | Conditional probability, independant events | | | Week 7 | Total probability formula, Bayes theorem | | | Week 8 | Applications | | | Week 9 | Mid-term | | | Week 10 | Definition and distribution of random variables | | | Week 11 | Classification of distributions and examples | | | Week 12 | Discrete distributions and examples | | | Week 13 | Absolute continuous distributions and examples | | | Week 14 | Probabilistic characteristics of random variables | | | Week 15 | Numerical characteristics of random variables | | | Week 16 | Final exam | | | |
| 1 | Shiryayev A.N. Probabilty.Springer-Verlag, 1984 | | | |
| 1 | Olasılık, Tamilla Nasırova, v.d., Karadeniz Teknik Üniversitesi Matbaası, 2009, Trabzon | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 14/11/2017 | 2 | 50 | | End-of-term exam | 16 | 05/01/2018 | 2 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 4 | 15 | 60 | | Sınıf dışı çalışma | 4 | 15 | 60 | | Arasınav için hazırlık | 20 | 1 | 20 | | Arasınav | 2 | 1 | 2 | | Ödev | 3 | 14 | 42 | | Dönem sonu sınavı için hazırlık | 30 | 1 | 30 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 216 |
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