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| IST7010 | Basic Concepts in Probability Theory | 3+0+0 | ECTS:7.5 | | Year / Semester | Spring Semester | | Level of Course | Third Cycle | | Status | Elective | | Department | DEPARTMENT of STATISTICS and COMPUTER SCIENCES | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | Prof. Dr. Zafer KÜÇÜK | | Co-Lecturer | None | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | To teach the basic concepts of probability theory. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | learn basic information about the probability theory
| 1,3,7 | 1 | | PO - 2 : | interpret the information obtained with the help of probability theory | 1,3,7 | 1 | | PO - 3 : | use probability theory in other disciplines | 1,3,7 | 1 | | 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 | | |
| Measure and probability spaces, extension theorem, measurable function and random variable, expectation, characteristic functions, independence, convergence. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Basic concepts in probability theory | | | Week 2 | Stochastic experiment, random events, events on the operations, examples | | | Week 3 | Basic concepts of combinatorial theory | | | Week 4 | Different definitions of probability: experimental definition, theoretical definition, the classical definition | | | Week 5 | Sigma algebra and algebra, probability measure, sample, conditional probability, independent events, additive probability | | | Week 6 | Bayes' theorem and examples | | | Week 7 | General Review and problem solving | | | Week 8 | Mid-term exam | | | Week 9 | Random variables and distributions: discrete, continuous and singular distribution | | | Week 10 | Multi-dimensional distributions | | | Week 11 | Numerical characteristics of random variables | | | Week 12 | Correlation coefficient and its properties, and conditional expected value of the conditional distribution function | | | Week 13 | Examples | | | Week 14 | Characteristic functions | | | Week 15 | Multi-dimensional characteristic function of distribution, manufacturers function, repetition and problem solving issues | | | Week 16 | End-of-term exam | | | |
| 1 | Nasirova, T., Khaniyev, T., Yapar, C., Ünver, İ. ve Küçük, Z. 2009; Olasılık, KTÜ Yayınları, Trabzon | | | |
| 1 | Akdeniz, F. 1998; Olasılık ve İstatistik, Baki Kitapevi, Adana | | | 2 | Öztürk, F. 1993; Matematiksel İstatistik, ANkara Üniversitesi Yayınları, Ankara | | | 3 | Feller W. 1970; An Introduction to Probability Theory and Its Application, Vol. II, John Wiley&Sons, New York | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 8 | 18/11/2012 | 2 | 30 | | Quiz | 12 | 13/12/2009 | 2 | 20 | | End-of-term exam | 15 | 04/01/2013 | 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 | 3 | 14 | 42 | | Sınıf dışı çalışma | 5 | 14 | 70 | | Laboratuar çalışması | 0 | 0 | 0 | | Arasınav için hazırlık | 25 | 1 | 25 | | Arasınav | 2 | 1 | 2 | | Uygulama | 0 | 0 | 0 | | Klinik Uygulama | 0 | 0 | 0 | | Ödev | 5 | 7 | 35 | | Proje | 6 | 5 | 30 | | Kısa sınav | 0 | 0 | 0 | | Dönem sonu sınavı için hazırlık | 20 | 1 | 20 | | Dönem sonu sınavı | 2 | 1 | 2 | | Diğer 1 | 0 | 0 | 0 | | Diğer 2 | 0 | 0 | 0 | | Total work load | | | 226 |
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