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| MAT2001 | Probability and Statistics I | 4+0+0 | ECTS:6 | | Year / Semester | Fall Semester | | Level of Course | First Cycle | | Status | Compulsory | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 4 hours of lectures per week | | Lecturer | Prof. Dr. Tülay YAZIR | | Co-Lecturer | PROF. DR. Tülay KESEMEN, | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The objective of this course is to initiate students to Probability Theory in which the main tools are those of Measure Theory. The proposed outline constitutes the prerequisites for Stochastic Calculus and other studies in the domain of stochastic processes. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | apply probability concepts to solve problem
| 1,4 | 1, | | LO - 2 : | apply concepts of independent events to solve problems
| 1,3 | 1, | | LO - 3 : | apply probability concepts to solve complex problems
| 1,4 | 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), LO : Learning Outcome | | |
| Random variable concept, probability space, probability distributions with one variable, multivariate probability distributions, mathematical expectation value, characteristics functions, producer functions, expectation value with condition, some inequalities, some discrete and concrete probability distributions
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Basics of the Probability Theory and Probability Space
| | | Week 2 | Conditional Probability, independent events, Bayes's theorems
| | | Week 3 | Examples and Random variables
| | | Week 4 | Distribution of functions of random variables, probability functions and distribution functions
| | | Week 5 | Expectations of random variables and variance
| | | Week 6 | Moment generating functions, properties of characteristic functions and properties.
| | | Week 7 | Multidimensional random variables and common distributions, common probability functions, density of common probability function
| | | Week 8 | Problem Solutions, covariance and correlation coefficients
| | | Week 9 | Mid-term exam
| | | Week 10 | Some discontinuous distributions (Bernoulli, Binom, geometric, hiper-geometric, Poisson)
| | | Week 11 | Properties of discontinuous distributions and problem solutions
| | | Week 12 | Some continuous distributions (Gamma, Beta)
| | | Week 13 | Normal distributions, standard normal distribution and properties of normal distributions
| | | Week 14 | Problem solutions
| | | Week 15 | Ki-Square distribution, student-T distribution, F-distribution and properties.
| | | Week 16 | End-of-term exam
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| 1 | [1] AKDENİZ, F. Olasılık ve İstatistik(2007) Nobel Kitabevi, ADANA. | | | |
| 1 | W.Micheal. Probability with Applications(1975) McGraw-Hill, Kagakusha | | | 2 | R.Sheldom A first course in probability(2006) Pearson Prentice Hall | | | 3 | Chandara,T.K. and Chattrjee,D. A first course in probability(2001) Alpha Science International | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 23/11/2021 | 2 | 50 | | End-of-term exam | 16 | 12/01/2021 | 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 | 14 | 56 | | Sınıf dışı çalışma | 6 | 14 | 84 | | Arasınav için hazırlık | 7 | 1 | 7 | | Arasınav | 5 | 1 | 5 | | Kısa sınav | 1.3 | 1 | 1.3 | | Dönem sonu sınavı için hazırlık | 10 | 1 | 10 | | Dönem sonu sınavı | 5 | 1 | 5 | | Total work load | | | 168.3 |
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