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| MAT5200 | Advanced Statistics | 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 | Prof. Dr. Tülay YAZIR | | Co-Lecturer | Assist. Prof. Dr. Tülay KESEMEN | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The aims of this course is to teach the basic concepts and methods of advanced statistics. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | apply conditional probability stokostic independence to the problems. | 1,3 | 1 | | PO - 2 : | apply limiting distrubutions statistical tests,statistical hypotetheses to the problem. | 1,3 | 1 | | PO - 3 : | applys pecial distributions to the problems. | 1,3 | 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 | | |
| Random variables and distribution functions, Special distributions and some important formulas, Point estimation and Cnfidence intervals, The Univariate and Multivariate Normal distributions,Noncentral Chi-Square,F,t-Distributions,Independence of lineer forms, Quadratic forms and Expecdet value Quadratic forms. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Random variables and distribution function, | | | Week 2 | Moment generating function and independence of random variables, | | | Week 3 | Special distributions and some important formulas, | | | Week 4 | Point estimations and Confidence intervals, | | | Week 5 | The Univariate normal distribution and Multivariate normal distribution, | | | Week 6 | Independent and Uncorrelated random vectors, | | | Week 7 | Noncentral Chi-Square distribution, | | | Week 8 | Mid-term exam | | | Week 9 | Noncenral F dİstribution | | | Week 10 | Noncentral t-Distribution | | | Week 11 | Distribution of Quadretic forms, | | | Week 12 | Independece of linear forms, | | | Week 13 | Independence of Quadretic forms, | | | Week 14 | Expected value of Quadratic forms, | | | Week 15 | Additional Theorems and Problems. | | | Week 16 | End-of-term exam | | | |
| 1 | Robert V. Hogg and Allen T. Craig 1978, Introduction to Mathematical Statistics, MACMİLLİAN publishing Co. | | | |
| 1 | T. W. Anderson, 1957, An Introduction to Multivariate Statistical Analysis, A Willey Publication in Mathematical Statistics. | | | 2 | S. R.Searle 1971, Linear Models, John Wiley and Sons. | | | 3 | F. A. Graybill 1976, Theory and Application of the Linear Model, Duxbury Press. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 4/2024 | 2 | 50 | | End-of-term exam | 16 | 6/2024 | 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 | | Arasınav için hazırlık | 15 | 1 | 15 | | Arasınav | 1 | 2 | 2 | | Ödev | 9 | 4 | 36 | | Dönem sonu sınavı için hazırlık | 22 | 1 | 22 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 189 |
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