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Information
| Code | ISB204 |
| Name | Theory of Statistics |
| Term | 2024-2025 Academic Year |
| Semester | 4. Semester |
| Duration (T+A) | 4-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 4 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. ALİ İHSAN GENÇ |
| Course Instructor |
1 2 |
Course Goal / Objective
The aim of this course is to give a mathematical basis for statistics.
Course Content
The scope is to study the statistics as functions of random variables by starting with the definition of a random vector.
Course Precondition
None
Resources
Matematiksel İstatistik, John E. Freund, Çeviri: Ümit Şenesen, Literatür Yayınları, 2015.
Notes
Statistical Inference, George Casella, Roger L. Berger, Second Ed., Duxbury Advanced Series, 2002.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Operates random vectoral evaluations. |
| LO02 | Finds moment generating functions and characteristic functions of random vectors. |
| LO03 | Finds the distributions of random vectors. |
| LO04 | Finds the distributions of sample statistics. |
| LO05 | Explains the methods of point estimation. |
| LO06 | Compares the point estimators. |
| LO07 | Explains the marginal and conditional distributions. |
| LO08 | Explains the stochastic independence. |
| LO09 | Explains the notions of covariance and correlation. |
| LO10 | Defines the notion of order statistics. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Explain the essence fundamentals and concepts in the field of Statistics | 4 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Emphasize the importance of Statistics in life | |
| PLO03 | Bilgi - Kuramsal, Olgusal | Define basic principles and concepts in the field of Law and Economics | |
| PLO04 | Bilgi - Kuramsal, Olgusal | Produce numeric and statistical solutions in order to overcome the problems | |
| PLO05 | Bilgi - Kuramsal, Olgusal | Use proper methods and techniques to gather and/or to arrange the data | |
| PLO06 | Bilgi - Kuramsal, Olgusal | Utilize computer programs and builds models, solves problems, does analyses and comments about problems concerning randomization | |
| PLO07 | Bilgi - Kuramsal, Olgusal | Apply the statistical analyze methods | 1 |
| PLO08 | Bilgi - Kuramsal, Olgusal | Make statistical inference (estimation, hypothesis tests etc.) | 3 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Generate solutions for the problems in other disciplines by using statistical techniques and gain insight | |
| PLO10 | Bilgi - Kuramsal, Olgusal | Discover the visual, database and web programming techniques and posses the ability of writing programs | |
| PLO11 | Beceriler - Bilişsel, Uygulamalı | Distinguish the difference between the statistical methods | |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Make oral and visual presentation for the results of statistical methods | |
| PLO13 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Have capability on effective and productive work in a group and individually | |
| PLO14 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Professional development in accordance with their interests and abilities, as well as the scientific, cultural, artistic and social fields, constantly improve themselves by identifying training needs | |
| PLO15 | Yetkinlikler - Öğrenme Yetkinliği | Develop scientific and ethical values in the fields of statistics-and scientific data collection |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Random vectors, joint distributions | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 2 | Joint probability mass function, joint probability density function | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 3 | Joint distribution function, joint moment generating function and properties | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 4 | Functions of more than one random variables and their distribution | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 5 | Functions of more than one random variables and their distribution II | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 6 | Conditional distributions, marginal distributions | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 7 | Conditional expected values and conditional variances | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 8 | Mid-Term Exam | Review the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Random samples and properties | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 10 | Distribution of sample statistics | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 11 | Distribution of sample statistics and standard error | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 12 | Limiting distributions, central limit theorem | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 13 | Order statistics and sample percentiles | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 14 | Method of moments and least squares method of estimation | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 15 | Maximum likelihood estimation method | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 16 | Term Exams | Review the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Review the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 4 | 56 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 4 | 56 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 12 | 12 |
| Final Exam | 1 | 28 | 28 |
| Total Workload (Hour) | 152 | ||
| Total Workload / 25 (h) | 6,08 | ||
| ECTS | 6 ECTS | ||