ISB204 Theory of Statistics

6 ECTS - 4-0 Duration (T+A)- 4. Semester- 4 National Credit

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
Prof. Dr. ALİ İHSAN GENÇ (A Group) (Ins. in Charge)


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

Update Time: 11.06.2024 02:06