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Information
| Code | IEM1830 |
| Name | Probability Theory |
| Term | 2024-2025 Academic Year |
| Term | Fall and Spring |
| Duration (T+A) | 4-0 (T-A) (17 Week) |
| ECTS | 8 ECTS |
| National Credit | 4 National Credit |
| Teaching Language | Türkçe |
| Level | Doktora Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. GÜLSEN KIRAL |
| Course Instructor |
1 |
Course Goal / Objective
It aims to use probabilistic methods. Interprets probability theory concepts. It also includes many definitions of probability theory and mathematical statistics for students focusing on discrete random events and their distributions.
Course Content
Probability axioms, Conditional probability and Independence, Random variables, Joint distribution functions, Rank statistics, Principles of Sufficiency, Limit Theorems, Principles of data reduction, Point estimation, Hypothesis testing, Interval estimations.
Course Precondition
There are no prerequisites.
Resources
Source books, statistical packages
Notes
1-Statistical Inference by G.Casella and R.Berger, Thomson Information A first course in Probability by S.Rosse,Prentice Hall.2- Knight K (2000).Mathematical Statistics, Chapman & Hall/CRC, US.3- Shao, J. (1999). Mathematical Statistics, Springer-Verlag New York,Incorporated 4- Matematiksel İstatistik Prof. Dr. İsmail ERDEM (Seçkin Yayınevi ) 2. Baskı.5-Yılmaz Akdi(2005). Matematiksel İstatistiğe Giriş. Bıçaklar Kitabevi 6--R.V.Hogg and A.T. Craig, Collier McMillan, 1995. Introduction to Mathematical Statistics 7-İ.Hasgür (2000). Matematiksel İstatistik. Seçkin Yayınevi.8-Matematiksel İstatistik Prof. Dr.Mustafa Aytaç (Ezgi Yayınevi (3. Baskı ).9-Freund, J.E. (2001). Matematiksel İstatistik.(Çeviren Şenesen, Ü.) İstanbul: Literatür Yayıncılık.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Defines the basic principles of probability calculations. |
| LO02 | Can understand probability axioms and evaluate how they are used. |
| LO03 | Explains concepts such as conditional probability and independence. |
| LO04 | Makes point estimation with estimator methods. |
| LO05 | Evaluates estimators with estimator features. |
| LO06 | Specifies the hypothesis and evaluates the hypothesis with hypothesis finding methods. |
| LO07 | Makes interval estimation with interval estimation methods. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Identify an econometric problem and propose a new solution to it | 3 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Develops new knowledge using current concepts in Econometrics, Statistics and Operations Research | 3 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Explain for what purpose and how econometric methods are applied to other fields and disciplines | |
| PLO04 | Beceriler - Bilişsel, Uygulamalı | Using her knowledge, brings original solutions to problems in Economics, Business Administration and other social sciences | 3 |
| PLO05 | Beceriler - Bilişsel, Uygulamalı | Creates a new model using mathematics, statistics and econometrics knowledge to solve the problem encountered | 4 |
| PLO06 | Beceriler - Bilişsel, Uygulamalı | Interprets the results obtained from the most appropriate method to predict the model | 3 |
| PLO07 | Beceriler - Bilişsel, Uygulamalı | Performs conceptual analysis to develop solutions to problems | 4 |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | Collects data on purpose | 3 |
| PLO09 | Beceriler - Bilişsel, Uygulamalı | Synthesizes the information obtained by using different sources within the framework of academic rules in a field that does not research | 4 |
| PLO10 | Beceriler - Bilişsel, Uygulamalı | Presents analysis results conveniently | 3 |
| PLO11 | Beceriler - Bilişsel, Uygulamalı | Converts its findings into a master's thesis or a professional report in Turkish or a foreign language | 3 |
| PLO12 | Beceriler - Bilişsel, Uygulamalı | It researches current approaches and methods to solve the problems it encounters and proposes new solutions | 4 |
| PLO13 | Beceriler - Bilişsel, Uygulamalı | Develops long-term plans and strategies using econometric and statistical methods | |
| PLO14 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Performs self-study using knowledge of Econometrics, Statistics and Operations to solve a problem | 3 |
| PLO15 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Leads the team by taking responsibility | 4 |
| PLO16 | Yetkinlikler - Öğrenme Yetkinliği | Being aware of the necessity of lifelong learning, it constantly renews itself by following the current developments in the field of study | 3 |
| PLO17 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Uses acquired knowledge in the field to determine the vision, aim, and goals for an organization/institution | 3 |
| PLO18 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Uses a package program of Econometrics, Statistics, and Operation Research or writes a new code | 4 |
| PLO19 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Interprets the feelings, thoughts and behaviors of the related persons correctly/expresses himself/herself correctly in written and verbal form | 4 |
| PLO20 | Yetkinlikler - Alana Özgü Yetkinlik | Applies social, scientific and professional ethical values | 3 |
| PLO21 | Yetkinlikler - Alana Özgü Yetkinlik | Interprets data on economic and social events by following current issues |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Fundamentals of Probability Theory and Axiomatics | read the relevant chapters from the source book | Öğretim Yöntemleri: Anlatım |
| 2 | Random variables and distribution functions | read the relevant chapters from the source book | Öğretim Yöntemleri: Anlatım |
| 3 | Conversions and Expectations | read the relevant chapters from the source book | Öğretim Yöntemleri: Anlatım |
| 4 | Multiple random variables, Joint and Marginal Distributions | read the relevant chapters from the source book | Öğretim Yöntemleri: Anlatım |
| 5 | Random sample properties | read the relevant chapters from the source book | Öğretim Yöntemleri: Anlatım |
| 6 | Data reduction principles, Likelihood function | read the relevant chapters from the source book | Öğretim Yöntemleri: Anlatım |
| 7 | Point estimation, Estimator finding | read the relevant chapters from the source book | Öğretim Yöntemleri: Anlatım |
| 8 | Mid-Term Exam | Reading the relevant parts in the book | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Point estimation, Estimator Evaluation | read the relevant chapters from the source book | Öğretim Yöntemleri: Anlatım |
| 10 | Methods of finding Hypothesis Tests | read the relevant chapters from the source book | Öğretim Yöntemleri: Anlatım |
| 11 | Hypothesis Tests Evaluation Methods | read the relevant chapters from the source book | Öğretim Yöntemleri: Anlatım |
| 12 | Asymptotic Distributions | read the relevant chapters from the source book | Öğretim Yöntemleri: Anlatım |
| 13 | Range forecasts, find range forecasters | read the relevant chapters from the source book | Öğretim Yöntemleri: Anlatım |
| 14 | Range predictions, evaluating range estimators | read the relevant chapters from the source book | Öğretim Yöntemleri: Anlatım |
| 15 | Review | Reading the relevant parts in the book | Öğretim Yöntemleri: Anlatım |
| 16 | Term Exams | Ölçme Yöntemleri: Yazılı Sınav |
|
| 17 | Term Exams | 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 | 8 | 112 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 2 | 4 | 8 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 12 | 12 |
| Final Exam | 1 | 24 | 24 |
| Total Workload (Hour) | 212 | ||
| Total Workload / 25 (h) | 8,48 | ||
| ECTS | 8 ECTS | ||