TÜRKÇE
ENGLISH
Information
| Unit | INSTITUTE OF SOCIAL SCIENCES |
| ECONOMETRICS (PhD) | |
| Code | IEM1833 |
| Name | Probability Theory and Mathematical Statistics I |
| 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 |
The current term course schedule has not been prepared yet.
|
Course Goal / Objective
The aim of the course is to make students familiar with all the concepts of probability theory.
Course Content
This course covers that Axioms of probability, conditional probability and independence, random variables, Joint Distribution functions, order statistics,The principles of competence, limit theorems, principles of data reduction, Point Estimation, hypothesis testing, Interval estimates.
Course Precondition
There are no prerequisites.
Resources
Knight, K. (1999). Mathematical statistics. CRC Press. Shao, J. (2008). Mathematical statistics. Springer Science & Business Media. Akdi, Y. (2005). Matematiksel istatistiğe giriş. Bıçaklar Kitabevi. Hogg, R. V., McKean, J. W., & Craig, A. T. (2013). Introduction to mathematical statistics. Pearson Education India.
Notes
Hasgür, İ. (2000). Matematiksel istatistik. Seçkin Yayınevi. Aytaç, M. (2012). Matematiksel istatistik. Ezgi Kitabevi Yayınları. Freund, J. E., Miller, I., Miller, M., & Şenesen, Ü. (2002). John E. Freund'dan matematiksel istatistik. Literatür.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Describes the basic principles of probability calculations. |
| LO02 | Explains concepts such as conditional probability and independence. |
| LO03 | Explain point estimation using estimator finding methods. |
| LO04 | Creates and explains hypotheses using hypothesis finding methods. |
| LO05 | Applies interval estimation with interval estimation methods. |
| LO06 | Understands the axioms of probability and explains how they are used. |
| LO07 | Explains estimators with their estimator properties. |
| LO08 | Explains common distribution functions. |
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 | 4 |
| 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 | 3 |
| PLO04 | Beceriler - Bilişsel, Uygulamalı | Using her knowledge, brings original solutions to problems in Economics, Business Administration and other social sciences | |
| 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 | 4 |
| PLO09 | Beceriler - Bilişsel, Uygulamalı | Synthesizes the information obtained by using different sources within the framework of academic rules in a field of research | 2 |
| 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 | |
| PLO12 | Beceriler - Bilişsel, Uygulamalı | It researches current approaches and methods to solve the problems it encounters and proposes new solutions | 2 |
| PLO13 | Beceriler - Bilişsel, Uygulamalı | Develops long-term plans and strategies using econometric and statistical methods | 2 |
| PLO14 | Beceriler - Bilişsel, Uygulamalı | Uses a package program/writes a new code for Econometrics, Statistics, and Operation Research | 3 |
| PLO15 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Performs self-study using knowledge of Econometrics, Statistics and Operations to solve a problem | 2 |
| PLO16 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Leads the team by taking responsibility | 4 |
| PLO17 | 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 |
| PLO18 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Uses acquired knowledge in the field to determine the vision, aim, and goals for an organization/institution | |
| 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 | 3 |
| PLO20 | Yetkinlikler - Alana Özgü Yetkinlik | Applies social, scientific and professional ethical values | 4 |
| PLO21 | Yetkinlikler - Alana Özgü Yetkinlik | Interprets data on economic and social events by following current issues | 3 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Probability theory and its Axiomatic Foundations | Reading | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Tartışma |
| 2 | Random variables and distribution functions | Reading | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Soru-Cevap |
| 3 | Transformations and expectations | Reading | Öğretim Yöntemleri: Anlatım |
| 4 | Multiple random variables, joint and marginal Distributions. | Reading | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Tartışma |
| 5 | Properties of a random sample | Reading | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 6 | Principles of data reduction, likelihood function | Reading | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 7 | Point estimation, finding estimators | Reading | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 8 | Mid-Term Exam | Preparing for the midterm exam | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Point estimation, evaluation of estimators | Reading | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 10 | Methods of finding hypothesis tests | Reading | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 11 | Hypothesis Tests Evaluation Methods | Reading | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 12 | Asymptotic Distributions | Reading | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 13 | Interval forecasts and finding interval estimators | Reading | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 14 | Interval forecasts and evaluation interval estimators | Reading | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 15 | Additional Topics | Reading | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Soru-Cevap |
| 16 | Term Exams | Final exam preparation | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Final exam preparation | 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 | ||