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Information
| Code | IEM1833 |
| Name | Probability Theory and Mathematical Statistics I |
| Term | 2023-2024 Academic Year |
| Semester | . Semester |
| 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 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
Source books, statistical packages
Notes
1-Statistical Inference by G.Casella and R.Berger, Thomson InformationA first course in Probability by S.Rosse,Prentice Hall2- Knight K. (2000).Mathematical Statistics, Chapman and Hall/CRC, US. 3- Shao, J. (1999). Mathematical Statistics, Springer-Verlag New York, Incorporated4- Matematiksel İstatistik Prof. Dr. İsmail ERDEM (Seçkin Yayınevi ) 2. Baskı 5-Yılmaz Akdi(2005). Matematiksel İstatistiğe Giriş. Bıçaklar Kitabevi6--R.V.Hogg and A.T. Craig, Collier McMillan, 1995. Introduction to Mathematical Statistics7-İ.Hasgür (2000). Matematiksel İstatistik. Seçkin Yayınevi8-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 | Describes the basic principles of probability calculations. |
| LO02 | Interprets concepts such as conditional probability and independence. |
| LO03 | Makes point estimation with methods for finding estimators. |
| LO04 | Creates and interprets hypotheses with hypothesis finding methods. |
| LO05 | Makes interval estimation with methods of interval estimation. |
| LO06 | Understands the axioms of probability and explains how they are used. |
| LO07 | Evaluates estimators with estimator features. |
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 that does not 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 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Performs self-study using knowledge of Econometrics, Statistics and Operations to solve a problem | 2 |
| 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 | |
| PLO18 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Uses a package program of Econometrics, Statistics, and Operation Research or writes a new code | 3 |
| 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 | Examining the relevant chapter in the book | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 2 | Random variables and distribution functions | Examining the relevant chapter in the book | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 3 | Transformations and expectations | Examining the relevant chapter in the book | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 4 | Multiple random variables, joint and marginal Distributions. | Examining the relevant chapter in the book | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 5 | Properties of a random sample | Examining the relevant chapter in the book | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 6 | Principles of data reduction, likelihood function | Examining the relevant chapter in the book | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 7 | Point estimation, finding estimators | Examining the relevant chapter in the book | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 8 | Mid-Term Exam | Examining the relevant chapter in the book | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Point estimation, evaluation of estimators | Examining the relevant chapter in the book | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 10 | Methods of finding hypothesis tests | Examining the relevant chapter in the book | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 11 | Hypothesis Tests Evaluation Methods | Examining the relevant chapter in the book | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 12 | Asymptotic Distributions | Examining the relevant chapter in the book | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 13 | Interval forecasts and finding interval estimators | Examining the relevant chapter in the book | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 14 | Interval forecasts and evaluation interval estimators | Examining the relevant chapter in the book | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 15 | Additional Topics | Examining the relevant chapter in the book | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 16 | Term Exams | Examining the relevant chapter in the book | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Examining the relevant chapter in the book | 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 | ||