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Information
| Code | IEM1834 |
| Name | Probability Theory and Mathematical Statistics II |
| Term | 2024-2025 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 lesson is to provide a strong foundation in the subjects of advanced probability theory and mathematical statistics.
Course Content
This course covers that Convergence in distribution, weak convergence, characteristic functions, inverse uniqueness theorem, Central Limit Theorem, empirical and asymptotic behavior of order statistics, asymptotic properties of the estimators, the asymptotic behaviour of the test statistics, conditional probability, Martingale, Kolmogorov entity's theorem.
Course Precondition
There are no prerequisites.
Resources
Probability and Statistics for Engineering and Scientists, R.E. Walpole, R.H. Myers, S.L. Myers, K. Ye, Prentice Hall,2007
Notes
Source books, statistical packages
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Defines advanced mathematics and statistics concepts . |
| LO02 | Relates between mathematics and other disciplines. |
| LO03 | Evaluates mathematical models for interdisciplinary problems. |
| LO04 | It expands the abilities of math, statistics, communication, problem solving and brainstorming. |
| LO05 | It exemplifies advanced probability theory and mathematical statistics. |
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 | 2 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Explain for what purpose and how econometric methods are applied to other fields and disciplines | 2 |
| 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 | 2 |
| 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 | 3 |
| 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 | 1 |
| 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 | 2 |
| 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 | 1 |
| PLO17 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Uses acquired knowledge in the field to determine the vision, aim, and goals for an organization/institution | 2 |
| 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 | 2 |
| PLO20 | Yetkinlikler - Alana Özgü Yetkinlik | Applies social, scientific and professional ethical values | |
| PLO21 | Yetkinlikler - Alana Özgü Yetkinlik | Interprets data on economic and social events by following current issues | 1 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Convergence in distribution, weak convergence. | Examining the relevant chapter in the book | Öğretim Yöntemleri: Anlatım |
| 2 | Characteristic function, inverse and uniqueness theorems. | Examining the relevant chapter in the book | Öğretim Yöntemleri: Anlatım |
| 3 | The Central Limit Theorem; Lindenberg and Lyapunov theorem, Feller's theorem. | Examining the relevant chapter in the book | Öğretim Yöntemleri: Anlatım |
| 4 | Empirical and asymptotic behavior of order statistics | Examining the relevant chapter in the book | Öğretim Yöntemleri: Anlatım |
| 5 | The asymptotic properties of estimators; asymptotic properties of Maximum likelihood estimators | Examining the relevant chapter in the book | Öğretim Yöntemleri: Anlatım |
| 6 | Optimal test; powerful tests. | Examining the relevant chapter in the book | Öğretim Yöntemleri: Anlatım |
| 7 | Neumann-Pearson Lemma. | Examining the relevant chapter in the book | Öğretim Yöntemleri: Anlatım |
| 8 | Mid-Term Exam | Examining the relevant chapter in the book | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Asymptotic behavior of Test statistics. | Examining the relevant chapter in the book | Öğretim Yöntemleri: Anlatım |
| 10 | Conditional probability; Hann Parse, absolute continuity and Singularity. | Examining the relevant chapter in the book | Öğretim Yöntemleri: Anlatım |
| 11 | Radon-Nikodym Theorem | Examining the relevant chapter in the book | Öğretim Yöntemleri: Anlatım |
| 12 | Conditional probability; properties of conditional probability, the conditional probability density function. | Examining the relevant chapter in the book | Öğretim Yöntemleri: Anlatım |
| 13 | Conditional Expected Value. | Examining the relevant chapter in the book | Öğretim Yöntemleri: Anlatım |
| 14 | Martingale; Sub-Martingales, The Martingale convergence theorem. | Examining the relevant chapter in the book | Öğretim Yöntemleri: Anlatım |
| 15 | Kolmogorov entity's theorem-finite dimensional distributions. | Examining the relevant chapter in the book | Öğretim Yöntemleri: Anlatım |
| 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 | ||