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Information
| Code | IEM732 |
| Name | Mathematical Statistics I |
| Term | 2023-2024 Academic Year |
| Term | Fall and Spring |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Yüksek Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. EBRU ÖZGÜR GÜLER |
| Course Instructor |
1 |
Course Goal / Objective
The objective of this course is to bring the knowlegde of techniques and basic results of probability and mathematical statistics to students.
Course Content
The content of this course covers probability, discrete random variables, continuous random variables with mathematical and statistical properties of these topics, and the maximum likelihood estimation.
Course Precondition
None
Resources
Matematiksel istatistik, Prof. Dr. Mustafa Aytaç, Ezgi Yayınevi ve Matematiksel istatistik, Yılmaz Akdi, Gazi Kitabevi
Notes
Matematiksel istatistik Problemler ve Çözümleri, Seçkin Yayınevi, Prof. Dr. İsmail Erdem. Matematiksel İstatistik, John E. Freund
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Explains basic probability concepts |
| LO02 | Discriminates mathematical and statistical properties of discrete random variables |
| LO03 | Discriminates mathematical and statistical properties of continous random variables |
| LO04 | Models real life data by using discrete and continuous random variables |
| LO05 | Describes foundations of the estimation theory and its applications in real life |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Explains contemporary concepts about Econometrics, Statistics, and Operation Research | 4 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Explains relationships between acquired knowledge about Econometrics, Statistics, and Operation Research | 4 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Explains how to apply acquired knowledge in the field to Economics, Business, and other social sciences | 1 |
| PLO04 | Beceriler - Bilişsel, Uygulamalı | Performs conceptual analysis to develop solutions to problems | 4 |
| PLO05 | Beceriler - Bilişsel, Uygulamalı | Models problems with Mathematics, Statistics, and Econometrics | 5 |
| PLO06 | Beceriler - Bilişsel, Uygulamalı | Interprets the results obtained from the most appropriate method to predict the model | 3 |
| PLO07 | Beceriler - Bilişsel, Uygulamalı | Synthesizes the information obtained by using different sources within the framework of academic rules in a field that does not research | |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | Uses acquired knowledge in the field to determine the vision, aim, and goals for an organization/institution | |
| PLO09 | Beceriler - Bilişsel, Uygulamalı | Searches for new approaches and methods to solve problems being faced | |
| PLO10 | Beceriler - Bilişsel, Uygulamalı | Presents analysis results conveniently | 4 |
| PLO11 | Beceriler - Bilişsel, Uygulamalı | Collects/analyzes data in a purposeful way | 1 |
| PLO12 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Converts its findings into a master's thesis or a professional report in Turkish or a foreign language | |
| PLO13 | Beceriler - Bilişsel, Uygulamalı | Develops solutions for organizations using Econometrics, Statistics, and Operation Research | 3 |
| PLO14 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Performs an individual work to solve a problem with Econometrics, Statistics, and Operation Research | 3 |
| PLO15 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Leads by taking responsibility individually and/or within the team | |
| 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 | |
| PLO17 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Uses a package program of Econometrics, Statistics, and Operation Research or writes a new code | |
| PLO18 | 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 | |
| PLO19 | Yetkinlikler - Alana Özgü Yetkinlik | Interprets data on economic and social events by following current issues | 3 |
| PLO20 | Yetkinlikler - Alana Özgü Yetkinlik | Applies social, scientific and professional ethical values |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Basic concepts, methods of enumeration | Related chapter of reference book | Öğretim Yöntemleri: Anlatım |
| 2 | Conditional probability, independent events, Bayes' theorem | Related chapter of reference book | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 3 | Discrete probability distributions, and their expectations | Related chapter of reference book | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 4 | Special discrete distributions - 1 | Related chapter of reference book | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 5 | Special discrete distributions - 2 | Related chapter of reference book | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 6 | Linear functions of independent random variables, multivariate discrete distributions | Related chapter of reference book | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 7 | General review | General review | Öğretim Yöntemleri: Alıştırma ve Uygulama, Problem Çözme |
| 8 | Mid-Term Exam | General review | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Continuous Distributions - 1 | Related chapter of reference book | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 10 | Continuous Distributions - 2 | Related chapter of reference book | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Problem Çözme |
| 11 | Continuous probability distributions and some special continuous distributions - 1 | Related chapter of reference book | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 12 | Continuous probability distributions and some special continuous distributions - 2 | Related chapter of reference book | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 13 | The normal distribution and the estimation in the continuous case | Related chapter of reference book | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 14 | The central limit theorem and approximations for discrete distributions | Related chapter of reference book | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Problem Çözme |
| 15 | Moments and moment generating functions | Related chapter of reference book | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 16 | Term Exams | General review | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | General review | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 3 | 42 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 5 | 70 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 15 | 15 |
| Final Exam | 1 | 30 | 30 |
| Total Workload (Hour) | 157 | ||
| Total Workload / 25 (h) | 6,28 | ||
| ECTS | 6 ECTS | ||