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Information
| Code | ECMZ201 |
| Name | Mathematical Statistics |
| Term | 2024-2025 Academic Year |
| Semester | 3. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | İngilizce |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. HÜSEYİN GÜLER |
| Course Instructor |
Doç. Dr. ÇİLER SİGEZE GÜNEY
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
The objective of this course is to present techniques and basic results of probability and mathematical statistics at an introductory level and provide the basic concepts of probability and its applications to real life data through random variables to students.
Course Content
Probability, random variables, discrete and continous distributions, estimation and sampling distribution, confidence intervals and hypothesis tests.
Course Precondition
None
Resources
A Brief Course in Mathematical Statistics by Elliot A. Tanis and Robert V. Hogg.
Notes
Introduction to Mathematical Statistics 7th Edition by Robert Hogg, Joseph McKean, Allen Craig
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Explains basic probability concepts |
| LO02 | Calculates the probability of a random event with different approaches |
| LO03 | Describes the concept of random variables |
| LO04 | Discriminates the probability and distribution functions of random variables |
| LO05 | Calculates moments of discrete and continuos random variables |
| LO06 | Discriminates some important discrete and continuous distributions |
| LO07 | Understands the foundations of the estimation theory |
| LO08 | Applies the foundations of the estimation theory in real life |
| LO09 | Uses appropriate statistical hypothesis tests |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Explain the basic concepts and theorems in the fields of Econometrics, Statistics and Operations research | 5 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Acquires basic Mathematics, Statistics and Operation Research concepts | 5 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Describes the necessary concepts of Business | |
| PLO04 | Beceriler - Bilişsel, Uygulamalı | Equipped with the foundations of Economics, and develops Economic models | |
| PLO05 | Beceriler - Bilişsel, Uygulamalı | Models problems with Mathematics, Statistics, and Econometrics | 3 |
| PLO06 | Beceriler - Bilişsel, Uygulamalı | Has the ability to analyze/interpret at the conceptual level to develop solutions to problems | |
| PLO07 | Beceriler - Bilişsel, Uygulamalı | Collects/analyses data | 1 |
| PLO08 | Bilgi - Kuramsal, Olgusal | Interprets the results analyzed with the model | 2 |
| PLO09 | Beceriler - Bilişsel, Uygulamalı | Combines the information obtained from different sources within the framework of academic rules in a field which does not research | |
| PLO10 | Beceriler - Bilişsel, Uygulamalı | It develops traditional approaches, practices and methods into new working methods when it deems necessary | |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Leads by taking responsibility individually and/or within the team | |
| PLO12 | Yetkinlikler - Öğrenme Yetkinliği | In addition to herself/himself professional development, constantly improves in scientific, cultural, artistic and social fields in line with interests and abilities | |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Being aware of the necessity of lifelong learning, it follows the current developments in the field / constantly renews itself | |
| PLO14 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Uses a package program of Econometrics, Statistics, and Operation Research | |
| PLO15 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Uses Turkish and at least one other foreign language, academically and in the business context | |
| PLO16 | 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 | |
| PLO17 | Yetkinlikler - Alana Özgü Yetkinlik | Interprets data on current economic and social issues | |
| PLO18 | Yetkinlikler - Alana Özgü Yetkinlik | Applies social, scientific and professional ethical values |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Basic concepts, methods of enumeration | Textbook - Chapter 1 | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 2 | Probability and probability rules | Textbook - Chapter 1 | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 3 | Conditional probability, independent events, Bayes' theorem | Textbook - Chapter 1 | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 4 | Discrete probability distributions, and their expectations | Textbook - Chapter 2 | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 5 | Special discrete distributions - 1 | Textbook - Chapter 2 | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Örnek Olay |
| 6 | Special discrete distributions - 2 | Textbook - Chapter 2 | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Örnek Olay |
| 7 | Linear functions of independent random variables, multivariate discrete distributions | Textbook - Chapter 2 | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 8 | Mid-Term Exam | General review for the midterm exam | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Continuous Distributions, and their expectations | Textbook - Chapter 3 | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 10 | Some special continuous distributions - 1 | Textbook - Chapter 3 | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Örnek Olay |
| 11 | Some special continuous distributions - 2 | Textbook - Chapter 3 | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Örnek Olay |
| 12 | The normal distribution | Textbook - Chapter 3 | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Problem Çözme |
| 13 | Estimation and sampling distributions | Textbook - Chapter 3 | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 14 | The central limit theorem | Textbook - Chapter 3 | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Benzetim, Örnek Olay |
| 15 | Hypothesis testing | Textbook - Chapter 4 | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 16 | Term Exams | General review for the final exam | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | General review for the final exam | 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 | ||