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Information
| Code | EKMZ201 |
| 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 | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Label | C Compulsory |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. EBRU ÖZGÜR GÜLER |
| Course Instructor |
Arş.Gör.Dr. Çiğdem KOŞAR TAŞ
(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
In this course, probability, random variables, discrete and continuous distributions, estimation and sampling distributions, confidence intervals and hypothesis testing will be covered.
Course Precondition
None
Resources
Aytaç, M. (2014). Matematiksel İstatistik [5. Baskı]. Bursa: Ezgi Kitabevi.
Notes
Akdeniz, F. (2011). Olasılık ve İstatistik [16. Baskı]. Adana: Nobel.
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 and its applications in real life |
| LO08 | Develops appropriate statistical hypothesis and tests them |
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 | 3 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Acquires basic Mathematics, Statistics and Operation Research concepts | 5 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Describes the necessary concepts of Business | 1 |
| PLO04 | Beceriler - Bilişsel, Uygulamalı | Equipped with the foundations of Economics, and develops Economic models | 1 |
| PLO05 | Beceriler - Bilişsel, Uygulamalı | Models problems with Mathematics, Statistics, and Econometrics | 4 |
| PLO06 | Beceriler - Bilişsel, Uygulamalı | Analyzes/interprets at the conceptual level to develop solutions to problems | 3 |
| PLO07 | Beceriler - Bilişsel, Uygulamalı | Collects/analyses data from reliable data sources for the purpose of study | 4 |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | Interprets the results analyzed with the model | 4 |
| PLO09 | Beceriler - Bilişsel, Uygulamalı | Combines the information obtained from different sources within the framework of academic rules in a field of research | |
| PLO10 | Beceriler - Bilişsel, Uygulamalı | Adapts traditional approaches, practices and methods to a new study when necessary | |
| PLO11 | Beceriler - Bilişsel, Uygulamalı | Uses a package program of Econometrics, Statistics, and Operation Research | |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Leads by taking responsibility individually and/or within the team | |
| PLO13 | 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 | |
| PLO14 | Yetkinlikler - Öğrenme Yetkinliği | Being aware of the necessity of lifelong learning, it constantly renews itself by following the current developments in its field. | |
| 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 | 3 |
| 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 is read | Öğretim Yöntemleri: Anlatım, Tartışma |
| 2 | Probability and probability rules | Textbook-Chapter 1 is read | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 3 | Conditional probability, independent events, Bayes' theorem | Textbook-Chapter 1 is read | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 4 | Random Variables: Probability function and probability density function, cumulative distributions | Textbook-Chapter 2 is read | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 5 | Joint probability functions, conditional probability functions | Textbook-Chapter 2 is read | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Problem Çözme |
| 6 | Linear functions of random variables: functions of one-dimensional random variables, functions of two-dimensional random variables | Textbook-Chapter 2 is read | Öğretim Yöntemleri: Anlatım |
| 7 | Expected value of a random variable, expected value of a function of a random variable, properties of the expected value process | Textbook-Chapter 3 is read | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Problem Çözme |
| 8 | Mid-Term Exam | General review for the midterm exam | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | The expected value of joint probability functions, the conditional expected value. | Textbook-Chapter 3 is read | Öğretim Yöntemleri: Anlatım |
| 10 | Variance of a random variable, properties of variance, conditional variance | Textbook-Chapter 3 is read | Öğretim Yöntemleri: Anlatım |
| 11 | Moments, moment generating function and properties of moment generating function | Textbook-Chapter 3 is read | Öğretim Yöntemleri: Anlatım |
| 12 | Limit theorems: Chebyshev's Inequality, Law of large numbers, Central limit theorem | Textbook-Chapter 3 is read | Öğretim Yöntemleri: Anlatım |
| 13 | Some discrete distributions: Bernoulli distribution, binomial distribution, geometric distribution | Textbook-Chapter 4 is read | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 14 | Some discrete distributions: negative binomial distribution, hypergeometric distribution, poisson distribution | Textbook-Chapter 4 is read | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 15 | Some continuous distributions: normal distribution, uniform distribution, exponential distribution | Textbook-Chapter 5 is read | 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 | ||