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Information
| Code | ISB537 |
| Name | Theory of Probability |
| Term | 2024-2025 Academic Year |
| Semester | . Semester |
| 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. GÜLESEN ÜSTÜNDAĞ ŞİRAY |
Course Goal / Objective
The goal are to gain basic information of theory of probability and to construct the necessary theoretical backround to statistical theory.
Course Content
The content of this course is probability,discrete and continious types random variables, properties of the distribution functions, inequalities, multivariate distributions, some special distributions, distributions of functions of random variables
Course Precondition
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Resources
1. Robert V. Hogg. Allen T. Craig. Introduction to Mathematical. Statistics. Fifth Edition. Macmillan Publishing Co. Inc. New York. 2. George Casella, Roger L. Berger. Statistical Inference. Duxbury Press. 3. Yılmaz Akdi. Matematiksel İstatistiğe Giriş. Gazi Kitabevi.
Notes
Lecture Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Define the basic principles of probability calculations. |
| LO02 | Use the the axioms of probability |
| LO03 | Define concepts of conditional probability and independency. |
| LO04 | Obtain the expected value and variance of a random variable. |
| LO05 | Obtain the moment generating functions of a random variable. |
| LO06 | Use the basic inequalities which is used in statistics |
| LO07 | Find the distribution function of a random variable. |
| LO08 | Know some special distributions. |
| LO09 | Find the distributions of the functions of random variables. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Have in-depth theoretical and practical knowledge about Probability and Statistics | 5 |
| PLO02 | Bilgi - Kuramsal, Olgusal | They have the knowledge to make doctoral plans in the field of statistics. | 5 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Has comprehensive knowledge about analysis and modeling methods used in statistics. | 3 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Has comprehensive knowledge of methods used in statistics. | 4 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Make scientific research on Mathematics, Probability and Statistics. | 3 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Indicates statistical problems, develops methods to solve. | 3 |
| PLO07 | Bilgi - Kuramsal, Olgusal | Apply innovative methods to analyze statistical problems. | |
| PLO08 | Bilgi - Kuramsal, Olgusal | Designs and applies the problems faced in the field of analytical modeling and experimental researches. | |
| PLO09 | Bilgi - Kuramsal, Olgusal | Access to information and do research about the source. | 4 |
| PLO10 | Bilgi - Kuramsal, Olgusal | Develops solution approaches in complex situations and takes responsibility. | |
| PLO11 | Bilgi - Kuramsal, Olgusal | Has the confidence to take responsibility. | |
| PLO12 | Beceriler - Bilişsel, Uygulamalı | They demonstrate being aware of the new and developing practices. | |
| PLO13 | Beceriler - Bilişsel, Uygulamalı | He/She constantly renews himself/herself in statistics and related fields. | 3 |
| PLO14 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Communicate in Turkish and English verbally and in writing. | |
| PLO15 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Transmits the processes and results of their studies clearly in written and oral form in national and international environments. | |
| PLO16 | Yetkinlikler - Öğrenme Yetkinliği | It considers the social, scientific and ethical values in the collection, processing, use, interpretation and announcement stages of data and in all professional activities. | |
| PLO17 | Yetkinlikler - Öğrenme Yetkinliği | Uses the hardware and software required for statistical applications. |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Probability, discrete and continious types random variables, properties of the distribution function | Reading the related references, problem solving | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 2 | Expectations of random variables, some special expectations. | Reading the related references, problem solving | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Problem Çözme, Alıştırma ve Uygulama |
| 3 | Moments and some special moment generating functions. | Reading the related references, problem solving | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Problem Çözme |
| 4 | Some special inequalities | Reading the related references, problem solving | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Problem Çözme |
| 5 | Distributions of two random variables, conditional distributions and expectations, the correlation coefficient | Reading the related references, problem solving | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Problem Çözme |
| 6 | Independent random variables, extension to several random variables | Reading the related references, problem solving | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Problem Çözme, Alıştırma ve Uygulama |
| 7 | Discrete type distributions | Reading the related references, problem solving | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Alıştırma ve Uygulama |
| 8 | Mid-Term Exam | Review the topics discussed in the lecture notes and sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Problem Çözme |
| 9 | Continious type distributions | Reading the related references, problem solving | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Problem Çözme |
| 10 | Normal and bivariate normal distributions | Reading the related references, problem solving | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 11 | Transformations of variables of discrete and continious types | Reading the related references, problem solving | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Problem Çözme |
| 12 | Distribution of functions of random vaiables | Reading the related references, problem solving | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Problem Çözme, Alıştırma ve Uygulama |
| 13 | Change of variable technique | Reading the related references, problem solving | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 14 | The Beta, t and F distributions. The moment-generating function technique | Reading the related references, problem solving | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Problem Çözme, Alıştırma ve Uygulama |
| 15 | Distribution of sample mean and sample variance. Expectations of functions of random variables | Reading the related references, problem solving | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Problem Çözme, Alıştırma ve Uygulama |
| 16 | Term Exams | Review the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Review the topics discussed in the lecture notes and sources | 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 | ||