ISB203 Probability Theory

6 ECTS - 4-0 Duration (T+A)- 3. Semester- 4 National Credit

Information

Code ISB203
Name Probability Theory
Term 2024-2025 Academic Year
Semester 3. Semester
Duration (T+A) 4-0 (T-A) (17 Week)
ECTS 6 ECTS
National Credit 4 National Credit
Teaching Language Türkçe
Level Lisans Dersi
Type Normal
Mode of study Yüz Yüze Öğretim
Catalog Information Coordinator Prof. Dr. ALİ İHSAN GENÇ
Course Instructor Prof. Dr. ALİ İHSAN GENÇ (A Group) (Ins. in Charge)


Course Goal / Objective

To give a mathematical basis for statistics

Course Content

Starting with the definitions of probability, the random variables and their properties are studied.

Course Precondition

None

Resources

Matematiksel İstatistik, John E. Freund, Çeviri: Ümit Şenesen, Literatür Yayınları, 2015.

Notes

Statistical Inference, George Casella, Roger L. Berger, Second Ed., Duxbury Advanced Series, 2002.


Course Learning Outcomes

Order Course Learning Outcomes
LO01 Comprehends the notions of sigma algebra, Borel measure and probability.
LO02 Defines measurable and probability spaces.
LO03 Orders the properties of distribution functions.
LO04 Orders the types of random variables and their properties.
LO05 Computes the moments of random variables.
LO06 Applies Chebyshev inequality and some other inequalities.
LO07 Defines moment generating function and characteristic function.
LO08 Defines percentiles of random variables.
LO09 Classifies the named statistical distributions and families like exponential family of distributions and location-scale families.


Relation with Program Learning Outcome

Order Type Program Learning Outcomes Level
PLO01 Bilgi - Kuramsal, Olgusal Explain the essence fundamentals and concepts in the field of Statistics 4
PLO02 Bilgi - Kuramsal, Olgusal Emphasize the importance of Statistics in life
PLO03 Bilgi - Kuramsal, Olgusal Define basic principles and concepts in the field of Law and Economics
PLO04 Bilgi - Kuramsal, Olgusal Produce numeric and statistical solutions in order to overcome the problems
PLO05 Bilgi - Kuramsal, Olgusal Use proper methods and techniques to gather and/or to arrange the data
PLO06 Bilgi - Kuramsal, Olgusal Utilize computer programs and builds models, solves problems, does analyses and comments about problems concerning randomization
PLO07 Bilgi - Kuramsal, Olgusal Apply the statistical analyze methods 1
PLO08 Bilgi - Kuramsal, Olgusal Make statistical inference (estimation, hypothesis tests etc.) 3
PLO09 Bilgi - Kuramsal, Olgusal Generate solutions for the problems in other disciplines by using statistical techniques and gain insight
PLO10 Bilgi - Kuramsal, Olgusal Discover the visual, database and web programming techniques and posses the ability of writing programs
PLO11 Beceriler - Bilişsel, Uygulamalı Distinguish the difference between the statistical methods
PLO12 Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği Make oral and visual presentation for the results of statistical methods
PLO13 Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği Have capability on effective and productive work in a group and individually
PLO14 Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği Professional development in accordance with their interests and abilities, as well as the scientific, cultural, artistic and social fields, constantly improve themselves by identifying training needs
PLO15 Yetkinlikler - Öğrenme Yetkinliği Develop scientific and ethical values in the fields of statistics-and scientific data collection


Week Plan

Week Topic Preparation Methods
1 Sigma algebra and probability space Source reading Öğretim Yöntemleri:
Anlatım, Tartışma, Problem Çözme
2 Consequences of Probability, random variables Source reading Öğretim Yöntemleri:
Anlatım, Tartışma, Problem Çözme
3 Distribution functions and their properties Source reading Öğretim Yöntemleri:
Anlatım, Tartışma, Problem Çözme
4 Discrete random variables, continuous random variables, probability mass functions, probability density functions Source reading Öğretim Yöntemleri:
Anlatım, Tartışma, Problem Çözme
5 Quantile function and generating random numbers from distributions Source reading Öğretim Yöntemleri:
Anlatım, Tartışma, Problem Çözme
6 Distributions of functions of random variables Source reading Öğretim Yöntemleri:
Anlatım, Tartışma, Problem Çözme
7 Moment generating function, moments, expected value,variance Source reading Öğretim Yöntemleri:
Anlatım, Tartışma, Problem Çözme
8 Mid-Term Exam Review the topics discussed in the lecture notes and sources Ölçme Yöntemleri:
Yazılı Sınav
9 Characteristic function, probability generating function Source reading Öğretim Yöntemleri:
Anlatım, Tartışma, Problem Çözme
10 Named discrete distributions and their properties Source reading Öğretim Yöntemleri:
Anlatım, Tartışma, Problem Çözme
11 Named discrete distributions and their properties II Source reading Öğretim Yöntemleri:
Anlatım, Tartışma, Problem Çözme
12 Named continuous distributions and their properties Source reading Öğretim Yöntemleri:
Anlatım, Tartışma, Problem Çözme
13 Named continuous distributions and their properties II Source reading Öğretim Yöntemleri:
Anlatım, Tartışma, Problem Çözme
14 Location-scale family Source reading Öğretim Yöntemleri:
Anlatım, Tartışma, Problem Çözme
15 Properties of exponential families Source reading Öğretim Yöntemleri:
Anlatım, Tartışma, Problem Çözme
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 4 56
Out of Class Study (Preliminary Work, Practice) 14 4 56
Assesment Related Works
Homeworks, Projects, Others 0 0 0
Mid-term Exams (Written, Oral, etc.) 1 12 12
Final Exam 1 28 28
Total Workload (Hour) 152
Total Workload / 25 (h) 6,08
ECTS 6 ECTS

Update Time: 11.06.2024 02:05