TÜRKÇE
ENGLISH
Information
| Unit | FACULTY OF SCIENCE AND LETTERS |
| ARTIFICIAL INTELLIGENCE AND MACHINE LEARNING PR. (ENGLISH) | |
| Code | YZZ205 |
| Name | Probability and Statistics |
| Term | 2026-2027 Academic Year |
| Semester | 3. Semester |
| Duration (T+A) | 3-1 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3.5 National Credit |
| Teaching Language | İngilizce |
| Level | Lisans Dersi |
| Type | Normal |
| Label | C Compulsory |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. YUSUF ALPER KAPLAN |
| Course Instructor |
Dr. Öğr. Üyesi Kasım ZOR
(Güz)
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
This course aims to provide students a rigorous foundation in probability theory and statistical inference with an emphasis on their application to problems in artificial intelligence and machine learning. Students will develop the mathematical and computational skills required to model uncertainty, analyse data, and evaluate statistical claims, thereby preparing them for subsequent coursework in machine learning, data engineering, and related disciplines.
Course Content
Introduction, Random Experiments and Probabilities, Probability Distributions, Sampling and Estimation, Hypothesis Testing, Multivariate Models, Regression, Classification, and Clustering.
Course Precondition
There are no formal prerequisites for the course.
Resources
Ethem Alpaydın, Fundamentals of Probability and Statistics for Machine Learning, 1st Ed., MIT Press, 2025.
Notes
Charu C. Aggarwal, Probability and Statistics for Machine Learning: A Textbook, 1st Ed., Springer, 2024. Jose Unpingco, Python for Probability, Statistics, and Machine Learning, 1st Ed., Springer, 2016. Michael Akritas, Probability & Statistics with R for Engineers and Scientists, 1st Ed., Pearson, 2016. Sujit K. Sahu, Introduction to Probability, Statistics & R: Foundations for Data-Based Sciences, 1st Ed., Springer, 2024. Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers, and Keying Ye, Probability & Statistics for Engineers & Scientists, 9th Ed., Pearson, 2016. Richard A. Johnson, Miller & Freund's Probability and Statistics for Engineers, 9th Ed., Pearson, 2018. Murray R. Spiegel, John Schiller, and R. Alu Srinavasan, Schaum's Outlines Probability and Statistics, 4th Ed., McGraw-Hill, 2013.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Apply the fundamental axioms of probability and combinatorial counting techniques to solve problems involving random experiments and events. |
| LO02 | Identify and work with common discrete and continuous probability distributions, and compute their expectations, variances, and related moments. |
| LO03 | Formulate and apply methods of statistical estimation, including maximum likelihood estimation, to infer population parameters from sample data. |
| LO04 | Construct and interpret confidence intervals and conduct hypothesis tests to draw statistically sound conclusions from data. |
| LO05 | Analyse multivariate data using covariance structures and dimensionality reduction techniques such as principal component analysis. |
| LO06 | Formulate and solve linear regression problems, and critically evaluate model fit and assumptions. |
| LO07 | Apply Bayesian decision theory and probabilistic generative models to formulate classification problems, and use mixture models to formulate clustering problems. |
| LO08 | Recognise the connections between probabilistic and statistical concepts and their applications in machine learning contexts, such as model evaluation and feature selection. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | It provides a broad range of knowledge about fundamental Computer Science concepts, algorithms and data structures. | 4 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Learns basic computer topics such as software development, programming languages, and database management. | 3 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Understands advanced computing fields such as data science, artificial intelligence, and machine learning. | 5 |
| PLO04 | - | Learn about topics such as computer networks, cyber security, and database design. | |
| PLO05 | Beceriler - Bilişsel, Uygulamalı | Develops skills in designing, implementing and analyzing algorithms. | 4 |
| PLO06 | Beceriler - Bilişsel, Uygulamalı | Gains the ability to use different programming languages effectively | 3 |
| PLO07 | Beceriler - Bilişsel, Uygulamalı | Learns data analysis, database management and big data processing skills. | 5 |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | Gains practical experience by working on software development projects. | |
| PLO09 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Strengthens collaboration and communication skills within the team. | |
| PLO10 | Yetkinlikler - Alana Özgü Yetkinlik | It provides a mindset open to technological innovations. | |
| PLO11 | Yetkinlikler - Öğrenme Yetkinliği | Encourages continuous learning and self-improvement competence. | |
| PLO12 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Develops the ability to solve complex problems. | 5 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Course Introduction and Scope, Introduction to Probability and Statistics for Machine Learning | Reading the lecture notes | Öğretim Yöntemleri: Anlatım, Tartışma, Alıştırma ve Uygulama, Deney / Laboratuvar |
| 2 | Random Experiments and Probabilities | Reading the lecture notes | Öğretim Yöntemleri: Anlatım, Tartışma, Alıştırma ve Uygulama, Deney / Laboratuvar |
| 3 | Random Experiments and Probabilities - 2 | Reading the lecture notes | Öğretim Yöntemleri: Anlatım, Tartışma, Alıştırma ve Uygulama, Deney / Laboratuvar |
| 4 | Probability Distributions | Reading the lecture notes | Öğretim Yöntemleri: Anlatım, Tartışma, Alıştırma ve Uygulama, Deney / Laboratuvar |
| 5 | Probability Distributions - 2 | Reading the lecture notes | Öğretim Yöntemleri: Anlatım, Tartışma, Alıştırma ve Uygulama, Deney / Laboratuvar |
| 6 | Sampling and Estimation | Reading the lecture notes | Öğretim Yöntemleri: Anlatım, Tartışma, Alıştırma ve Uygulama, Deney / Laboratuvar |
| 7 | Sampling and Estimation - 2 | Reading the lecture notes | Öğretim Yöntemleri: Anlatım, Tartışma, Alıştırma ve Uygulama, Deney / Laboratuvar |
| 8 | Midterm Examination | Reviewing the previous topics | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Hypothesis Testing | Reading the lecture notes | Öğretim Yöntemleri: Anlatım, Tartışma, Alıştırma ve Uygulama, Deney / Laboratuvar |
| 10 | Hypothesis Testing - 2 | Reading the lecture notes | Öğretim Yöntemleri: Anlatım, Tartışma, Alıştırma ve Uygulama, Deney / Laboratuvar |
| 11 | Multivariate Models | Reading the lecture notes | Öğretim Yöntemleri: Anlatım, Tartışma, Alıştırma ve Uygulama, Deney / Laboratuvar |
| 12 | Regression | Reading the lecture notes | Öğretim Yöntemleri: Anlatım, Tartışma, Alıştırma ve Uygulama, Deney / Laboratuvar |
| 13 | Regression - 2 | Reading the lecture notes | Öğretim Yöntemleri: Anlatım, Tartışma, Alıştırma ve Uygulama, Deney / Laboratuvar |
| 14 | Classification | Reading the lecture notes | Öğretim Yöntemleri: Anlatım, Tartışma, Alıştırma ve Uygulama, Deney / Laboratuvar |
| 15 | Clustering | Reading the lecture notes | Öğretim Yöntemleri: Anlatım, Tartışma, Alıştırma ve Uygulama, Deney / Laboratuvar |
| 16 | Final Examination | Reviewing the previous topics | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Final Examination | Reviewing the previous topics | 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 | 5 | 70 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 10 | 2 | 20 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 2 | 2 |
| Final Exam | 1 | 2 | 2 |
| Total Workload (Hour) | 150 | ||
| Total Workload / 25 (h) | 6,00 | ||
| ECTS | 6 ECTS | ||