Course Details

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Course Information
SemesterCourse Unit CodeCourse Unit TitleT+P+LCreditNumber of ECTS CreditsLast Updated Date
1IE521PROBABILITY THEORY3+0+037,514.05.2025

 
Course Details
Language of Instruction English
Level of Course Unit Doctorate's Degree
Department / Program INDUSTRIAL ENGINEERING
Type of Program Formal Education
Type of Course Unit Compulsory
Course Delivery Method Face To Face
Objectives of the Course The aim of this course is to teach students the basic concepts and methods of probability theory and to enable them to use this knowledge to solve real life problems involving uncertainty. It is aimed to understand the theoretical foundations of probability, to model stochastic processes and to make probabilistic inferences in statistical analyses. In addition, it is aimed to develop students' analytical thinking skills in decision-making processes by understanding probability distributions, probability laws and their applications.
Course Content This course enables students to analyze fundamental and advanced topics in probability theory. It encourages students to apply core concepts such as probability distributions, random variables, expectation, and variance, as well as utilize special distributions like Binomial, Poisson, and Normal. Through problem-solving, simulations, and case studies, students will create practical solutions to complex probabilistic models.
Course Methods and Techniques The course will be taught through theoretical lectures, sample problem solving, class discussions and practical exercises. In addition, group work and interactive learning techniques will be used to increase student participation. Homework assignments and projects will be given to reinforce the topics and practical exercises will be carried out with simulation and software tools when necessary.
Prerequisites and co-requisities None
Course Coordinator Associate Prof.Dr. Ramazan Ünlü
Name of Lecturers Associate Prof.Dr. Ramazan Ünlü ramazan.unlu@agu.edu.tr
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources Montgomery, Douglas C., and Runger, George C. Applied Statistics and Probability for Engineers. Wiley, 2013.
Course Notes It will be shared weekly from the canvas.
Documents Canvas üzerinden paylaşılacaktır.
Assignments Canvas üzerinden paylaşılacaktır.
Exams Canvas üzerinden paylaşılacaktır.

Course Category
Mathematics and Basic Sciences %50
Engineering %25
Engineering Design %0
Social Sciences %0
Education %0
Science %0
Health %0
Field %25

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Yarıl yılSonu Sınavı/Dönem Projesinin Başarı Notuna Katkısı 1 % 20
Quiz/Küçük Sınav 11 % 20
Final examination 1 % 35
Uygulama Çalışmaları (Laboratuar,Sanal Mahkeme,Stüdyo Çalışmaları vb.) 11 % 20
Diğer (Staj vb.) 1 % 5
Total
25
% 100

 
ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Yazılı Sınav 1 3 3
Ev Ödevi 6 3 18
Sınıf İçi Aktivitesi 11 1 11
Kısa Sınav 12 1 12
Okuma 5 2 10
Kişisel Çalışma 14 4 56
Ders dışı çalışma 14 4 56
Yüz Yüze Ders 14 4 56
Final Sınavı 1 3 3
Total Work Load   Number of ECTS Credits 7,5 225

 
Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 Define sample spaces and assign probabilities to events using probability axioms.
2 Determine the independence of events, calculate the conditional probabilities of events.
3 Recognize the appropriate discrete and continuous distribution in a specific application and use it for analysis.
4 Use cumulative distribution/probability density functions to calculate probabilities, means, and variances.
5 Use joint probability mass and joint probability density functions to calculate conditional and marginal probability laws, and covariance.
6 Simulate the law of large numbers and the central limit theorem using a programming language.

 
Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Probabilistic Models, Axioms of probability Review of the lecture slides. Lecture slides
2 Conditional probability, Bayes’ theorem, Multiplication Rule, Total Probability Theorem, Independence Review of the lecture slides. Lecture Slides
3 Discrete Random Variables, PMF, CDF, Expectation, and Variance
4 Analysis of Discrete Uniform, Bernoulli, Binomial, and Geometric distributions Review of the lecture slides. Lecture Slides
5 Negative Binomial, Hypergeometric and Poisson distributions Review of the lecture slides. Lecture Slides
6 Lecture Free Week Review of the lecture slides. Lecture Slides
7 Fall Break
8 Continuous random variables, PDF, CDF, expectation, variance Review of the lecture slides. Lecture Slides
9 Continuous Uniform and Normal Distribution Review of the lecture slides. Lecture Slides
10 Exponential and Gamma Distributions Review of the lecture slides. Lecture Slides
11 Weibull, Lognormal, Beta Distribution and Moment Generating Functions Review of the lecture slides. Lecture Slides
12 Joint probability distributions, conditioning, independence Review of the lecture slides. Lecture Slides
13 Adam’s and Eve’s Laws, Independence, Covariance Joint probability distributions, conditioning, independence Review of the lecture slides. Lecture Slides
14 Derived distributions, correlation, covariance Review of the lecture slides. Lecture Slides
15 Computer Applications of Special Discrete and Continuous Distributions

 
Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12
C1 2 2 2 2 1 2
C2 2 2 2 2 1 2 1 2
C3 2 2 2 3 1 2 1 2
C4 2 3 1 3 1 2 1 2
C5 2 3 1 3 1 2 1 2
C6 2 3 1 3 1 2 1 2 2 1

  Contribution: 1: Very Slight 2:Slight 3:Moderate 4:Significant 5:Very Significant

  
  https://sis.agu.edu.tr/oibs/bologna/progCourseDetails.aspx?curCourse=75479&lang=en
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