Probability (ING241) | GSÜ - ECTS Information Guide

Content

Objective

This course, which is offered as a compulsory course in the program, will help students perceive the basic concepts of probability theory and achieve proficiency in using the methods related to this discipline (probabilities of events, rules regarding random variables and the concept of moment, transformations of random variables, Gauss' suggestions). In this context, the objectives of the course are determined as follows:
• Introduce the student to the concept of probability, especially random variables in relation to uncertain events.
• To ensure that students master different probability distributions
• To enable students to benefit from probability theory in the problems they may encounter in the business world, especially in the analysis of uncertainty.

Course Content

Week 1: Course introduction and introduction to probability
Week 2: Probability of an event, probability axioms, conditional probability, independent events, Bayes theorem
Week 3: Random variables and probability distributions
Week 4: Probability distribution function, probability mass function, probability density function
Week 5: Expected value, variance and standard deviation
Week 6: Two and higher dimensional random variables
Week 7: Moments
Week 8: Midterm Exam
Week 9: Some important discrete distributions
Week 10: Some important discrete distributions (continued)
Week 11: Some important discrete distributions (continued)
Week 12: Some important sustained distributions
Week 13: Some important continuous distributions (continued)
Week 14: Some important continuous distributions (continued)

Course Learning Outcomes

The student who successfully completes this course:
1. Explain the relationship between set theory and probability axioms.
2. Can distinguish different functions of random variables.
3. Describe the characteristics of random variables.
4. List the important discrete and continuous distributions.
5. Apply probability theory to real life examples with the help of probability distribution functions.

Teaching and Learning Methods

Lecture, discussion, question-answer.

References

• Soong, T.T., Fundamentals of Probability and Statistics for Engineers, John Wiley & Sons, 2004.
• Akdeniz, F., Olasılık ve İstatistik, Baki Kitapevi, Eylül 1998.
• Ross, S.M., Introduction to probability models, Academic Press, 2003, 8th Ed.
• Lipschutz, S., Lipson, M., Olasılık, Schaum serisi, Nobel Akademik Yayıncılık, 2013.

Weekly Contents

Theory Topics
Week	Weekly Contents
1	Course introduction and introduction to probability
2	Probability of an event, probability axioms, conditional probability, independent events, Bayes theorem
3	Random variables and probability distributions
4	Probability distribution function, probability mass function, probability density function
5	Expected value, variance and standard deviation
6	Two and higher dimensional random variables
7	Moments
8	Midterm Exam
9	Some important discrete distributions
10	Some important discrete distributions
11	Some important discrete distributions
12	Some important continuous distributions
13	Some important continuous distributions
14	Some important continuous distributions

Practice Topics
Week	Weekly Contents
1
2
3
4
5
6
7
8
9
10
11
12
13
14

Assessment System

Contribution to Overall Grade
Activities	Number	Contribution
Contribution of in-term studies to overall grade	1	40
Contribution of final exam to overall grade	1	60
Total	2	100

In-Term Studies
Activities	Number	Contribution
Assignments	0	0
Presentation	0	0
Midterm Examinations (including preparation)	0	0
Project	0	0
Laboratory	0	0
Other Applications	0	0
Quiz	0	0
Term Paper/ Project	0	0
Portfolio Study	0	0
Reports	0	0
Learning Diary	0	0
Thesis/ Project	0	0
Seminar	0	0
Other	0	0
Total	0	0

Relation of Proficiency

No	Program Learning Outcomes	Contribution
No	Program Learning Outcomes	1	2	3	4	5
1	Knowledge and understanding of a wide range of basic sciences (math, physics, ...) and the main concepts of engineering					X
2	Ability to combine the knowledge and skills to solve engineering problems and provide reliable solutions				X
3	Ability to select and apply methods of analysis and modeling to ask, reformulate and solve the complex problems of industrial engineering
4	Ability to conceptualize complex systems, processes or products under practical constraints to improve their performance, ability to use innovative methods of design
5	Ability to design, select and apply methods and tools needed to solve problems related to the practice of industrial engineering, ability to use computer technology
6	Ability to design experiments, collect and interpret data and analyze results
7	Ability to work independently, ability to participate in working groups and have a multidisciplinary team spirit
8	Ability to communicate effectively, ability to speak at least two foreign languages
9	Awareness of the need for continuous improvement of lifelong learning, ability to keep abreast of scientific and technological developments to use the tools of information management
10	Awareness of professional and ethical responsibility
11	Knowledge of the concepts of professional life as "project management", "risk management" and "management of change"
12	Knowledge on entrepreneurship, innovation and sustainability
13	Understanding of the effects of Industrial Engineering applications on global and social health, environment and safety.
14	Knowledge of the problems of contemporary society
15	Knowledge of the legal implications of the practice of industrial engineering

ECTS

Activities	Number	Period	Total Workload
Class Hours	14	3	42
Working Hours out of Class	13	2	26
Midterm Examinations (including preparation)	1	10	10
Final Examinations (including preparation)	1	17	17
Total Workload			95
Total Workload / 25			3.80
Credits ECTS			4