Probability(IND211)
| Course Code | Course Name | Semester | Theory | Practice | Lab | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| IND211 | Probability | 4 | 3 | 0 | 0 | 3 | 4 |
| Prerequisites | |
| Admission Requirements |
| Language of Instruction | Turkish |
| Course Type | Compulsory |
| Course Level | Bachelor Degree |
| Course Instructor(s) | Mehtap DURSUN KARAHÜSEYİN mdursun@gsu.edu.tr (Email) Esin MUKUL TAYLAN emukul@gsu.edu.tr (Email) |
| Assistant | |
| Objective |
This course as a compulsory course will help the students to comprehend fundamental concepts of probability theory and gain the ability to use methods of this discipline (probabilities of events, rules for random variables and moment concept, transformations of random variables, Gauss’ theorem). In this context, the aim of this course is determined as: • introducing the students the probability theory, especially random variables related to uncertain events. • ensuring that the student master the different probability distributions. • helping the students to use probability theory to analyze problems encountered in business domain especially problems including uncertainty. |
| Content |
1. week : Introduction to probability 2. week : Axioms of probability, conditional probability, Bayes theorem 3. week : Random variables and probability distributions 4. week : Probability distribution functions, probability mass functions, probability density functions 5. week : Expected value and moments 6. week : Central moments, variance, and standard deviation 7. week : Discrete random variables: probability distribution functions, probability mass functions 8. week : Bernoulli trials, binom distribution, geometric distribution, negative binom distribution, poisson distribution 9. week : Mid term 10. week : Continuous random variables: probability distribution functions, probability density functions 11. week : Uniform distribution, Normal distribution, Central limit theory, Lognormal distribution, Gamma and related distributions 12. week : Exponential distribution, Erlang distribution, Weibull distribution, Chi-square distributiın, Beta and related distributions 13. week : Function of random variables 14. week : Marginal probability distributions, moment generating function |
| Course Learning Outcomes |
Upon successful completion of this course, the student could: 1. explain the relationship between the set theory and probability axioms. 2. differentiate various functions of random variables. 3. define characteristics of random variables. 4. enumerate important discrete and continuous distributions. 5. explain the relationship between important probability distributions.. 6. apply probability theory to real life scenarios using probability distribution functions. 7. give examples for applications of probability theory to industrial domain. |
| 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. • Sheldon M., Ross, M., Introduction to probability models, Academic Press, 2003, 8th Ed. • Course notes |
Theory Topics
| Week | Weekly Contents |
|---|---|
| 1 | Introduction to probability |
| 2 | Axioms of probability, conditional probability, Bayes theorem |
| 3 | Random variables and probability distributions |
| 4 | Probability distribution functions, probability mass functions, probability density functions |
| 5 | Expected value and moments |
| 6 | Central moments, variance, and standard deviation |
| 7 | Discrete random variables: probability distribution functions, probability mass functions |
| 8 | Bernoulli trials, binom distribution, geometric distribution, negative binom distribution, poisson distribution |
| 9 | Mid term |
| 10 | Continuous random variables: probability distribution functions, probability density functions |
| 11 | Uniform distribution, Normal distribution, Central limit theory, Lognormal distribution, Gamma and related distributions |
| 12 | Exponential distribution, Erlang distribution, Weibull distribution, Chi-square distributiın, Beta and related distributions |
| 13 | Functions of random variables |
| 14 | Marginal probability distributions, moment generating function |
Practice Topics
| Week | Weekly Contents |
|---|
Contribution to Overall Grade
| Number | Contribution | |
|---|---|---|
| Contribution of in-term studies to overall grade | 4 | 60 |
| Contribution of final exam to overall grade | 1 | 40 |
| Toplam | 5 | 100 |
In-Term Studies
| Number | Contribution | |
|---|---|---|
| Assignments | 2 | 10 |
| Presentation | 0 | 0 |
| Midterm Examinations (including preparation) | 1 | 25 |
| Project | 0 | 0 |
| Laboratory | 0 | 0 |
| Other Applications | 0 | 0 |
| Quiz | 1 | 25 |
| 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 |
| Toplam | 4 | 60 |
| No | Program Learning Outcomes | Contribution | ||||
|---|---|---|---|---|---|---|
| 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 | X | ||||
| 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 | X | ||||
| 6 | Ability to design experiments, collect and interpret data and analyze results | X | ||||
| 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 | |||||
| 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 |
| Quiz | 1 | 7 | 7 |
| Total Workload | 102 | ||
| Total Workload / 25 | 4.08 | ||
| Credits ECTS | 4 | ||