Course Detail
Course Description
Course | Code | Semester | T+P (Hour) | Credit | ECTS |
---|---|---|---|---|---|
PROBABILITY and RANDOM VARIABLES | - | Fall Semester | 3+0 | 3 | 6 |
Course Program |
Prerequisites Courses | |
Recommended Elective Courses |
Language of Course | English |
Course Level | First Cycle (Bachelor's Degree) |
Course Type | Required |
Course Coordinator | Prof.Dr. Afgan ASLAN |
Name of Lecturer(s) | Assoc.Prof. Yasin GÖÇGÜN |
Assistant(s) | |
Aim | This is a second year undergraduate course (third year for CoE) on introduction to probability and random variables. The course introduces fundamental differences between statistics and probability and then introduces basic topics of probability. Probability axioms, probability density functions, joint pdfs, and random variables with related topics are covered throughout the course. |
Course Content | This course contains; Class Info, Introduction to Statistics and Probability,Basic probability,Conditional probability,Discrete random variables,Discrete distributions and their statistics. ,Continuous Random Variables and their statistics,Continuous Random Variables (Cont.),Midterm overview,Continuous Distributions,Multiple Discrete Random Variables,Multiple Continuous Random Variables,Conditional Probability Mass Functions,Conditional Probability Density Functions,Conditional Probability Density Functions. |
Dersin Öğrenme Kazanımları | Teaching Methods | Assessment Methods |
Model simple probabilistic phenomena mathematically. | 12, 16, 21, 9 | A, E |
Calculate probabilities of events in a known event space, expected values, variances of random variables, and conditional probability. | 12, 16, 21, 9 | A, E |
Develops mathematical tools for discrete and continuous random variables | 12, 16, 21, 9 | A, E |
Determines the common probability distributions and the understanding of where to use them. | 12, 16, 21, 9 | A, E |
Work with multiple random variables, their joint distributions, their conditional distributions, and their one and two dimensional transformations. | 12, 16, 21, 9 | A, E |
Teaching Methods: | 12: Problem Solving Method, 16: Question - Answer Technique, 21: Simulation Technique, 9: Lecture Method |
Assessment Methods: | A: Traditional Written Exam, E: Homework |
Course Outline
Order | Subjects | Preliminary Work |
---|---|---|
1 | Class Info, Introduction to Statistics and Probability | Syllabus, Text 1-Chap. 1, Text 2-Chap. 1 &2 |
2 | Basic probability | Text 1-Chap. 2, Text 2-Chap 3 |
3 | Conditional probability | Text 1-Chap. 2, Text 2-Chap 4 |
4 | Discrete random variables | Text 1-Chap. 3, Text 2-Chap 5 |
5 | Discrete distributions and their statistics. | Text 1-Chap. 3, Text 2-Chap 6 |
6 | Continuous Random Variables and their statistics | Text 1-Chap. 4, Text 2-Chap 10 |
7 | Continuous Random Variables (Cont.) | Text 1-Chap. 4, Text 2-Chap 10 |
8 | Midterm overview | All Lectures till Week 8 |
9 | Continuous Distributions | Text 1-Chap. 4, Text 2-Chap 11 |
10 | Multiple Discrete Random Variables | Text 1-Chap. 5, Text 2-Chap 7 |
11 | Multiple Continuous Random Variables | Text 1-Chap. 5, Text 2-Chap 12 |
12 | Conditional Probability Mass Functions | Text 1-Chap. 5, Text 2-Chap 8 |
13 | Conditional Probability Density Functions | Text 1-Chap. 5, Text 2-Chap 13 |
14 | Conditional Probability Density Functions | Text 1-Chap. 5, Text 2-Chap 13 |
Resources |
1. Applied Statistics and Probability for Engineers, Sixth Edition, Douglas C. Montgomery and George C. Runger, ISBN : 13 9781118539712 2. Intuitive Probability and Random Processes Using MatLab - Steven M. Kay, 2016, ISBN-13: 978-0-387-24157-9 |
1) A. Papoulis, Probability, Random Variables, and Stochastic Processes, Mc Graw Hill, 1984. 2) Alberto Leon-Garcia, Probability, Statistics, and Random Processes For Electrical Engineering, Prentice Hall, Third Edition, 2008. 3) A. Papoulis, Probability, Random Variables and Stochastic Processes, McGraw-Hill , Third Edition,1991 |
Course Contribution to Program Qualifications
Course Contribution to Program Qualifications | |||||||
No | Program Qualification | Contribution Level | |||||
1 | 2 | 3 | 4 | 5 | |||
1 | Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied knowledge in these areas in the solution of complex engineering problems. | X | |||||
2 | Ability to formulate, and solve complex engineering problems; ability to select and apply proper analysis and modeling methods for this purpose. | X | |||||
3 | Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the desired result; ability to apply modern design methods for this purpose. | ||||||
4 | Ability to select and use modern techniques and tools needed for analyzing and solving complex problems encountered in engineering practice; ability to employ information technologies effectively. | X | |||||
5 | Ability to design and conduct experiments, gather data, analyze and interpret results for investigating complex engineering problems or discipline specific research questions. | X | |||||
6 | Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually. | X | |||||
7 | Ability to communicate effectively, both orally and in writing; knowledge of a minimum of one foreign language; ability to write effective reports and comprehend written reports, prepare design and production reports, make effective presentations, and give and receive clear and intelligible instructions. | X | |||||
8 | Awareness of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself. | X | |||||
9 | Knowledge on behavior according ethical principles, professional and ethical responsibility and standards used in engineering practices. | X | |||||
10 | Knowledge about business life practices such as project management, risk management, and change management; awareness in entrepreneurship, innovation; knowledge about sustainable development. | ||||||
11 | Knowledge about the global and social effects of engineering practices on health, environment, and safety, and contemporary issues of the century reflected into the field of engineering; awareness of the legal consequences of engineering solutions. |
Assessment Methods
Contribution Level | Absolute Evaluation | |
Rate of Midterm Exam to Success | 30 | |
Rate of Final Exam to Success | 70 | |
Total | 100 |
ECTS / Workload Table | ||||||
Activities | Number of | Duration(Hour) | Total Workload(Hour) | |||
Course Hours | 14 | 3 | 42 | |||
Guided Problem Solving | 14 | 1 | 14 | |||
Resolution of Homework Problems and Submission as a Report | 4 | 15 | 60 | |||
Term Project | 0 | 0 | 0 | |||
Presentation of Project / Seminar | 0 | 0 | 0 | |||
Quiz | 0 | 0 | 0 | |||
Midterm Exam | 1 | 24 | 24 | |||
General Exam | 1 | 36 | 36 | |||
Performance Task, Maintenance Plan | 0 | 0 | 0 | |||
Total Workload(Hour) | 176 | |||||
Dersin AKTS Kredisi = Toplam İş Yükü (Saat)/30*=(176/30) | 6 | |||||
ECTS of the course: 30 hours of work is counted as 1 ECTS credit. |
Detail Informations of the Course
Course Description
Course | Code | Semester | T+P (Hour) | Credit | ECTS |
---|---|---|---|---|---|
PROBABILITY and RANDOM VARIABLES | - | Fall Semester | 3+0 | 3 | 6 |
Course Program |
Prerequisites Courses | |
Recommended Elective Courses |
Language of Course | English |
Course Level | First Cycle (Bachelor's Degree) |
Course Type | Required |
Course Coordinator | Prof.Dr. Afgan ASLAN |
Name of Lecturer(s) | Assoc.Prof. Yasin GÖÇGÜN |
Assistant(s) | |
Aim | This is a second year undergraduate course (third year for CoE) on introduction to probability and random variables. The course introduces fundamental differences between statistics and probability and then introduces basic topics of probability. Probability axioms, probability density functions, joint pdfs, and random variables with related topics are covered throughout the course. |
Course Content | This course contains; Class Info, Introduction to Statistics and Probability,Basic probability,Conditional probability,Discrete random variables,Discrete distributions and their statistics. ,Continuous Random Variables and their statistics,Continuous Random Variables (Cont.),Midterm overview,Continuous Distributions,Multiple Discrete Random Variables,Multiple Continuous Random Variables,Conditional Probability Mass Functions,Conditional Probability Density Functions,Conditional Probability Density Functions. |
Dersin Öğrenme Kazanımları | Teaching Methods | Assessment Methods |
Model simple probabilistic phenomena mathematically. | 12, 16, 21, 9 | A, E |
Calculate probabilities of events in a known event space, expected values, variances of random variables, and conditional probability. | 12, 16, 21, 9 | A, E |
Develops mathematical tools for discrete and continuous random variables | 12, 16, 21, 9 | A, E |
Determines the common probability distributions and the understanding of where to use them. | 12, 16, 21, 9 | A, E |
Work with multiple random variables, their joint distributions, their conditional distributions, and their one and two dimensional transformations. | 12, 16, 21, 9 | A, E |
Teaching Methods: | 12: Problem Solving Method, 16: Question - Answer Technique, 21: Simulation Technique, 9: Lecture Method |
Assessment Methods: | A: Traditional Written Exam, E: Homework |
Course Outline
Order | Subjects | Preliminary Work |
---|---|---|
1 | Class Info, Introduction to Statistics and Probability | Syllabus, Text 1-Chap. 1, Text 2-Chap. 1 &2 |
2 | Basic probability | Text 1-Chap. 2, Text 2-Chap 3 |
3 | Conditional probability | Text 1-Chap. 2, Text 2-Chap 4 |
4 | Discrete random variables | Text 1-Chap. 3, Text 2-Chap 5 |
5 | Discrete distributions and their statistics. | Text 1-Chap. 3, Text 2-Chap 6 |
6 | Continuous Random Variables and their statistics | Text 1-Chap. 4, Text 2-Chap 10 |
7 | Continuous Random Variables (Cont.) | Text 1-Chap. 4, Text 2-Chap 10 |
8 | Midterm overview | All Lectures till Week 8 |
9 | Continuous Distributions | Text 1-Chap. 4, Text 2-Chap 11 |
10 | Multiple Discrete Random Variables | Text 1-Chap. 5, Text 2-Chap 7 |
11 | Multiple Continuous Random Variables | Text 1-Chap. 5, Text 2-Chap 12 |
12 | Conditional Probability Mass Functions | Text 1-Chap. 5, Text 2-Chap 8 |
13 | Conditional Probability Density Functions | Text 1-Chap. 5, Text 2-Chap 13 |
14 | Conditional Probability Density Functions | Text 1-Chap. 5, Text 2-Chap 13 |
Resources |
1. Applied Statistics and Probability for Engineers, Sixth Edition, Douglas C. Montgomery and George C. Runger, ISBN : 13 9781118539712 2. Intuitive Probability and Random Processes Using MatLab - Steven M. Kay, 2016, ISBN-13: 978-0-387-24157-9 |
1) A. Papoulis, Probability, Random Variables, and Stochastic Processes, Mc Graw Hill, 1984. 2) Alberto Leon-Garcia, Probability, Statistics, and Random Processes For Electrical Engineering, Prentice Hall, Third Edition, 2008. 3) A. Papoulis, Probability, Random Variables and Stochastic Processes, McGraw-Hill , Third Edition,1991 |
Course Contribution to Program Qualifications
Course Contribution to Program Qualifications | |||||||
No | Program Qualification | Contribution Level | |||||
1 | 2 | 3 | 4 | 5 | |||
1 | Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied knowledge in these areas in the solution of complex engineering problems. | X | |||||
2 | Ability to formulate, and solve complex engineering problems; ability to select and apply proper analysis and modeling methods for this purpose. | X | |||||
3 | Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the desired result; ability to apply modern design methods for this purpose. | ||||||
4 | Ability to select and use modern techniques and tools needed for analyzing and solving complex problems encountered in engineering practice; ability to employ information technologies effectively. | X | |||||
5 | Ability to design and conduct experiments, gather data, analyze and interpret results for investigating complex engineering problems or discipline specific research questions. | X | |||||
6 | Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually. | X | |||||
7 | Ability to communicate effectively, both orally and in writing; knowledge of a minimum of one foreign language; ability to write effective reports and comprehend written reports, prepare design and production reports, make effective presentations, and give and receive clear and intelligible instructions. | X | |||||
8 | Awareness of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself. | X | |||||
9 | Knowledge on behavior according ethical principles, professional and ethical responsibility and standards used in engineering practices. | X | |||||
10 | Knowledge about business life practices such as project management, risk management, and change management; awareness in entrepreneurship, innovation; knowledge about sustainable development. | ||||||
11 | Knowledge about the global and social effects of engineering practices on health, environment, and safety, and contemporary issues of the century reflected into the field of engineering; awareness of the legal consequences of engineering solutions. |
Assessment Methods
Contribution Level | Absolute Evaluation | |
Rate of Midterm Exam to Success | 30 | |
Rate of Final Exam to Success | 70 | |
Total | 100 |