## Course Detail

## Course Description

Course | Code | Semester | T+P (Hour) | Credit | ECTS |
---|---|---|---|---|---|

PROBABILITY and RANDOM VARIABLES | COE2249080 | Spring Semester | 3+0 | 3 | 6 |

Course Program | ( B ) Çarşamba 17:30-18:15 ( B ) Çarşamba 18:30-19:15 ( B ) Çarşamba 19:30-20:15 ( B ) Çarşamba 20:30-21:15 ( A ) Salı 15:30-16:15 ( A ) Salı 16:30-17:15 ( A ) Salı 17:30-18:15 ( A ) Salı 18:30-19:15 |

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) | Prof.Dr. Afgan ASLAN |

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 | 1. An ability to apply knowledge of mathematics, science, and engineering | X | |||||

2 | 2. An ability to identify, formulate, and solve engineering problems | X | |||||

3 | 3. An ability to design a system, component, or process to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical, health and safety, manufacturability, and sustainability | ||||||

4 | 4. An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice | X | |||||

5 | 5. An ability to design and conduct experiments, as well as to analyze and interpret data | X | |||||

6 | 6. An ability to function on multidisciplinary teams | X | |||||

7 | 7. An ability to communicate effectively | X | |||||

8 | 8. A recognition of the need for, and an ability to engage in life-long learning | X | |||||

9 | 9. An understanding of professional and ethical responsibility | X | |||||

10 | 10. A knowledge of contemporary issues | ||||||

11 | 11. The broad education necessary to understand the impact of engineering solutions in a global, economic, environmental, and societal context |

## 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 | COE2249080 | Spring Semester | 3+0 | 3 | 6 |

Course Program | ( B ) Çarşamba 17:30-18:15 ( B ) Çarşamba 18:30-19:15 ( B ) Çarşamba 19:30-20:15 ( B ) Çarşamba 20:30-21:15 ( A ) Salı 15:30-16:15 ( A ) Salı 16:30-17:15 ( A ) Salı 17:30-18:15 ( A ) Salı 18:30-19:15 |

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) | Prof.Dr. Afgan ASLAN |

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 | 1. An ability to apply knowledge of mathematics, science, and engineering | X | |||||

2 | 2. An ability to identify, formulate, and solve engineering problems | X | |||||

3 | 3. An ability to design a system, component, or process to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical, health and safety, manufacturability, and sustainability | ||||||

4 | 4. An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice | X | |||||

5 | 5. An ability to design and conduct experiments, as well as to analyze and interpret data | X | |||||

6 | 6. An ability to function on multidisciplinary teams | X | |||||

7 | 7. An ability to communicate effectively | X | |||||

8 | 8. A recognition of the need for, and an ability to engage in life-long learning | X | |||||

9 | 9. An understanding of professional and ethical responsibility | X | |||||

10 | 10. A knowledge of contemporary issues | ||||||

11 | 11. The broad education necessary to understand the impact of engineering solutions in a global, economic, environmental, and societal context |

### Assessment Methods

Contribution Level | Absolute Evaluation | |

Rate of Midterm Exam to Success | 30 | |

Rate of Final Exam to Success | 70 | |

Total | 100 |