ECTS - Analytical Probability Theory
Analytical Probability Theory (MDES615) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Analytical Probability Theory | MDES615 | Area Elective | 3 | 0 | 0 | 3 | 5 |
| Pre-requisite Course(s) |
|---|
| N/A |
| Course Language | English |
|---|---|
| Course Type | Elective Courses |
| Course Level | Ph.D. |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture. |
| Course Lecturer(s) |
|
| Course Objectives | The objective of the course is to study the properties of probability distributions and their applications with the help of analytic methods. The course is based on the modern approach to Probability Theory. Since engineering scientists need powerful analytic tools of Probability Theory to analyze algorithms and computer systems, a great number of practical examples are included into the course. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | Sigma-algebra of sets, measure, integral with respect to measure; probability space; independent events and independent experiments; random variables and probability distributions; moments and numerical characteristics; random vectors and independent random variables; convergence of random variables; transform methods; sums of independent random v |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | Sigma-algebra of sets, measure, measurable functions. Integral with respect to measure | Ch.1.1-1.7 |
| 2 | Probability space. Basic properties of probability. Independent and dependent events. Pairwise independence, independence at level k, stochastic independence. | Ch. 1.9-1.11 |
| 3 | Introduction to the reliability theory: reliability of series-parallel systems and non-series-parallel systems. Independent experiments. Bernoulli trials. Reliability of an m-out-of-n system. | Ch. 1.12 |
| 4 | Random variables, their distributions. Distribution function. The probability mass function and probability density. | Ch. 2.1, 2.2, 2.4 |
| 5 | Pure and mixed type distributions. Lebesgue decomposition theorem. | Ch. 3.1 |
| 6 | Classical probability distributions, their properties and applications. The usage of Poisson distribution. | Ch. 2.5, 3.4 |
| 7 | Memoryless property of the exponential distribution. Reliability function. | Ch. 3.2, 3.3 |
| 8 | Functions of random variables, their distributions. Numerical characteristics of random variables. Moments. Chebyshev inequality. | Ch. 4.1, 4.2 |
| 9 | Random vectors. Distribution of a random vector and distribution of components | Ch. 2.9, 3.6 |
| 10 | Independent random variables, their properties. Conditional distribution and conditional expectation. | Ch. 5.1, 5.2, 5.3 |
| 11 | Independent random variables, their properties. The convolution theorem. Erlang distribution. | Ch. 2.9 |
| 12 | Transform methods: Moment generating functions, their properties and applications. | Ch. 4.5 |
| 13 | Sums of independent random variables. Hypoexponential distribution. Standby redundancy. | Ch. 3.8 |
| 14 | Convergence in distribution. Limit distribution. The central limit theorem | Ch. 4.7 |
| 15 | Overall review | - |
| 16 | Final exam | - |
Sources
| Course Book | 1. K. S. Trivedi, Probability and Statistics with Reliability, Queueing, and Computer Science Applications, 2nd Edition, Wiley, 2002. |
|---|---|
| Other Sources | 2. W.Feller. An Introduction to probability theory and its applications, v.I,II. J.Wiley and Sons, New-York, 1986 |
| 3. K.L. Chung. A Course in Probability Theory Revised. Acad. Press, 3rd Ed. | |
| 4. M.H. DeGroot, M.J. Shervish. Probability and Statistics. Addison Wesley, 2002 |
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| Attendance/Participation | - | - |
| Laboratory | - | - |
| Application | - | - |
| Field Work | - | - |
| Special Course Internship | - | - |
| Quizzes/Studio Critics | - | - |
| Homework Assignments | - | - |
| Presentation | - | - |
| Project | 2 | 20 |
| Report | - | - |
| Seminar | - | - |
| Midterms Exams/Midterms Jury | 2 | 40 |
| Final Exam/Final Jury | 1 | 40 |
| Toplam | 5 | 100 |
| Percentage of Semester Work | 60 |
|---|---|
| Percentage of Final Work | 40 |
| Total | 100 |
Course Category
| Core Courses | X |
|---|---|
| Major Area Courses | |
| Supportive Courses | |
| Media and Managment Skills Courses | |
| Transferable Skill Courses |
The Relation Between Course Learning Competencies and Program Qualifications
| # | Program Qualifications / Competencies | Level of Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | Is independently able to build a problem in the area of study, solve the problem by developing solution techniques and assess the solutions. | X | ||||
| 2 | Is capable of creating a groundwork in the fundamental branches of mathematics as well as in his/her research area | X | ||||
| 3 | follows the latest national and international literature in Mathematics and in his/her area of research; and uses them in his/her related studies | X | ||||
| 4 | observes and adopts the scientific ethical values in his/her professional and social life | X | ||||
| 5 | presents in Turkish and English in academic/scientific events the results of his/her research or the latest studies and findings on a special topic and participates in discussions | X | ||||
| 6 | Develops skills to work independently or as a member of a team | X | ||||
| 7 | Develops competences in the areas of creative and critical thinking, problem solving and producing original studies. Follows recent scientific studies, is capable of making an analysis, synthesis and assessment of the knowledge acquired | X | ||||
| 8 | Is open to lifelong improvement of his/her acquired knowledge, skills and competences. | X | ||||
| 9 | Is able to apply the acquired knowledge and problem-solving skills to interdisciplinary studies, proposes different solution methods to problems in terms of mathematical models and from a mathematical point of view | X | ||||
| 10 | Uses the mathematical based softwares, informatics and communication technologies for scientific purposes | X | ||||
ECTS/Workload Table
| Activities | Number | Duration (Hours) | Total Workload |
|---|---|---|---|
| Course Hours (Including Exam Week: 16 x Total Hours) | 16 | 3 | 48 |
| Laboratory | |||
| Application | |||
| Special Course Internship | |||
| Field Work | |||
| Study Hours Out of Class | 16 | 2 | 32 |
| Presentation/Seminar Prepration | |||
| Project | 2 | 12 | 24 |
| Report | |||
| Homework Assignments | |||
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 2 | 8 | 16 |
| Prepration of Final Exams/Final Jury | 1 | 10 | 10 |
| Total Workload | 130 | ||