Probability (MAT331)
| Course Code | Course Name | Semester | Theory | Practice | Lab | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| MAT331 | Probability | 5 | 3 | 2 | 0 | 5 | 8 |
| Prerequisites | |
| Admission Requirements |
| Language of Instruction | |
| Course Type | Compulsory |
| Course Level | Bachelor Degree |
| Course Instructor(s) | Muhammed ULUDAĞ muhammed.uludag@gmail.com (Email) Nihal YURDAKUL UYAR (Email) |
| Assistant | |
| Objective | The aim of this course is to provide students with a solid foundation in probability theory, covering both discrete and continuous models. Students will learn how to model uncertainty mathematically, analyze random phenomena, and apply probability concepts to solve problems in science, engineering, and real life. |
| Content |
• Principles of combinatorial analysis • Axioms of probability • Conditional probability and independence • Discrete random variables and their distributions • Continuous random variables and density functions • Joint, marginal, and conditional distributions • Expectation, variance, and other moments • Law of large numbers and central limit theorem • Selected applications in statistics and data science |
| Course Learning Outcomes |
By the end of the course, students will be able to: 1. Define and work with discrete and continuous probability distributions. 2. Compute probabilities, expectations, and variances for random variables. 3. Apply conditional probability and independence in modeling. 4. Analyze problems involving multiple random variables. 5. Understand and apply limit theorems (LLN, CLT) to real-world problems. 6. Use probability as a tool for reasoning in science and engineering contexts. |
| Teaching and Learning Methods |
• Lectures with theoretical explanations • Interactive discussions to strengthen conceptual understanding • Problem-solving sessions with exercises and examples • Use of software tools (e.g., Python) for applications when appropriate |
| References | • Sheldon Ross, A First Course in Probability (latest edition) |
Theory Topics
| Week | Weekly Contents |
|---|---|
| 1 | Permutations and combinations, Sample space and events, Axioms of Probability |
| 2 | Conditional probability, Bayes' Formula, Random variables, Discrete random variables |
| 3 | Expected Value, Expectation of a Function of a random variable, Variance |
| 4 | The Bernoulli and binomial random variables, The Poisson random variable, Other discrete probability distributions |
| 5 | Continuous random variables and their expectation and variance |
| 6 | The uniform random variable, Normal random variables, Exponential random variables |
| 7 | The distribution of a Function of a random variable, Midterm Examination |
| 8 | Joint distribution functions, Independent random variables, Sums of independent random variables |
| 9 | Conditional Distributions, Joint probability distribution of functions of random variables |
| 10 | Properties of expectation, Expectation of sums of random variables, Moments of the number of events that occur |
| 11 | Covariance, Variance of sums and Correlations |
| 12 | Conditional expectation and prediction, Moment generating Functions |
| 13 | Chebyshev’s inequality, The weak law of large numbers, |
| 14 | The central limit theorem, The strong law of large numbers |
Practice Topics
| Week | Weekly Contents |
|---|
Contribution to Overall Grade
| Number | Contribution | |
|---|---|---|
| Contribution of in-term studies to overall grade | 1 | 40 |
| Contribution of final exam to overall grade | 1 | 60 |
| Toplam | 2 | 100 |
In-Term Studies
| 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 |
| Make-up | 0 | 0 |
| Toplam | 0 | 0 |
| No | Program Learning Outcomes | Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | understands principles of deductive reasoning; has experience to verify well-foundedness and exactness of mathematical statements in systematic ways; | X | ||||
| 2 | can properly state and use concepts and results of major mathematical interest; | X | ||||
| 3 | masters current computational techniques and algorithms; has a good ability in their use; can identify relevant tools, among those one has learned, suitable to solve a problem and is able to judge whether or not one is in possession of these tools; | X | ||||
| 4 | is able to express one’s mathematical ideas in an organised way both in written and oral forms; | X | ||||
| 5 | understands relations connecting substantial concepts and results; can switch from one viewpoint to another on mathematical objects (pictures, formulae, precise statements, heuristic trials, list of examples,...); | X | ||||
| 6 | has followed individually a guided learning strategy; has pursued steps toward the resolution of unfamiliar problems; | |||||
| 7 | has a theoretical and practical knowledge in computer science well adapted for learning a programming language; | |||||
| 8 | has investigated the relevance of modeling and using mathematical tools in natural sciences and in the professional life; is conscious about historical development of mathematical notions; | |||||
| 9 | has followed introduction to some mathematical or non-mathematical disciplines after one’s proper choice; had experience to learn selected subjects according to one’s proper arrangement; | X | ||||
| 10 | masters French language as well as other foreign languages, to a level sufficient to study or work abroad. | X | ||||
| Activities | Number | Period | Total Workload |
|---|---|---|---|
| Class Hours | 14 | 4 | 56 |
| Working Hours out of Class | 14 | 4 | 56 |
| Assignments | 4 | 2 | 8 |
| Presentation | 0 | 0 | 0 |
| Midterm Examinations (including preparation) | 1 | 20 | 20 |
| Project | 0 | 0 | 0 |
| Laboratory | 0 | 0 | 0 |
| Other Applications | 0 | 0 | 0 |
| Final Examinations (including preparation) | 1 | 30 | 30 |
| Quiz | 2 | 10 | 20 |
| Term Paper/ Project | 0 | 0 | 0 |
| Portfolio Study | 0 | 0 | 0 |
| Reports | 0 | 0 | 0 |
| Learning Diary | 0 | 0 | 0 |
| Thesis/ Project | 0 | 0 | 0 |
| Seminar | 0 | 0 | 0 |
| Other | 0 | 0 | 0 |
| Make-up | 0 | 0 | 0 |
| Total Workload | 190 | ||
| Total Workload / 25 | 7.60 | ||
| Credits ECTS | 8 | ||