Probability
muhammed.uludag@gmail.com
Content
Objective
-The aim of this course is to introduce the fundamental concepts of probability theory and basic statistical methods used in data science and applied mathematics. Students will learn how to model uncertainty, analyze random phenomena, and interpret probabilistic models.
Course Content
This course covers the basic concepts of probability, conditional probability, and independence. Random variables and probability distributions will be introduced through both discrete and continuous models. Discrete distributions such as Bernoulli, Binomial, and Poisson distributions, as well as continuous distributions including Uniform, Normal, and Exponential distributions, will be studied. Joint distributions and related concepts will also be discussed. In addition, expectation, variance, and covariance will be introduced together with important theoretical result such as the Central Limit Theorem.-
Course Learning Outcomes
Upon successful completion of this course, students will be able to:
Explain the fundamental concepts of probability theory.
Compute conditional probabilities and analyze independence between events.
Define and work with random variables and probability distributions.
Analyze discrete and continuous probability distributions.
Compute expectation, variance, and covariance of random variables.
Interpret and use joint probability distributions.
Explain the Central Limit Theorem.
Apply probabilistic methods to simple problems arising in data science and applied mathematics.
Weekly Contents
| Week | Weekly Contents |
|---|---|
| 1 | Introduction to Probability and Sample Spaces |
| 2 | Conditional Probability and Independence |
| 3 | Random Variables |
| 4 | Discrete Probability Distributions: Bernoulli and Binomial |
| 5 | Poisson Distribution and Applications |
| 6 | Continuous Probability Distributions: Uniform Distribution |
| 7 | Normal and Exponential Distributions |
| 8 | Midterm |
| 9 | Joint Distributions and Marginal Distributions |
| 10 | Expectation, Variance, and Covariance |
| 11 | Central Limit Theorem and Applications |
Assessment System
| Activities | Number | Contribution |
|---|---|---|
| Contribution of in-term studies to overall grade | 0 | 0 |
| Contribution of final exam to overall grade | 0 | 0 |
| Total | 0 | 0 |
| Activities | 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 |
| Total | 0 | 0 |
Relation of Proficiency
| 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; | X | ||||
| 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; | X | ||||
| 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; | |||||
| 10 | masters French language as well as other foreign languages, to a level sufficient to study or work abroad. | X | ||||
ECTS
| Activities | Number | Period | Total Workload |
|---|---|---|---|
| Class Hours | 0 | 0 | 0 |
| Working Hours out of Class | 0 | 0 | 0 |
| Assignments | 0 | 0 | 0 |
| Presentation | 0 | 0 | 0 |
| Midterm Examinations (including preparation) | 0 | 0 | 0 |
| Project | 0 | 0 | 0 |
| Laboratory | 0 | 0 | 0 |
| Other Applications | 0 | 0 | 0 |
| Final Examinations (including preparation) | 0 | 0 | 0 |
| Quiz | 0 | 0 | 0 |
| 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 |
| Yıl Sonu | 0 | 0 | 0 |
| Hazırlık Yıl Sonu | 0 | 0 | 0 |
| Hazırlık Bütünleme | 0 | 0 | 0 |
| Total Workload | 0 | ||
| Total Workload / 25 | 0.00 | ||
| Credits ECTS | 0 | ||