ECTS - Probability Theory and Statistics
Probability Theory and Statistics (MATH392) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Probability Theory and Statistics | MATH392 | 6. Semester | 4 | 0 | 0 | 4 | 7 |
| Pre-requisite Course(s) |
|---|
| MATH136 ve MATH136 |
| Course Language | English |
|---|---|
| Course Type | Compulsory Departmental Courses |
| Course Level | Bachelor’s Degree (First Cycle) |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture, Question and Answer, Problem Solving. |
| Course Lecturer(s) |
|
| Course Objectives | The objective of the course is to introduce and provide understanding for basic notions of Probability and Statistics such as probability space, random variable, probability distribution, independence of random events and random variables. Students will learn the methods of statistical analysis, the theory and techniques of parameter estimation and hypothesis testing. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | Probability spaces, conditional probability and independence, random variables and probability distributions, numerical characteristics of random variables, classical probability distributions, random vectors, descriptive statistics, sampling, point estimation, interval estimation, testing hypotheses. |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | Axiomatic Definition of Probability. Probability Space. Classical Probability. Counting. Uniform Space. | [1] Ch. 1, pp. 12-17, 39-43; [2] II, Ch. IV, pp. 112-117 |
| 2 | Independence of Two and Several Events. Pairwise Independence. Law of Total Probability. Bayes’ Theorem. | [1] Ch. 2, pp. 49-53, 56-69 |
| 3 | Independent Experiments. Bernoulli Trials. | [2] I, Ch. VI, pp. 146-156; [1] Ch. 5, pp. 247-251 |
| 4 | Random Variables. Distribution of A Random Variable and A Distribution Function. Discrete, Absolutely Continuous and Singular Distributions. | [1] Ch. 3, pp. 97-113; [2] II, Ch. V, pp. 141-143 |
| 5 | Numerical Characteristics of Random Variables. Mathematical Expectation and Variance, Their Properties. Chebyshev Inequality. | [1] Ch. 4, pp. 181-199 |
| 6 | Classical Random Variables. Their Properties And Applications. | [1], Ch. 5, pp. 247-258, 264-273 |
| 7 | Random Vectors. Distribution of A Random Vector and Distribution of Its Projections. Independent Random Variables. | [1] Ch. 3, pp. 118-135 |
| 8 | Organization and Description of Data. Frequency Distributions, Their Graphic Presentations. Parameters and Statistics. | [3], Ch. 1, pp. 1-21 |
| 9 | Special Probability Distributions. Moment-Generating Functions. | [1] Ch. 5, pp. 295-305, 404-408 |
| 10 | The Central Limit Theorem, Its Applications. | [1] Ch. 5, pp. 286-295 |
| 11 | Point Estimation. Unbiased, Consistent, Sufficient Estimators. | [1] Ch. 7, pp. 427-433, 440-444 |
| 12 | Interval Estimation. Confidence Intervals. | [1] Ch. 7, pp. 409-416 |
| 13 | Statistical Hypotheses. Simple and Composite Hypotheses. Null and Alternative Hypotheses. Type I and II Errors. Level of Significance. | [1] Ch. 8, pp. 463-469, 472-484 |
| 14 | Testing Statistical Hypotheses. Tests Concerning Means, Proportions and Variances. | [1], Ch. 8, pp. 472-484 |
| 15 | Survey of The Course. | |
| 16 | Final exam. |
Sources
| Course Book | 1. M.H. DeGroot, M.J. Shervish. Probability and Statistics. Addison Wesley, 2002 |
|---|---|
| Other Sources | 2. W.Feller. An Introduction to probability theory and its applications, v.I,II. J.Wiley and Sons, New-York, 1979 |
| 3. John E. Freund, Mathematical Stasistics, Prentice Hall, 1992. |
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| Attendance/Participation | - | - |
| Laboratory | - | - |
| Application | - | - |
| Field Work | - | - |
| Special Course Internship | - | - |
| Quizzes/Studio Critics | - | - |
| Homework Assignments | 4 | 20 |
| Presentation | - | - |
| Project | - | - |
| Report | - | - |
| Seminar | - | - |
| Midterms Exams/Midterms Jury | 2 | 40 |
| Final Exam/Final Jury | 1 | 40 |
| Toplam | 7 | 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 | Acquires skills to use the advanced theoretical and applied knowledge obtained at the mathematics bachelors program to do further academic and scientific research in both mathematics-based graduate programs and public or private sectors. | X | ||||
| 2 | Transplants and applies the theoretical and applicable knowledge gained in their field to the secondary education by using suitable tools and devices. | X | ||||
| 3 | Acquires the skill of choosing, using and improving problem solving techniques which are needed for modeling and solving current problems in mathematics or related fields by using the obtained knowledge and skills. | X | ||||
| 4 | Acquires analytical thinking and uses time effectively in the process of deduction | X | ||||
| 5 | Acquires basic software knowledge necessary to work in the computer science related fields and together with the skills to use information technologies effectively. | X | ||||
| 6 | Obtains the ability to collect data, to analyze, interpret and use statistical methods necessary in decision making processes. | X | ||||
| 7 | Acquires the level of knowledge to be able to work in the mathematics and related fields and keeps professional knowledge and skills up-to-date with awareness in the importance of lifelong learning. | X | ||||
| 8 | Takes responsibility in mathematics related areas and has the ability to work affectively either individually or as a member of a team. | X | ||||
| 9 | Has proficiency in English language and has the ability to communicate with colleagues and to follow the innovations in mathematics and related fields. | X | ||||
| 10 | Has the ability to communicate ideas with peers supported by qualitative and quantitative data. | X | ||||
| 11 | Has professional and ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications. | X | ||||
ECTS/Workload Table
| Activities | Number | Duration (Hours) | Total Workload |
|---|---|---|---|
| Course Hours (Including Exam Week: 16 x Total Hours) | |||
| Laboratory | |||
| Application | |||
| Special Course Internship | |||
| Field Work | |||
| Study Hours Out of Class | 16 | 4 | 64 |
| Presentation/Seminar Prepration | |||
| Project | |||
| Report | |||
| Homework Assignments | 4 | 10 | 40 |
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 2 | 15 | 30 |
| Prepration of Final Exams/Final Jury | 1 | 16 | 16 |
| Total Workload | 150 | ||