# 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 4 0 0 4 7
Pre-requisite Course(s)
MATH 136 Mathematical Analysis II or MATH 152 Calculus II or MATH 158 Extended Calculus II
Course Language English N/A Bachelor’s Degree (First Cycle) Face To Face Lecture, Question and Answer, Problem Solving. 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. The students who succeeded in this course; have knowledge of fundamental concepts of Probability Theory, including notion of probability space, properties of probability. understand the notion of independence and conditional probability as well as the usage of the Bayes Theorem. understand the notions of random variable, random vector, and probability distribution together with the knowledge of classical probability distributions and their applications understand basic statistical concepts and methods. Skills to apply methods of descriptive statistics understand the central limit theorem and its importance for the statistical inference. Ability to use the parameters estimation methods and perform hypothesis testing as well as interpret obtained results. 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 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

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 40 100

### Course Category

Core Courses X

### The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Has the ability to apply scientific knowledge gained in the undergraduate education and to expand and extend knowledge in the same or in a different area X
2 Can apply gained knowledge and problem solving abilities in inter-disciplinary research X
3 Has the ability to work independently within research area, to state the problem, to develop solution techniques, to solve the problem, to evaluate the obtained results and to apply them when necessary X
4 Takes responsibility individually and as a team member to improve systematic approaches to produce solutions in unexpected complicated situations related to the area of study X
5 Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework X
6 Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility X
7 Has the ability to follow recent developments within the area of research, to support research with scientific arguments and data, to communicate the information on the area of expertise in a systematically by means of written report and oral/visual presentation X
8 To have an oral and written communication ability in at least one of the common foreign languages ("European Language Portfolio Global Scale", Level B2) X
9 Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge X
10 Follows scientific, cultural, and ethical criteria in collecting, interpreting and announcing data in the research area and has the ability to teach. X
11 Has professional 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

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