COURSE INTRODUCTION AND APPLICATION INFORMATION


Course Name
Introduction to Probability Theory II
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
MATH 204
Spring
2
2
3
6
Prerequisites
 MATH 203To attend the classes (To enrol for the course and get a grade other than NA or W)
Course Language
English
Course Type
Required
Course Level
First Cycle
Mode of Delivery -
Teaching Methods and Techniques of the Course
Course Coordinator -
Course Lecturer(s)
Assistant(s)
Course Objectives This course aims to consider basic theory and applications of probability theory including jointly distributed and multivariate random variables, independent random variables and their sums, some special discrete and continuous distributions and copulas, covariance and correlation coefficient, order statistics, some special inequalities, the weak and strong law of large numbers, and central limit theorem.
Learning Outcomes The students who succeeded in this course;
  • will be able to analyze jointly distributed and multivariate random variables.
  • will be able to analyze independent random variables and their sums.
  • will be able to anaylze some special discrete and continuous distributions and copulas.
  • will be able to calculate covariance and correlation coefficient.
  • will be able to analyze order statistics and some special inequalities.
  • will be able to analyze the weak and strong law of large numbers and central limit theorem.
Course Description This course aims to provide basic theory and applications of Probability Theory.

 



Course Category

Core Courses
X
Major Area Courses
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Required Materials
1 Multivariate random variables and their joint distribution functions Chapter 6
2 Sum of two random variables and convolution formula Chapter 6
3 Independent random variables and sums of two random variables Chapter 6
4 Joint probability distribution of functions of random variables Chapter 6
5 Exchangeable random variables Chapter 6
6 Some special discrete distributions Chapter 6
7 Some special continuous distributions Chapter 6
8 Some copulas Chapter 6
9 Expectation of sums of random variables Chapter 7
10 Covariance and correlation coefficient Chapter 7
11 Conditional expectation Chapter 7
12 Order statistics Chapter 6
13 Chebyshev, Markov, and Pearson inequalities Chapter 8
14 Weak Law of Large Numbers, Strong Law of Large Numbers Chapter 8
15 Central Limit Theorem Chapter 8
16 Review of the semester
Course Notes/Textbooks “A First Course in Probabilty” by Sheldon Ross.
Suggested Readings/Materials “Probability and Statistics for Engineers and Scientists” by Ronald Walpole, Raymond Myers, Sharon Myer.

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
1
10
Laboratory / Application
Field Work
Quizzes / Studio Critiques
3
15
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterm
1
35
Final Exam
1
40
Total

Weighting of Semester Activities on the Final Grade
5
60
Weighting of End-of-Semester Activities on the Final Grade
1
40
Total

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Course Hours
(Including exam week: 16 x total hours)
16
4
64
Laboratory / Application Hours
(Including exam week: 16 x total hours)
16
Study Hours Out of Class
15
4
Field Work
Quizzes / Studio Critiques
3
4
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterms
1
22
Final Exams
1
25
    Total
183

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1 To have a grasp of basic mathematics, applied mathematics and theories and applications of statistics. X
2 To be able to use theoretical and applied knowledge acquired in the advanced fields of mathematics and statistics, X
3 To be able to define and analyze problems and to find solutions based on scientific methods, X
4 To be able to apply mathematics and statistics in real life with interdisciplinary approach and to discover their potentials, X
5 To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself, X
6 To be able to criticize and renew her/his own models and solutions, X
7 To be able to tell theoretical and technical information easily to both experts in detail and nonexperts in basic and comprehensible way, X
8

To be able to use international resources in English and in a second foreign language from the European Language Portfolio (at the level of B1) effectively and to keep knowledge up-to-date, to communicate comfortably with colleagues from Turkey and other countries, to follow periodic literature,

X
9

To be familiar with computer programs used in the fields of mathematics and statistics and to be able to use at least one of them effectively at the European Computer Driving Licence Advanced Level,

X
10

To be able to behave in accordance with social, scientific and ethical values in each step of the projects involved and to be able to introduce and apply projects in terms of civic engagement,

X
11 To be able to evaluate all processes effectively and to have enough awareness about quality management by being conscious and having intellectual background in the universal sense, X
12

By having a way of abstract thinking, to be able to connect concrete events and to transfer solutions, to be able to design experiments, collect data, and analyze results by scientific methods and to interfere,

X
13

To be able to continue lifelong learning by renewing the knowledge, the abilities and the compentencies which have been developed during the program, and being conscious about lifelong learning,

14

To be able to adapt and transfer the knowledge gained in the areas of mathematics and statistics to the level of secondary school,

15

To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively.

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

 

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