CLICK HERE FOR THE COURSE SYLLABUS (.pdf)


COURSE INTRODUCTION AND APPLICATION INFORMATION

 
Course Name
Code
Semester
Theory
(hour/week)
Application/Laboratory
(hour/week)
Local Credits
ECTS
Probability Theory
STAT 503
Fall/Spring
3
0
3
7.5

Prerequisites
None

Course Language
English
Course Type
Elective
Course Level
Second Cycle
Course Coordinator -
Course Lecturer(s)
Course Assistants -
Course Objectives This course aims to make the students familiar with the basics of Probability Theory and its applications.
Course Learning Outcomes The students who succeeded in this course;
  • will be able to apply all basic combinatorial formulas to probability theory.
  • will be able to find probabilities of different events.
  • will be able to work with discrete distribiutions, being able to compute important characteristis for them.
  • will be able to work with continuous distributions and find basic charactheristics for them.
  • will be able to derive the weak law, strong law of large numbers and the central limit theorem for the sums of independent random variables.
Course Content In this course, a short introduction to the combinatorial analysis is given. The axioms of probability theory and historical background is discussed. Random events, random variables as well as their basic characteristics are studied. Limit theorems for sums of independent random variables are also considered.

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Related Preparation
1 Combinatorial analysis. “A first course in probability” by Sheldon Ross, Prentice Hall: 1:20.
2 The axioms of  probability. “A first course in probability” by Sheldon Ross, Prentice Hall: 24:35.
3 İndependent events, conditional probability, total probability formula. “A first course in probability” by Sheldon Ross, Prentice Hall: 64:87.
4 The basic notations for discrete random variables. “A first course in probability” by Sheldon Ross, Prentice Hall. 127:137.
5 The Bernoulli, binomial, Poisson, geometric and negative binomial random variables. “A first course in probability” by Sheldon Ross, Prentice Hall: 139:158.
6 The basic notations for continuous random variables. “A first course in probability” by Sheldon Ross, Prentice Hall: 188:198.
7 The uniform and exponential random variables. The normal law “A first course in probability” by Sheldon Ross, Prentice Hall: 198:206.
8 Midterm Exam
9 Jointly distributed and multivariate random variables. “A first course in probability” by Sheldon Ross, Prentice Hall: 239:260.
10 Sums of independent random variables. Convolution formula. “A first course in probability” by Sheldon Ross, Prentice Hall: 261:270.
11 Order statistics. “A first course in probability” by Sheldon Ross, Prentice Hall: 273:277.
12 Properties of expectation. Covariance, variance, correlation. “A first course in probability” by Sheldon Ross, Prentice Hall: 304:340.
13 The moment generating functıon. “A first course in probability” by Sheldon Ross, Prentice Hall: 361:371
14 The central limit theorem and the law of large numbers. Other limit laws. “A first course in probability” by Sheldon Ross, Prentice Hall: 400:418.
15 Review for Final Exam
16 Review of the Semester  

 

SOURCES

Course Notes / Textbooks “A first course in probability” by Sheldon Ross, Prentice Hall.
References “Probability and Statistics for Engineers and Scientists”   Ronald Walpole,  Raymond Myers,  Sharon Myers, Keying Ye. Prentice Hall.

 

EVALUATION SYSTEM

Semester Requirements Number Percentage of Grade
Attendance/Participation
1
15
Laboratory
Application
Field Work
Special Course Internship (Work Placement)
Quizzes/Studio Critics
Homework Assignments
1
20
Presentation/Jury
Project
Seminar/Workshop
Midterms/Oral Exams
1
30
Final/Oral Exam
1
35
Total

PERCENTAGE OF SEMESTER WORK
3
65
PERCENTAGE OF FINAL WORK
1
35
Total

 

COURSE CATEGORY

Course Category

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

 

THE RELATIONSHIP BETWEEN COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS

#
Program Qualifications / Outcomes
* Level of Contribution
1
2
3
4
5
1

To develop and deepen his/her knowledge on theories of mathematics and statistics and their applications in level of expertise, and to obtain unique definitions which bring innovations to the area, based on master level competencies,

X
2

To have the ability of original, independent and critical thinking in Mathematics and Statistics and to be able to develop theoretical concepts,

X
3

To have the ability of defining and verifying problems in Mathematics and Statistics,

X
4

With an interdisciplinary approach, to be able to apply theoretical and applied methods of mathematics and statistics in analyzing and solving new problems and to be able to discover his/her own potentials with respect to the application,

X
5

In nearly every fields that mathematics and statistics are used, to be able to execute, conclude and report a research, which requires expertise, independently,

X
6

To be able to evaluate and renew his/her abilities and knowledge acquired in the field of Applied Mathematics and Statistics with critical approach, and to be able to analyze, synthesize and evaluate complex thoughts in a critical way,

X
7

To be able to convey his/her analyses and methods in the field of Applied Mathematics and Statistics to the experts in a scientific way,

X
8

To be able to use national and international academic resources (English) efficiently, to update his/her knowledge, to communicate with his/her native and foreign colleagues easily, to follow the literature periodically, to contribute scientific meetings held in his/her own field and other fields systematically as written, oral and visual.

X
9

To be familiar with computer software commonly used in the fields of Applied Mathematics and Statistics and to be able to use at least two of them efficiently,

X
10

To contribute the transformation process of his/her own society into an information society and the sustainability of this process by introducing scientific, technological, social and cultural advances in the fields of Applied Mathematics and Statistics,

X
11

As having rich cultural background and social sensitivity with a global perspective, to be able to evaluate all processes efficiently, to be able to contribute the solutions of social, scientific, cultural and ethical problems and to support the development of these values,

X
12

As being competent in abstract thinking, to be able to connect abstract events to concrete events and to transfer solutions, to analyze results with scientific methods by designing experiment and collecting data and to interpret them,

X
13

To be able to produce strategies, policies and plans about systems and topics in which mathematics and statistics are used and to be able to interpret and develop results,

X
14

To be able to evaluate, argue and analyze prominent persons, events and phenomena, which play an important role in the development and combination of the fields of Mathematics and Statistics, within the perspective of the development of other fields of science,

X
15

In Applied Mathematics and Statistics, to be able to sustain scientific work as an individual or a group, to be effective in all phases of an independent work, to participate decision-making process and to make and execute necessary planning within an effective time schedule.

X

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

ECTS / WORKLOAD TABLE

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)
16
3
Laboratory
Application
Special Course Internship (Work Placement)
Field Work
Study Hours Out of Class
15
6
Presentations / Seminar
Project
Homework Assignments
1
7
Quizzes
Midterms / Oral Exams
1
40
Final / Oral Exam
1
40
    Total Workload

CLICK HERE FOR THE COURSE SYLLABUS (.pdf)

 
 

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