GRADUATE SCHOOL

PH.D. In Applied Mathematics and Statistics

STAT 601 | Course Introduction and Application Information

Course Name
Probability Theory and Mathematical Statistics
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
STAT 601
Fall
3
0
3
7.5

Prerequisites
None
Course Language
English
Course Type
Required
Course Level
Third Cycle
Mode of Delivery -
Teaching Methods and Techniques of the Course -
Course Coordinator -
Course Lecturer(s)
Assistant(s) -
Course Objectives To provide advance concepts of probability theory. The course illustrates many definitions of probability theory and mathematical statistics analysis for students who would like to focus on discrete random events and their distributions.
Learning Outcomes The students who succeeded in this course;
  • will be able to describe the basic principles for computing probabilities.
  • will be able to show how probability axioms are used.
  • will be able to deal with conditional probabilities and the concept of independence.
  • will be able to make point estimates using methods to find point estimators.
  • will be able to evaluate estimators using estimator properties.
  • will be able to construct hypotheses using methods to find hypothesis.
  • will be able to construct interval estimates using methods to find interval estimators.
Course Description Axioms of Probability, Conditional Probability and Independence, Random variables, Joint distribution functions, Order statistics, Sufficiency Principles, Limit Theorems, Principles of Data Reduction, Point Estimation, Hypothesis Testing, Interval Estimations

 



Course Category

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

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Related Preparation
1 Sample space Sheldon Ross,''A First Course in Probability'' 9th edition,Pearson,2012. ISBN-13: 978-0321794772.Chapter 1
2 Classical probability Sheldon Ross,''A First Course in Probability'' 9th edition,Pearson,2012. ISBN-13: 978-0321794772.Chapter 1
3 Axioms of probability Sheldon Ross,''A First Course in Probability'' 9th edition,Pearson,2012. ISBN-13: 978-0321794772.Chapter 2
4 Properties of probability Sheldon Ross,''A First Course in Probability'' 9th edition,Pearson,2012. ISBN-13: 978-0321794772.Chapter 4
5 Conditional probability and independence of events Sheldon Ross,''A First Course in Probability'' 9th edition,Pearson,2012. ISBN-13: 978-0321794772. Chapter 3
6 Total probability formula and Bayes' formula Sheldon Ross,''A First Course in Probability'' 9th edition,Pearson,2012. ISBN-13: 978-0321794772. Chapter 3
7 Random variables and properties of distribution function Sheldon Ross,''A First Course in Probability'' 9th edition,Pearson,2012. ISBN-13: 978-0321794772. Chapter 4
8 Midterm Exam
9 Types of random variables, some discrete random variables, some continuous random variables, expected value Sheldon Ross,''A First Course in Probability'' 9th edition,Pearson,2012. ISBN-13: 978-0321794772.Chapters 4 & 5
10 Expectation of a function of a random variable, variance Sheldon Ross,''A First Course in Probability'' 9th edition,Pearson,2012. ISBN-13: 978-0321794772.Chapters 4 & 5
11 Hazard rate functions, the wellknown distribution functions, mean residual life function Sheldon Ross,''A First Course in Probability'' 9th edition,Pearson,2012. ISBN-13: 978-0321794772.Chapters 4 & 5
12 Multivariate random variables and their joint distribution functions, sum of two random variables and convolution form, Independent random variables and sums of two random variablesula, Sheldon Ross,''A First Course in Probability'' 9th edition,Pearson,2012. ISBN-13: 978-0321794772. Chapter 6
13 Joint probability distribution of functions of random variables, some special discrete distributions, some special continuous distributions Sheldon Ross,''A First Course in Probability'' 9th edition,Pearson,2012. ISBN-13: 978-0321794772. Chapter 6
14 Point estimation, evaluating estimators, methods of finding Hypothesis tests, interval estimations, finding interval estimators G.Casella and R.Berger "Statistical Inference", Cengage Learning, 2nd Edition, 2001. ISBN-13: 978-0534243128
15 Semester Review
16 Final Exam

 

Course Notes/Textbooks

Sheldon Ross,''A First Course in Probability'' 9th edition,Pearson,2012. ISBN-13: 978-0321794772. 

G.Casella and R.Berger "Statistical Inference", Cengage Learning, 2nd Edition, 2001. ISBN-13: 978-0534243128

Suggested Readings/Materials

"A First course in Probability" by S.Ross, Prentice Hall, 6th edition, 2001. ISBN-13: 978-0130338518  

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exams
Midterm
1
50
Final Exam
1
50
Total

Weighting of Semester Activities on the Final Grade
1
50
Weighting of End-of-Semester Activities on the Final Grade
1
50
Total

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Theoretical Course Hours
(Including exam week: 16 x total hours)
16
3
48
Laboratory / Application Hours
(Including exam week: '.16.' x total hours)
16
0
Study Hours Out of Class
14
6
84
Field Work
0
Quizzes / Studio Critiques
0
Portfolio
0
Homework / Assignments
0
Presentation / Jury
0
Project
0
Seminar / Workshop
0
Oral Exam
0
Midterms
1
40
40
Final Exam
1
53
53
    Total
225

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Competencies/Outcomes
* Contribution Level
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

 


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