GRADUATE INSTITUTE of NATURAL and APPLIED SCIENCES / DEPARTMENT of STATISTICS and COMPUTER SCIENCES Statistics-Joint Doctorate Course Catalog https://www.ktu.edu.tr/fbeistatistik Phone: +90 0462 +90 (462) 377 3112

FBE

GRADUATE INSTITUTE of NATURAL and APPLIED SCIENCES / DEPARTMENT of STATISTICS and COMPUTER SCIENCES / Statistics-Joint Doctorate

To teach the basic concepts of probability theory.

Programme Outcomes

CTPO

TOA

Upon successful completion of the course, the students will be able to :

PO - 1 :

learn basic information about the probability theory

1,3,7

1

PO - 2 :

interpret the information obtained with the help of probability theory

1,3,7

1

PO - 3 :

use probability theory in other disciplines

1,3,7

1

CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), PO : Learning Outcome

Contents of the Course

Measure and probability spaces, extension theorem, measurable function and random variable, expectation, characteristic functions, independence, convergence.

Course Syllabus

Week

Subject

Related Notes / Files

Week 1

Basic concepts in probability theory

Week 2

Stochastic experiment, random events, events on the operations, examples

Week 3

Basic concepts of combinatorial theory

Week 4

Different definitions of probability: experimental definition, theoretical definition, the classical definition

Week 5

Sigma algebra and algebra, probability measure, sample, conditional probability, independent events, additive probability

Week 6

Bayes' theorem and examples

Week 7

General Review and problem solving

Week 8

Mid-term exam

Week 9

Random variables and distributions: discrete, continuous and singular distribution

Week 10

Multi-dimensional distributions

Week 11

Numerical characteristics of random variables

Week 12

Correlation coefficient and its properties, and conditional expected value of the conditional distribution function

Week 13

Examples

Week 14

Characteristic functions

Week 15

Multi-dimensional characteristic function of distribution, manufacturers function, repetition and problem solving issues

Week 16

End-of-term exam

Textbook / Material

1

Nasirova, T., Khaniyev, T., Yapar, C., Ünver, İ. ve Küçük, Z. 2009; Olasılık, KTÜ Yayınları, Trabzon

Recommended Reading

1

Akdeniz, F. 1998; Olasılık ve İstatistik, Baki Kitapevi, Adana

2

Öztürk, F. 1993; Matematiksel İstatistik, ANkara Üniversitesi Yayınları, Ankara

3

Feller W. 1970; An Introduction to Probability Theory and Its Application, Vol. II, John Wiley&Sons, New York