Türkçe | English
FACULTY of SCIENCE / DEPARTMENT of STATISTICS and COMPUTER SCIENCES

Course Catalog
http://www.ktu.edu.tr/isbb
Phone: +90 0462 +90 (462) 3773112
FENF
FACULTY of SCIENCE / DEPARTMENT of STATISTICS and COMPUTER SCIENCES /
Katalog Ana Sayfa
  Katalog Ana Sayfa  KTÜ Ana Sayfa   Katalog Ana Sayfa
 
 

IST1000Introduction to Probability4+0+0ECTS:6
Year / SemesterSpring Semester
Level of CourseFirst Cycle
Status Compulsory
DepartmentDEPARTMENT of STATISTICS and COMPUTER SCIENCES
Prerequisites and co-requisitesNone
Mode of DeliveryFace to face
Contact Hours14 weeks - 4 hours of lectures per week
LecturerProf. Dr. Zafer KÜÇÜK
Co-LecturerNone
Language of instructionTurkish
Professional practise ( internship ) None
 
The aim of the course:
To make students understand the basic concepts of the probability theory: Sample Spaces, Events, Discrete and Continuous sample, Kolmogorov's axioms, the conditional probability of events, independence and Bayes' formula of total probability, Bernoulli scheme, random variables and distribution of random variables.
 
Learning OutcomesCTPOTOA
Upon successful completion of the course, the students will be able to :
LO - 1 : understand the basic concepts of probability theory2,81,
LO - 2 : construct a mathematical model of stochastic experiment 2,81,
LO - 3 : have the ability to calculate probability of events2,81,
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), LO : Learning Outcome

 
Contents of the Course
Historical development and subject of the probability theory. Sample space. Events and operations over events. Frequency of event. Definition of the probability in discrete sample space. Classical probability. Algebra and Borel sigma algebra. Definition of the probability in continuous sample space. Kolmogorov's axioms. Probability space. Properties of the probability measure. Geometrical probability. Independence of events. Formula of product of probabilities. Conditional probability. Total probability formula. Bayes's formulas. Sequence of independent trails. Bernoulli scheme. Limit theorems in Bernoulli scheme (Mouavr-Laplace's local and integral formulas, Poisson's theorem, Law of large numbers). Polynomial scheme. Sample Markov chains. Concept of random variable. Operations over random variables. Distribution function and its properties.
 
Course Syllabus
 WeekSubjectRelated Notes / Files
 Week 1Historical development and subject of the probability theory.
 Week 2Sample space. Events and operations over events.
 Week 3Frequency of event.Definition of the probability in discrete sample space. Classical definition and applications of probability.
 Week 4Definitions and applcations of Algebra and Borel sigma algebra. Definition of the probability in continuous sample space.
 Week 5Kolmogorov's axioms. Probability space. Properties of the probability measure.
 Week 6Geometrical probability and its applications. Independence of events, multiplication formula and applications of events.
 Week 7Conditional probability and its applcations. Formula of total probability formula. Bayes's formulas and their applications.
 Week 8Mid-term exam
 Week 9Sequance of independent trails. Bernoulli scheme.
 Week 10Limit theorems in Bernoulli scheme (Mouavr-Laplace's local and integral formulas, Poisson's theorem).
 Week 11Law of large numbers. Bernoulli and Poisson theorems.
 Week 12Polynomial scheme.
 Week 13Simple Markov chains.
 Week 14Concept of random variable (assessbility in comparison to algebra) Operations over random variables.
 Week 15Distribution of variables, distribution functions and its basic properties.
 Week 16End-of-term exam
 
Textbook / Material
1Akdeniz F. Olasılık ve İstatistik, Ankara Ü., Ankara, 1984,
2Akdeniz F. Olasılık ve İstatistik, Ankara Ü., Ankara, 1984,
3Nasirova T., Khaniyev T. Yapar C., Ünver İ., Küçük Z. Olasılık. KTÜ Matbaası, Trabzon, 2009.
4Nasirova T., Khaniyev T. Yapar C., Ünver İ., Küçük Z. Olasılık. KTÜ Matbaası, Trabzon, 2009.
 
Recommended Reading
1Kolmogorov A.N. Foundations of the Theory of Probability. New York, 1956.
2Kolmogorov A.N. Foundations of the Theory of Probability. New York, 1956.
3Ceyhan İnal H., Günay S.Olasılık ve matematiksel istatistik, Ankara,1982.
4Ceyhan İnal H., Günay S.Olasılık ve matematiksel istatistik, Ankara,1982.
5Ersoy N., Erbaş S.D. Olasılık ve İstatistiğe giriş, Gazi Ü., Ankara, 1992.
6Ersoy N., Erbaş S.D. Olasılık ve İstatistiğe giriş, Gazi Ü., Ankara, 1992.
 
Method of Assessment
Type of assessmentWeek NoDate

Duration (hours)Weight (%)
Mid-term exam 9 11/04/2019 1,5 50
End-of-term exam 16 04/06/2019 1,5 50
 
Student Work Load and its Distribution
Type of workDuration (hours pw)

No of weeks / Number of activity

Hours in total per term
Yüz yüze eğitim 4 14 56
Sınıf dışı çalışma 5 14 70
Laboratuar çalışması 0 0 0
Arasınav için hazırlık 10 1 10
Arasınav 2 1 2
Uygulama 0 0 0
Klinik Uygulama 0 0 0
Ödev 5 4 20
Proje 0 0 0
Kısa sınav 0 0 0
Dönem sonu sınavı için hazırlık 10 1 10
Dönem sonu sınavı 2 1 2
Diğer 1 0 0 0
Diğer 2 0 0 0
Total work load170