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 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 /

 IST1000 Introduction to Probability 4+0+0 ECTS:6 Year / Semester Spring Semester Level of Course First Cycle Status Compulsory Department DEPARTMENT of STATISTICS and COMPUTER SCIENCES Prerequisites and co-requisites None Mode of Delivery Face to face Contact Hours 14 weeks - 4 hours of lectures per week Lecturer Dr. Öğr. Üyesi Buğra Kaan TİRYAKİ Co-Lecturer None Language of instruction Turkish 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 Outcomes CTPO TOA Upon successful completion of the course, the students will be able to : LO - 1 : understand the basic concepts of probability theory 2,8 1, LO - 2 : construct a mathematical model of stochastic experiment 2,8 1, LO - 3 : have the ability to calculate probability of events 2,8 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), 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 Week Subject Related Notes / Files Week 1 Historical development and subject of the probability theory. Week 2 Sample space. Events and operations over events. Week 3 Frequency of event.Definition of the probability in discrete sample space. Classical definition and applications of probability. Week 4 Definitions and applcations of Algebra and Borel sigma algebra. Definition of the probability in continuous sample space. Week 5 Kolmogorov's axioms. Probability space. Properties of the probability measure. Week 6 Geometrical probability and its applications. Independence of events, multiplication formula and applications of events. Week 7 Conditional probability and its applcations. Formula of total probability formula. Bayes's formulas and their applications. Week 8 Mid-term exam Week 9 Sequance of independent trails. Bernoulli scheme. Week 10 Limit theorems in Bernoulli scheme (Mouavr-Laplace's local and integral formulas, Poisson's theorem). Week 11 Law of large numbers. Bernoulli and Poisson theorems. Week 12 Polynomial scheme. Week 13 Simple Markov chains. Week 14 Concept of random variable (assessbility in comparison to algebra) Operations over random variables. Week 15 Distribution of variables, distribution functions and its basic properties. Week 16 End-of-term exam
 Textbook / Material
 1 Akdeniz F. Olasılık ve İstatistik, Ankara Ü., Ankara, 1984, 2 Nasirova T., Khaniyev T. Yapar C., Ünver İ., Küçük Z. Olasılık. KTÜ Matbaası, Trabzon, 2009.