Probability Theory I

Course Information
TitleΘΕΩΡΙΑ ΠΙΘΑΝΟΤΗΤΩΝ Ι / Probability Theory I
Code0502
FacultySciences
SchoolMathematics
Cycle / Level1st / Undergraduate
Teaching PeriodWinter
CommonNo
StatusActive
Course ID40000520

Programme of Study: UPS of School of Mathematics (2014-today)

Registered students: 301
OrientationAttendance TypeSemesterYearECTS
CoreCompulsory Course327

Class Information
Academic Year2015 – 2016
Class PeriodWinter
Faculty Instructors
Weekly Hours4
Class ID
600004697
Type of the Course
  • Background
Course Category
General Foundation
Mode of Delivery
  • Face to face
Digital Course Content
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
  • Greek (Instruction, Examination)
  • English (Examination)
Prerequisites
General Prerequisites
Basic knowledge of Mathematical Analysis
Learning Outcomes
Acquaintance with the Probabilistic-Stochastic Thought. Historical development of the notion of probability. Growth of skilfulness of using the combinational analysis methods and calculations and use of Combinational Analysis in the resolution of problems of probabilities. Transformation of a problem in terms of probabilities, definition of facts, calculation of simple and conditioned probabilities, application of known theorems (total probability, Bayes rule, Poincare theorem, product law). Comprehension of the notion of distribution function (d.f.) and the one of density of probability (p.d.f.) (for continuous distributions) and of probability function (p.f.) (for discrete distributions). Finding the d.f. and p.d.f. or p.f of a random variable that is defined as a function of given random variables. Finding parameters (mean value, variance and moments) of a given random variable. Calculation and use of the probability- or moment- generating functions. Introduction to the study of discrete bivariate distributions. Comprehension of the generation of the basic uni-variate discrete distributions: uniform, Bernoulli, binomial, Poisson, geometric, hypergeometric, and continuous distributions: uniform, exponential, normal, gamma, betta and trinomial bivariate distribution.
General Competences
  • Apply knowledge in practice
Course Content (Syllabus)
Historical problems. Randomnes, the sample distribution space, events, Venn diagrams. Classical definition of mathematical probability, statistical regularity, axiomatic foundation of probability - Finite sample distribution spaces, combinatorics, geometric probabilities - Conditional probability, independence - Univariate random variables, distribution functions, function of a random variable, moments, moment-generating function, probability generating function, discrete bivariate distributions - Useful univariate distributions: Discrete (Bernouli, Binomial, Hypergeometric, Geometric, Negative Binomial, Poisson), Continuous (Uniform, Normal, Exponential, Gamma) - Applications.
Keywords
probability, random variables, distribution functions, moment-generating andprobability generating functions
Educational Material Types
  • Notes
  • Slide presentations
  • Book
Use of Information and Communication Technologies
Use of ICT
  • Use of ICT in Course Teaching
  • Use of ICT in Communication with Students
Description
PowerPoint presentation of the theory
Course Organization
ActivitiesWorkloadECTSIndividualTeamworkErasmus
Lectures391.3
Tutorial130.4
Total521.7
Student Assessment
Student Assessment methods
  • Written Exam with Extended Answer Questions (Summative)
  • Written Exam with Problem Solving (Summative)
Bibliography
Course Bibliography (Eudoxus)
Βιβλίο [11058]: Θεωρία πιθανοτήτων I, Κουνιάς Στρατής, Μωϋσιάδης Πολυχρόνης Θ. Βιβλίο [45497]: Θεωρία Πιθανοτήτων και Εφαρμογές, Χαραλαμπίδης Χαράλαμπος Α.
Additional bibliography for study
1. Billingsley, P.Q. (1986): Probability and measure. Second edition, John Wiley and sons, Inc. New York. 2. Cameron, P.J. (1994): Combinatorics: Topics, Techniques, Algorithms. Cambridge University Press. 3. Feller, W. (Vol I 3rd ed. 1968, Vol II 1966). An Introduction to Probability. Theory and its applications, John Wiley and sons, Inc. New York. 4. Gnedenko, B.V. (1962). The theory of Probability, Chelsea Publishing company, New York. 5. Hall, M. (1986): Combinatorial Theory. 2nd ed. John Wiley and sons, Inc. New York. 6. Hodges, J.L. and Lehmann, E.L.(1965): Elements of finite probability. Holdenday, San Francisco. 7. Κάκκουλου, Θ. (1971): Ασκήσεις Θεωρίας Πιθανοτήτων, Αθήνα. 8. Liu, C.L. (1999): Στοιχεία Διακριτών Μαθηματικών (απόδοση στα Ελληνικά Κ. Μπους και Δ. Γραμμένος) Παν. Εκδ. Κρήτης. 9. Moran, P.A.P.. (1968): An introduction to Probability Theory, Clarendon, Press Oxford. 10. Μωυσιάδη Πολ.(2001): Εφαρμοσμένη Συνδυαστική. Η τέχνη να μετράμε χωρίς μέτρημα, Εκδ. ΖΗΤΗ, Θεσσαλονίκη. 11. Parzen E. (1960). Modern Probability and Its Applications 12. Renyi, A. (1970): Probability Theory, North Holland Co., Amsterdam. 13. Scheaffer, R.L. and Young, L.J. (3rd ed. 2009): Introduction to Probability and Its Applications. Cengage Learning. Ιστορία των Πιθανοτήτων 1. Κουνιά, Στρ. : Ιστορική Αναδρομή στις Πιθανότητες, περιοδικό Μαθηματική Επιθεώρηση, 10, 1978, σελ. 3-27. 2. Παπασταυρίδη, Σ. : Πιθανότητα: Ιστορία, Θεωρία και Πράξη, περιοδικό Ευκλείδης γ΄, 10, 1985-86, σελ. 9- 19. 3. Χαραλαμπίδη, Χ. : Ανασκόπηση της Διαχρονικής Εξέλιξης του Λογισμού Πιθανοτήτων, Πρακτικά 19ου Πανελλήνιου Συνεδρίου Μαθηματικής Παιδείας, Ελληνική Μαθηματική Εταιρεία, 2002, σελ. 35-61. 4. Everitt, B.S.: Οι Κανόνες της Τύχης. Πιθανότητες, Κίνδυνοι και Στατιστική, εκδόσεις Κάτοπτρο, 2001. 5. Hacking, I.: The Emergence of Probability. A philosophical study of early ideas about probability, induction and statistical inference, Cambridge University Press, 1975. 6. Krüger, L., Daston, L. and Heidelberger, M.(eds.): The Probabilistic Revolution. Vol. 1: Ideas in History, The MIT Press, 1987.
Last Update
10-10-2013