Probability Theory I
| Title | ΘΕΩΡΙΑ ΠΙΘΑΝΟΤΗΤΩΝ Ι / Probability Theory I |
| Code | 0502Α |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 1st / Undergraduate |
| Teaching Period | Winter |
| Common | No |
| Status | Active |
| Course ID | 600019632 |
Programme of Study: UPS of School of Mathematics (2014-today)
Registered students: 676
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| Core | Compulsory Course | 3 | 2 | 6 |
| Academic Year | 2020 – 2021 |
| Class Period | Winter |
| Faculty Instructors |
|
| Instructors from Other Categories |
|
| Weekly Hours | 4 |
| Class ID | 600166637
|
| Section | Instructors |
|---|---|
| 1. ΤΜΗΜΑ Α | Ioannis Antoniou |
| 2. ΤΜΗΜΑ Β | Ioannis Antoniou |
Course Type 2016-2020
- Background
- Scientific Area
Course Type 2011-2015
General Foundation
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600166637
- eLearning (Moodle): https://elearning.auth.gr/course/view.php?id=11496
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
- Greek (Instruction, Examination)
- English (Examination)
Prerequisites
Required Courses
- 0201 Calculus I
- 0202 Calculus II
General Prerequisites
Basic knowledge of Mathematical Analysis
Learning Outcomes
1. Acquaintance with the Probabilistic-Stochastic Thought.
2. know how to use the combinational analysis methods in solving problems of probabilities.
3. use conditional probabilities, total probability, Bayes rule, Poincare theorem, product law and apply them to probability problems.
4. know the notion of distribution function, probability function and probability density function, how to calculate them for discrete and continuous random variables and how to manipulate functions of random variables,
5. can calculate parameters of distributions (mean, variance and other moments), calculate and manipulate probability generator function and moment generator function,
6. know and use basic univariate 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
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 52 | 1.7 | ✓ | ||
| Reading Assigment | 155 | 5.2 | |||
| Exams | 3 | 0.1 | |||
| Total | 210 | 7 |
Student Assessment
Student Assessment methods
- Written Exam with Extended Answer Questions (Formative, Summative)
- Written Exam with Problem Solving (Formative, 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
22-07-2020
