Theory of Probability and Statistics (MAE531)

General

School	School of Science
Academic Unit	Department of Mathematics
Level of Studies	Undergraduate
Course Code	ΜΑΕ531
Semester	5
Course Title	Theory of Probability and Statistics
Independent Teaching Activities	Lectures (Weekly Teaching Hours: 3, Credits: 6)
Course Type	Special Background
Prerequisite Courses	-
Language of Instruction and Examinations	Greek
Is the Course Offered to Erasmus Students	Yes (in English, reading Course)
Course Website (URL)

Learning Outcomes

Learning outcomes	Description of the level of learning outcomes for each qualifications cycle, according to the Qualifications Framework of the European Higher Education Area Descriptors for Levels 6, 7 & 8 of the European Qualifications Framework for Lifelong Learning and Appendix B Guidelines for writing Learning Outcomes Extension and generalization of concepts taught in MAF331 and MAF43# Creation of a suitable base for deepening the scope of Statistical Science. At the end of the course the student should be able to: Model procedures and situations that occur in everyday reality or in other scientific areas in the Theory of Probability. Understand the basic limit theorems of Probability Theory (laws of large numbers, central limit theorem) and use them for approximating probability calculations. Find the distribution of a function of random variables. Make basic calculations of probability, averages, dispersions, etc., in problems involving randomness with more than one random variable.
General Competences	Working independently Decision-making Production of free, creative and inductive thinking Criticism and self-criticism

Syllabus

Random vectors-Multivariate distribution function-Joint probability- Joint probability density function. Marginal distributions. Conditional distributions. Special bivariate and multivariate distributions (multinomial, bivariate and multivariate normal etc). Expectation, Variance-Covariance matrix. Moments and Moment generating function of random vector. Distribution of a function of random variables. Order Statistics. Convergence of random variables. Sampling distributions.

Teaching and Learning Methods - Evaluation

Delivery

Classroom (face-to-face)

Use of Information and Communications Technology

-

Teaching Methods

Activity	Semester Workload
Lectures	39
Working independently	78
Exercises-Homeworks	33
Course total	150

Student Performance Evaluation

Final written exam in Greek (in case of Erasmus students in English).

Attached Bibliography

Texts in English

Mood, A. M., Graybill, F. A. and Boes, D. C. (1974). Introduction to the Theory of Statistics. 3d ed. ISBN-13 978007085465# McGraw-Hill. New York.

Texts in Greek

Παπαϊωάννου, T. (1997). Θεωρία Πιθανοτήτων και Στατιστικής. ISBN 960-351-130- # Εκδόσεις Σταμούλη ΑΕ.
Κούτρας Μάρκος Β.(2012). Εισαγωγή στη Θεωρία Πιθανοτήτων και Εφαρμογές. ISBN 978-960-351-903-# Εκδόσεις Σταμούλη ΑΕ.