Theory of Probability

The probability concept. Classical and empirical definition of probability. Conditional probability and independence. Bayes law. Combinatorial analysis. The concept of random variables. One-dimensional distributions. Functions of random variables. Mean value, variance, correlation functions , correlation coefficient. Multi-dimensional distributions. Central limit theorem. Moment generating functions. Random walks. Stochastic processes. Master Equation, Langevin Equation, Fokker-Planck Equation, Markov Chains.

Code	Semester	Type	Hours	Labs	ECTS
ΜΘ130	2	Compulsory	4	2Ε	6

E-class

bibliography:

• “ΕΙΣΑΓΩΓΗ ΣΤΗ ΘΕΩΡΙΑ ΠΙΘΑΝΟΤΗΤΩΝ”, HOEL P., PORT S., STONE C., Εκδόσεις ΙΤΕ-ΠΑΝΕΠΙΣΤΗΜΙΑΚΕΣ ΕΚΔΟΣΕΙΣ ΚΡΗΤΗΣ, ISBN 978-960-524-156-8, 2009”
• “Πιθανότητες, τυχαίες μεταβλητές και στοχαστικές διαδικασίες”, Papoulis Athanasios, Pillai S. Unnikrishna, Εκδόσεις ΤΖΙΟΛΑ, ISBN 978-960-418-127-8, 2007”