Probability Models

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Probability Models
Course ID: 
Course Description: 

Revision on Probability Theory, Basic properties, Conditional probabilities, Law of Total Probability, Bayes Theorem, Independent Events, Continuous and Discrete random variables, Probabillity density function, Probaility distribution, Discrete probability distributions, Continuous probability distributions, Expectation, Variance, Poisson Processes, Transient analysis of Discrete Time Markov Chains, Asymptotic analysis of DTMC, Ergodicity, Hitting time, Transient analysis of Continuous Time Markov Chains, Asymptotic analysis, of CTMC, examples and real test cases.

__________________________________________________________________________________ The main aim of the course is to familiarize student with stochastic phenomena and stochastic processes of the real world that can be described and explained by the language of mathematics. The course is actually a high-leveled extension of Probability Theory and it can be adapted to the needs of a Financial Engineer in order to be a useful tool for examining complex financial and engineering problems. __________________________________________________________________________________

Assessment methods: 

Optional mid-term exam (+2 pt) and Final examination (exceptionally 2 mid-term exams for 2020-21).

Recommended Reading:

1. Εισαγωγή στις Στοχαστικές Ανελίξεις ,Ουρανία Χρυσαφίνου, Εκδ. ΣΟΦΙΑ, Αθήνα,2004

2. Πιθανότητες, Τυχαίες Μεταβλητές και Στοχαστικές Διαδικασίες, Papoulis,  Athanasios, Μετάφραση : Γαβριηλίδης, Λεωνίδας, Εκδ. ΤΖΙΟΛΑΣ, Θεσσαλονίκη,1994.

3. Introduction to Stochastic Processes, E. Cinlar, Prentice-Hall, Engenwood Cliffs, 1975

4. Probability and Statistics with Reliability, Queuing, and Computer Science Applications, K.S. Trivedi, Wiley-Interscience, 2002. 

5. Introduction to Probability Models, S.M. Ross, Academic Press, 2009.

6. Εισαγωγή στις πιθανότητες, Μπερτσέκας Π.Δ., Τσιτσικλής Ν.Γ, Τζιόλας, 2016