## PROBABILITIES

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.

### Objectives

Introduction to the concepts of discrete probability and combinations

Non required

### Syllabus

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.

COURSE DETAILS
 Level: Type: Undergraduate (A-) Instructors: MARKOS AVLONITIS Department: DEPARTMENT OF INFORMATICS Institution: Ionian University Subject: Mathematics Rights: CC - Attribution-NonCommercial-NoDerivatives