Probability Theory II

Description

The algebra of events - Probability Space - The axioms of Probability - Random variables - The notion of stochastic distribution - Multidimensional random variables - Multidimensional distribution functions - Marginal distributions - Denumerable multidimensional random variables - Continuous multidimensional distributions - Multidimensional normal distribution - Stochastic independence - Conditional Probability - Conditional density - Conditional distributions - Mean values for multidimensional random variables - Conditional mean values - Regression line - Mean square error - Random variable transforms - Compound distributions - Inequalities - Multiple Correlation coefficient - Ordered random variables - Characteristic functions - The sum of independent random variables - Characteristic functions of multidimensional random variables - Moment generating functions - Probability generating functions - Limit theory of random variables - Convergences - Relations between convergences - Central Limit Theorem - Laws of large numbers - The log log law.

Books: 
Θεωρία Πιθανοτήτων Ι των Σ. Κουνιά, Π. Μωυσιάδη.
Θεωρία Πιθανοτήτων και Εφαρμογές του Χ.Α. Χαραλαμπίδη.
Semester: 
Units: 
3
Credit Units (ECTS): 
5.5
Hours: 
3ώρες
ID: 
0505
Course Type: 
X