Enrollment year
2014/2015
Department
DEPARTMENT OF MATHEMATICS "FELICE CASORATI"
Curriculum
PERCORSO COMUNE
Period
1st semester (01/10/2015 - 15/01/2016)
Lesson hours
84 lesson hours
Prerequisites
Mathematical analysis and linear algebra of the first year of the course in mathematics
Learning outcomes
The purpose of the course is to tell the beginning student of mathematics the basic facts of the theory of probability
Course contents
It should be noticed that no theory of measure is requested
Extended summary
1.- Definition of probability.
2.- Probability distribution of a random number
3.- Conditional probabilities and stochastic independence
4.- Distribution of a random vector and conditional distributions in some special cases
5.- Numerical characteristics of a probability distribution: expectation, variance, moments, regression, covariance, correlation
6.- Integral transformations: characteristic function, moment generating function and their application to the calculus of distinguished probability distributions, which are of interest for statistics
7.- Some remarkable inequalities and hints of limit theorems in probability theory: elementary examples of weak laws of large numbers and Lindeberg- Lévy version of the central limit theorem
Teaching methods
Lectures and exercises sessions
Reccomended or required readings
Written examination followed by an oral examination
Assessment methods
Notes by E. Regazzini, available at http://www-dimat.unipv.it/~bassetti/
See also
Robert Ash (2008) Basic Pobability Theory, Dover
THEORY
Further information
Notes by E. Regazzini, available at http://www-dimat.unipv.it/~bassetti/
See also
Robert Ash (2008) Basic Pobability Theory, Dover
THEORY
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