PROBABILITY - NOTIONS
Stampa
Enrollment year
2015/2016
Academic year
2016/2017
Regulations
DM270
Academic discipline
Department
DEPARTMENT OF MATHEMATICS "FELICE CASORATI"
Course
MATHEMATICS
Curriculum
PERCORSO COMUNE
Year of study
Period
1st semester (03/10/2016 - 13/01/2017)
ECTS
9
Lesson hours
84 lesson hours
Language
ITALIAN
Activity type
ORAL TEST
Teacher
BASSETTI FEDERICO (titolare) - 6 ECTS
DOLERA EMANUELE - 3 ECTS
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
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
Notes by E. Regazzini, available at http://www-dimat.unipv.it/~bassetti/
See also
Robert Ash (2008) Basic Pobability Theory, Dover
Assessment methods
Written examination followed by an oral examination.
Further information
Written examination followed by an oral examination.
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