
Course unit
INTRODUCTION TO PROBABILITY (Ult. numero di matricola pari)
SCP4063485, A.A. 2016/17
Information concerning the students who enrolled in A.Y. 2016/17
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Basic courses 
MAT/06 
Probability and Mathematical Statistics 
9.0 
Course unit organization
Period 
Second semester 
Year 
1st Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Practice 
2.0 
26 
24.0 
No turn 
Lecture 
7.0 
56 
119.0 
No turn 
Examination board
Examination board not defined
Prerequisites:

Basic calculus for functions of one real variable. 
Target skills and knowledge:

The course is concerned with the fundamental notions of Probability, whose aim is the modeling of random phenomena. The emphasis is on basic general concept; the aim is to develop the capability of applying these concept to concrete and relevant examples. 
Examination methods:

Written exam. The teacher could require, in special cases, to complete the exam with an oral part. 
Assessment criteria:

The exercises have the aim of verifying the full understanding of basic notion of probability, as well as the capability of applying them to concrete examples. Clarity and coherence of the solutions will also determine the final evaluation. 
Course unit contents:

Random experiments, sample space, probability.
Sample space with finitely many elements, combinatorics.
Conditional probability and independence.
Discrete random variables, discrete density and distribution.
Multivariate discrete random variables, joint and marginal densities. Independence of discrete random variables.
Expectation for discrete random variables. Variance, covariance, moments.
Basic discrete distributions: Binomial, Hypergeometric, Geometric, Negative Binomial, Poisson.
Conditional density and conditional expectation for discrete random variables.
Absolutely continuous random variables and their expectation.
Basin continuous distributions: Uniform, Gamma Normal.
Multivariate continuous random variables, joint densities, independence.
Conditional density and conditional expectation for absolutely continuous random variables.
Law of large numbers and central limit theorem. Normal approximation. 
Planned learning activities and teaching methods:

The presentation of theoretical notions is complemented by examples and exercises. 
Textbooks (and optional supplementary readings) 

Sheldon M. Ross, Calcolo delle probabilità. : Apogeo, 2013.


