Course Details
Name:
Calcolo Delle Probabilità / Probability
Basic information
Credits:
Laurea in Ingegneria dell'Informazione: 6 Ects (a)
Degree(s):
Compulsory 1^{st} year Laurea in Ingegneria dell'Informazione curriculum Automatica
Language:
Italian
Course Objectives
Students should develop a certain familiarity with the basic probabilistic tools and should become able to
- model simple real problems and to propose a solution
- solve theoretical problems in secrete and continuous basic probability, using the appropriate mathematical tools.
- understand the main probabilistic structures to be able to employ them even in more complex situations;
- read a basic probability textbook;
- gain access to a more advanced probability course
Course Content
- Probability spaces: combinatorics, axiomatic approach, uniform probability spaces,
conditional probability and independence
- Discrete random variables
Distributions: Bernoulli, binomial, Poisson, Hypergeometric, geometric,
Joint distributions and independence
Transforms of random variables, distributions of max, min, sums of random variables.
Expectation, expectation of a function of a r.v., moments, variance and covariance,
correlation, lineare regression
Examples and applications
- Continuous r.v.'s
Distribution functions: definitions and properties.
Main distributions : uniform, exponential, Gaussian, Gamma, Beta.
Distributions of transform, of max and min .
Expectation, moments, variance and covariance.
Joint distributions, sums of independent r.v.'s, conditional distributions.
Conditional expectation and conditional variance
Moment generating functions or characteristic functions
Multivariate Gaussian laws.
- Convergence of r.v.'s and approximation.
The law of large numbers, the central limit theorem, normal approximation.
- If enough time
An introduction to Markov chains: recurrence and transience, invariant probabilities,
ergodic theorem.
Learning Outcomes (Dublin Descriptors)
On successful completion of this course, the student should
- Students should develop a certain familiarity with the basic probabilistic tools
- model simple real problems and to propose a solution
- solve theoretical problems in secrete and continuous basic probability,
using the appropriate mathematical tools.
- understand the main probabilistic structures to be able to employ them even in more complex
situations;
- being able to report the main points of the theory of probability and its theorems
- read a basic probability textbook;
gain access to a more advanced probability course
Prerequisites and Learning Activities
Fundamentals of Calculus are strongly recommended
Teaching Methods
Language: Italian
Lectures and recitation classes
Assessment Methods and Criteria
Written and possibly oral exams.
Textbooks
- D. Ross, Calcolo delle probabilità. Apogeo. testo consigliato
- P. Baldi, Calcolo delle probabilità. McGraw-Hill.
- Schaum's outline series : Probabilità. testo consigliato
Online Teaching Resources
Recent teaching material
This list contains only the latest published resources. Resources marked with an asterisk belong to other courses (indicated between brackets)
Course page updates
This course page is available (with possible updates) also for the following academic years:
Course information last updated on: 22 settembre 2015, 18:46