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
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Course page updates
This course page is available (with possible updates) also for the following academic years:
Course information last updated on: 19 giugno 2019, 15:33