- Docente: Roberta Nibbi
- Credits: 6
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: First cycle degree programme (L) in Engineering Management (cod. 0925)
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from Sep 16, 2024 to Dec 16, 2024
Learning outcomes
A sound theoretical basis as well as a working knowledge of the fundamental mathematical methods aimed at coping with uncertainty in physical and other phenomena.
Course contents
Foundations of probability theory. Events and sets.
Kolmogorov's axioms. Joint probability, conditional probability,
independence.
Total probability theorem and Bayes' theorem.
Random variables. Discrete and continuous random
variables. Cumulative distribution function. Continuous random
variables with probability density. Characteristic numerical values
of random variables: expected value (mean), variance, standard
deviation, mean square error, moments. Pairs and vectors of random
variables: joint and marginal cumulative distribution functions,
joint and marginal probability densities. Laws of conditional
distribution, independence. Characteristic numerical values: mean
values, covariance matrix, moments. Correlated and uncorrelated
random variables.
Models of random variables. Bernoulli scheme. Binomial, Poisson,
uniform, normal, exponential random variables. Relationships among
some of these kinds of random variables.
Functions of random variables. Characteristic numerical
values: representation of the expected value and of the variance,
with applications to some notablecases (sum and product of two
random variables, linear combination of a finite number of random
variables, case of independent, identically distributed random
variables, etc.). Notions on the determination of the probability
distribution for a function of one or more random variables.
Limit theorems in probability. Sequences of random
variables and notions of convergence. Markov inequality, Chebyshev
inequality. Laws of large numbers. Central limit theorem.
Introduction to statistics. Sample mean, median and mode,
sample variance and standard deviation, percentiles. Bivariate data
sets and sample correlation coefficient. Statistical inference.
Sampling. Estimators and confidence intervals, efficiency of point
estimators. Hypothesis testing. Linear regression.
Readings/Bibliography
H. Hsu, Probabilità, variabili casuali e processi stocastici, ed.
McGraw-Hill Italia.
P. Erto, Probabilità e statistica per le scienze e l'ingegneria
2/ed, ed. McGraw-Hill Italia.
A. M. Mood, F. A. Graybill, D. C. Boes, Introduzione alla
statistica, ed. McGraw-Hill Italia.
Teaching methods
Standard lectures held by the teacher alternating with exercise classes.
Assessment methods
A comprehensive written exam, containing also theoretical
questions, should be passed after the end of the course
An additional oral exam is available on the student's
request after passing the written part.
Teaching tools
Blackboard, slides and projector.
Office hours
See the website of Roberta Nibbi
SDGs




This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.