Learning objectives
Understanding and capability to communicate the foundation of probability theory. Capability to solve exercises on probability theory, to use the specific functions, to recognize and employ the random variable models studied during the course.
Course unit content
Introduction to descriptive statistics and inferential statistics. Elements of probability theory. Discrete and continuous random variables. Central limit theorem. Parameter estimation. Confidence intervals.
Full programme
Data organization e description, mean, median, mode, histograms, variance and standard deviation.
Normal model and correlation.
Sample space and events, probability axioms, binomial coefficient, conditional probability, Bayes' formula, independent events.
(approx. 6 hours)
Continuous and discrete random variables, probability density and cumulative functions, joint, conditional and marginal distributions, expected value, covariance, moment generating function. Random variables functions and transformations.
Random variable models: Bernoulli, Poisson, hypergeometric, binomial, uniform, normal, exponential, gamma, chi-square, t, F.
(approx. 24 hours)
Sample mean, central limit theorem, sample variance.
Maximum likelihood estimators, confidence intervals, bayesian estimators.
(approx. 18 hours)
Bibliography
Sheldon M. Ross
Introduction to probability and statistics for engineers and scientists
Elsevier, fifth edition, 2014.
A. Bononi, G. Ferrari
"Introduzione a Teoria della probabilità e aleatorie con applicazioni all'ingegneria e alle scienze"
Soc. Esculapio, Bologna, aprile 2008.
Teaching methods
Classroom lectures and exercises.
Homework exercises in autonomy.
Software use (Matlab) for problem resolution.
Assessment methods and criteria
Written exam with possible supplementary oral.
Other information
Classes will be held according to University instructions as regards the pandemic situation.
