Learning outcomes of the course unit
This course presents the basics of probability theory and teaches some standard statistical inference techniques that are commonly applied in management and production.
Course contents summary
Probability spaces, conditioning, independence, total probabilities and Bayes formulae.
Continuous and discrete random variables, distribution functions (cumulative, density, mass), joint distributions, transformations. Expected vaalue, variance, generating function. Sum of i.i.d. random variables.
Common types of random variables (Bernoulli, binomial, Poisson, hypergeometric, uniform, exponential, gaussian, chi-square, gamma, t and F).
Convergence in probability, law of large numbers, central limit theorem, continuity correction.
Populations anc samples, descriptive statistics, estimators (bias and consistency), sample mean and sample variance.
Parametric confidence intervals (gaussian, Bernoulli and exponential populations).
Nonbayesian parametric tests, bi- and unilateral (same populations as above), tests for comparing two populations parameters (gaussian, Bernoulli and Poisson).
S. Ross - Probabilità e statistica per l'ingegneria e le scienze - Apogeo 2003.
Written test (on exercises only) that can be substituted with two partial tests along the term for those who are attending the course. One can ask for an optional oral examination (on the theory only).
Resolution of problems and excercises.