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 value, variance, median, mode. Min, max and sum of independent random variables.
Common types of random variables (Bernoulli, binomial, Poisson, hypergeometric, uniform, exponential, Gaussian, chi-square, gamma and t).
Convergence in probability, law of large numbers, central limit theorem, continuity correction.
Populations, 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 gaussian populations.
S. Ross - Probabilità e statistica per l'ingegneria e le scienze - Apogeo 2003.
(the english version is ok too)
The written exam is on problems, not theory. After that one can ask for an optional oral examination.