Learning objectives
This course presents the basics of probability theory and teaches some standard statistical inference techniques that are commonly applied in management and production.
Course unit content
Elementary combinatorics.<br />
Probability spaces, conditioning, independence, total probabilities and Bayes formulae.<br />
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.<br />
Common types of random variables (Bernoulli, binomial, Poisson, hypergeometric, uniform, exponential, Gaussian, chi-square, gamma and t).<br />
Convergence in probability, law of large numbers, central limit theorem, continuity correction.<br />
Populations, samples, descriptive statistics, estimators (bias and consistency), sample mean and sample variance.<br />
Parametric confidence intervals (gaussian, Bernoulli and exponential populations).<br />
Nonbayesian parametric tests, bi- and unilateral (same populations as above), tests for comparing two gaussian populations.
Bibliography
S. Ross - Probabilità e statistica per l'ingegneria e le scienze - Apogeo 2003.<br />
(the english version is ok too)
Teaching methods
The written exam is on problems, not theory. After that one can ask for an optional oral examination.