Teacher

prof. Ruggero BELLIO

Credits

6 CFU

Objectives

The course will provide the basic elements of probability theory and some introductory concepts of statistics. Some techniques useful for engineering will be provided.

Acquired skills

- Knowledge of  basic statistics
- Knowledge of basic probability
- Ability of solving probabilistic problems
- Knowledge of basic statistical modelling
-Ability of solving basic statistical problems

Contents

Descriptive statistics: Introduction; Summary statistics; Graphical summaries; Measures of association and correlation. (8 hours)
Basic probability: Fundamental elements; Conditional probability and independence; Reliability models. (12 hours)
Random variables: Random variables; Functions of random variables; Jointly distributed random variables. (18 hours)
Propagation of error: Measurement error; Linear combinations of measurements; Uncertainty for functions of measurements. (3 hours)
Commonly used probability distributions: Bernoulli; Binomial and related distributions; Poisson; Normal and lognormal; Exponential; Gamma and Weibull. (14 hours)
Sequences of random variables and limit theorems: Law of large numbers; Moment generating function and central limit theorem. (4 hours)
Sampling and introduction to statistical inference: Sampling methods; Statistics and their distribution; Model goodness of fit. (4 hours)
Point estimation: Point estimators; Parameter estimation for commonly used distributions. (7 hours)
Confidence intervals: Introduction; Confidence intervals for the mean and for the difference between two means. (7 hours)
Hypothesis testing: Statistical tests; Significance levels; Tests for means and two-sample tests; Other useful tests. (9 hours)
Linear regression: Analysis of correlation; Simple linear regression; Introduction to multiple linear regression. (4 hours)

References:

- W. Navidi: Probabilità e statistica per l'ingegneria e le scienze; McGraw-Hill (Milano) 2006 (Main text).
- S.M. Ross: Probabilità e statistica per l'ingegneria e le scienze (seconda edizione); Ed. Apogeo (Milano) 2008 (Supplementary text)

Additional material and information available at the course web page.