Environmental Engineering

MIRKO D'OVIDIO

The aim is that of providing students with some fundamental probabilistic and
statistical notions, which are the basis of the logical-mathematical reasoning under
uncertainty, with incomplete information. This will stimulate those critical skills
which allow to face, besides "routine" problems, new problems too. In particular,
students should acquire some basic notions which concern conditional and
unconditional probabilities, discrete and continuous probability distributions,
and statistical inference. Basic notions and theoretical results on conditional and unconditional probabilities, prevision, variance, correlation coefficient, probability density, cumulative distribution function, joint, marginal and conditional distributions, characteristic function, basic notions on statistical inference. Students will improve their ability in the bibliographic research, in data analysis and the application of theoretical results with regards to engineering approach

Students will be able to deal with random variables and elementary random models (discrete and continuos case). Moreover, they will be able to solve parametric estimation problems.

mathematical analysis, geometry

Descriptive statistics. Events. Operations on events. Probability and measures. Probability of events. Random variables. Probability distributions. Expected value and moments. Conditional events and conditional probability. Stochastic independence. Bayes theorem. Cumulative distribution function and density function. Random vectors and marginal distributions. Transformations of random variables. Sum of random variables. Convergences and limit theorems. Statistical inference: estimators and their properties, estimation and discussion. Statistical hypothesis testing.

1) Appunti di Probabilità e Statistica. Mirko D'Ovidio.
2) Calcolo delle Probabilità. Paolo Baldi. McGraw-Hill.

in presence

strongly recommended

Oral and written exams aimed at verifying the achievement of the course objectives. In particular, the evaluation takes into account acquired skills (written exam, 50%) the acquired theoretical knowledge and the ability to process and communicate (oral exam, 50%).

Please, consult the web page https://www.sbai.uniroma1.it/~mirko.dovidio/PGS/lectures

Evaluate the probability of some events (example: number of success in n independent trials). Evaluate the density of a given transformation.