Unit PROBABILITY AND MATHEMATICAL STATISTICS
- Course
- Informatics
- Study-unit Code
- 55007206
- Curriculum
- In all curricula
- Teacher
- Andrea Capotorti
- Teachers
-
- Andrea Capotorti
- Hours
- 47 ore - Andrea Capotorti
- CFU
- 6
- Course Regulation
- Coorte 2020
- Offered
- 2021/22
- Learning activities
- Base
- Area
- Formazione matematico-fisica
- Academic discipline
- MAT/06
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- Italian
- Contents
- Basic notions of descriptive statistic; linear regression, parametric estimation, confidence intervals, hypothesis testing.
Coherence principle. - Reference texts
- Main references:
Iacus S.M., Masarotto G.: Laboratorio di statistica con R. McGraw-Hill.
Erto P.: Probabilita' e Statistica per le scienze e l'ingegneria, Mc-Graw-Hill, ed. 2004
R. Scozzafava: Incertezza e Probabilità (Zanichelli).
Alternatively:
S. Ross, Introduction to probability and Statistics for Engineers and
Scientists, Academic Press, 2009. - Educational objectives
- Knowledge and ability on basic probability, descriptive and inferential statistical notions.Students will be able to face and solve practical and theoretical problems about descriptive statistic, linear regression and hypothesis tests. They will be also able to consciously express the learned notions.
- Prerequisites
- Basic calculus notions, basic notion of Algebra and combinatorics. Basic computer abilty. To fully understand the subjects are recomended the know what is teached in the courses "Analisi Matematica I & II", "Informatica I"
- Teaching methods
- Theoretical lessons on all the subjects and practical exercises developed also with the specific statistical software R
- Other information
- For students with Specific Learning Disorders and/or Disabilities please refer to the we page: http://www.unipg.it/disabilita-e-dsa
- Learning verification modality
- Practical exercises in R apt to check ability in solving practical basic statistical problems and oral examination apt to verify the consciuosness and ability in manipulation of the studied notions.
Exercises in R will be 5 or 6 based on real or simulated data. Each exercise will have a maximum degree (usually between 3 and 10, depending on the complexity required).
To pass to the oral test, a degree of at least 18/30 must be taken in pratical part in R.
On request, the exam can be done in English. - Extended program
- Descriptive statistics: statistical unitary, frequencies or in classes distributions; graphical representations; mean values: mode, median, arithmetic mean, means “a la Chisini”; means properties; variability indices; quantiles, Boxplots; double empirical distribution: joint, marginal, conditional frequencies, chi-squared dependence index.Liner regression: min-squared estimates; previsions; R2 index.
Principal probability distributions: binomial, geometric, Poisson, uniform, exponential, normal. Distributions of sample statistics: chi-squared and t-student.
Parametric estimation: main estimators and their properties.Interval estimation: general method; specific cases for the mean and variance of normal populations.Hypothesis testing: generic parametric tests and particular cases with normal populations; non parametric tests: binomial, adaptation an independence tests.