Unit PROBABILITY AND MATHEMATICAL STATISTICS
- Course
- Informatics
- Study-unit Code
- 55007206
- Curriculum
- In all curricula
- Teacher
- Alessio Troiani
- Teachers
-
- Alessio Troiani
- Hours
- 42 ore - Alessio Troiani
- CFU
- 6
- Course Regulation
- Coorte 2023
- Offered
- 2024/25
- 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
- Written test consisting of two parts: a practical part aimed at verifying the ability to face and solve practical problems of basic statistics and a theoretical part (multiple choice and/or short answer test with full score only in case of correct answer, possible penalty in case of wrong answer) aimed at verifying the mastery of the notions studied.
Theoretical questions may concernt topics in probability or statistics and may require the solution of exercises.
The practical part (to be done with R if technically possible) consists of a set of questions (generally between 3 and 6) to be developed on the basis of simulated data or directly provided.
FOR ATTENDING STUDENTS: there are two partial tests with the same overall assessment methods but on topics only on the first or second part of the course, respectively.
The average of the two tests will constitute the final grade.
For carrying out the practical test, the reference material is mainly the one within the first recommended text (statistics laboratory in R) and the material present in Unistudium.
For theoretical questions, reference is made to what is contained in the remaining recommended texts.
There may be an oral exam in case of problems during the written test.
On request the exam can be done in English.
For students with Specific Learning Disorders and/or Disabilities please refer to the we page: http://www.unipg.it/disabilita-e-dsa - 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.