Unit PROBABILITY AND STATISTICS I
- Course
- Mathematics
- Study-unit Code
- A001545
- Curriculum
- In all curricula
- Teacher
- Andrea Capotorti
- CFU
- 12
- Course Regulation
- Coorte 2021
- Offered
- 2022/23
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa integrata
PROBABILITY ANS STATISTICS - I MODULE
| Code | A001546 |
|---|---|
| CFU | 6 |
| Teacher | Andrea Capotorti |
| Teachers |
|
| Hours |
|
| Learning activities | Caratterizzante |
| Area | Formazione modellistico-applicativa |
| Academic discipline | MAT/06 |
| Type of study-unit | Obbligatorio (Required) |
| 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 | For Math student: 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 3 and 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 jointly with the other written part of module II. FOR ATTENDING STUDENTS: two partial tests are foreseen with the same overall verification methods relating to the practical test in R, but based only on the first or second part of the course, respectively. The average mark of the two parts will contribute to establishing the admission mark or not to the oral exam which must be taken by the last session of the first useful exam session. In the overall judgment, the practical part and the oral exam have equal importance. - For Computer Science students (borrowed course): Practical test R to verify the ability to face and solve practical problems of basic statistics and 3 theoretical questions (multiple choice test with full score only in case of correct answer, no penalty in case of wrong answer) aimed at verifying the mastery of the notions studied. The practical test in R consists of 5 or 6 points to be developed on the basis of simulated data or directly provided. It must be carried out within an hour and a half and the various points have indicated the maximum achievable score (normally variable between 3 and 10 depending on the complexity of the analysis required). The theoretical questions provided through multiple choice tests have the value of 2 points each. 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 in R, 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. - 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. |
PROBABILITY AND STATISTICS - II MODULE
| Code | A001547 |
|---|---|
| CFU | 6 |
| Teacher | Alessandra Cretarola |
| Teachers |
|
| Hours |
|
| Learning activities | Affine/integrativa |
| Area | Attività formative affini o integrative |
| Academic discipline | SECS-S/06 |
| Type of study-unit | Obbligatorio (Required) |
| Language of instruction | Italian. |
| Contents | Introduction to probability theory and its applications. |
| Reference texts | P. Baldi, Calcolo delle Probabilità, McGraw-Hill, second edition, 2011. Suggestion for further exercises: F. Biagini, M. Campanino: Elementi di Probabilità e Statistica, Springer, 2006. Alternatively: S. Antonelli, G. Regoli: Probabilità discreta; esercizi con richiami di teoria, Liguori Ed., 2005. Further teaching material, such as updated notes from the lecturer and solving of the proposed exercises and past exam papers, is available on Unistudium. |
| Educational objectives | This course is the first approach to Probability and is aimed at giving the students a good understanding of the basic elements of Probability Theory through rigorous definitions, theorems and proofs. The main aim of this teaching is to make students able to reason in a probabilistic framework and use probabilistic models for solving problems involving uncertainty. The student will be able to describe, link and compare the main statements and results given and to show the theorems considered. She/he will solve problems relating the theoretical expertise with the selection and building of models following the guidelines given in the practice lessons. |
| Prerequisites | Basic calculus notions, basic notion of Algebra and combinatorics. To fully understand the subjects, the contents provided in the courses Analisi Matematica I & II are recommended. |
| Teaching methods | The course is organized as follows: - lectures on all the topics of the program; - proposal and resolution of problems relating to all program arguments. |
| 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 | Examination is divided into a preliminary written and a consequently oral examination. - Written part, of about 2h mean duration, is organized into 2 parts, one on Probability (related to this course) and the other one on Statistics (related to I Module). The part of the written exam devoted to Probability is composed of 2 exercises and is apt to verify problem solving skill and is about all the subjects. - The oral examination can be done by students who will pass the written part with a mark of at least 18/30 or those who have passed intermediate similar tests ("esoneri") during the term. It is of 30 min in the average, it is related to all the Probability and Statistics program, and is apt to verify the presentation skill and the learning level. On request, the exam can be done in English. |
| Extended program | Theoretical aspects about: events, conditional probability, independence. The Bayes theorem. Random variables, probability distributions, density and distribution functions, discrete and continuous random variables and their properties. Expected value, variance, moments. Jointly distributed random variables: joint and marginal distributions, conditional distributions. Relations among random variables; transformations of random variables; joint probability distribution of functions of random variables. |