PROBABILITY AND STATISTICS FOR COMPUTER SCIENCE
- Overview
- Assessment methods
- Learning objectives
- Contents
- Bibliography
- Teaching methods
- Contacts/Info
The knowledge and skills necessary for fruitful learning of this teach-ing regarding algebra and infinitesimal calculus, and are taught in the first-year courses of "Algebra and Geometry" and "Mathematical Analysis".
The objective of the exam is to ascertain the acquisition of the knowledge and skills described in the first section, evaluating the level of knowledge, and above all the ability to put into practice the knowledge for solving problems in conditions of uncertainty.
The written test, lasting 2-3 hours, consists in the solution of exercises.
The oral test focuses on a discussion of the written test and the in-depth presentation of a topic to be agreed upon with the instructor.
The course allows students to acquire solid knowledge and skills on the main aspects of probability theory and mathematical statistics (descriptive and inferential).
At the end of the course, the students will be able to:
1. know and understand the language and the basic notions of probability theory and mathematical statistics,
2. know and know how to apply the fundamental principles of combinatorics to solve simple problems,
3. state and prove same of the main theorems of probability theory and mathematical statistics,
4. build models of random phenomena using the notable distributions,
5. analyze and briefly describe sets of data,
6. make estimates of parameters in models with random phenomena and conduct hypothesis tests,
7. use the notions learned to solve problems in conditions of uncertainty,
8. explain rigorously questions of probability and statistics, formalizing and correctly arguing intuitions in oral and written form.
The course also provides some basic elements that will be useful for continuing studies in computer science. The acquisition of the basic language of probability theory and statistics will make possible subsequent insights, self-organized by the student to address work-related needs.
The course consists of a total of 48 hours of lessons, which include both the presentation of theoretical concepts and exercises.
The contents are presented in the chronological order in which they are listed below.
Introduction to probability theory (learning objective 3): Deterministic, stochastic, "uncertain" variables. The notion of (statistical and systematic) error and its measure. Elements of probability. Frequentist definition of probability.
Combinatorics (training objective 2): Combinatorics. Distributions, combinations, permutations.
Conditional probability and independent events (training objective 3): Conditional probability, correlation and statistical independence. Bayes theorem.
Descriptive statistics (learning objective 5): Mean, median and mode. Variance and standard deviation. Weighted means. Estimators. Error propagation.
Discrete and continuous probability distributions (learning objective 4):
Bernoulli, Poisson, Gauss distributions. Moment-generating function.
Convergence theorems (educational objective 3): Central limit theorem.
Inferential statistics (learning objective 6): Parameter estimation and Maximum Likelihood optimal fit. Chi-squared.
All the topics covered contribute to the achievement of training objectives 1, 7 and 8.
- John Taylor, Introduzione all'analisi degli errori. Lo studio delle incer-tezze nelle misure fisiche, Zanichelli,
- Pasquale Erto, Probabilità e statistica per le scienze e l'ingegneria, McGraw-Hill
- E. Piazza, Probabilità e Statistica, Esculapio Editore
The course consists of lessons and exercise classes.
For questions/comments students are invited to directly contact the teacher by e-mail at the following address massi-mo.caccia@uninsubria.it. The teacher responds only to e-mails signed and from the domain studenti.uninsubria.it.
Parent course
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