SCV0609 - PROBABILITY AND STATISTICS FOR COMPUTER SCIENCE

courses

ID:

SCV0609

Duration (hours):

48

CFU:

SSD:

PROBABILITÀ E STATISTICA MATEMATICA

Located in:

Como - Università degli Studi dell'Insubria

Year:

2025

Date/time interval

Primo Semestre (22/09/2025 - 19/12/2025)

Course Objectives

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.

Course Prerequisites

The knowledge and skills necessary for fruitful learning of this teaching regarding algebra and infinitesimal calculus, and are taught in the first-year courses of "Algebra and Geometry" and "Mathematical Analysis".

Teaching Methods

The course is essentially based on lectures giving space, when possible, to moments of dialogued lessons and brain storming activities. In order to stimulate the curiosity and involvement of learners, the teacher introduces the topics by proposing problems posed by concrete situations and providing links with the real world, computer science and the history of mathematics and science. Subsequently, the concepts introduced are rigorously formalized and argued using the mathematical language. Theoretical topics are accompanied by exercises to allow the active partecipations of the students, wich will formulate simple random models and solve problems under conditions of uncertainty.

Assessment Methods

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 exam consists of an open book written test, lasting a total of two hours, consisting of 5 or 6 exercises. The written test is passed by obtaining a score greater than or equal to 18 out of 30. The evaluation criteria adopted by the teacher to evaluate the quality of a test are the following: - accuracy and completeness of the information, - degree of detail on the subject, - level of logic and resolution skills.

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 (h 6, learning objective 3): Historical notes on probability theory. Deterministic and random phenomena. Sample spaces. Events and operations between events. Incompatible events. Classical definition of probability. Frequentist definition of probability. Subjective definition of probability. Axiomatic definition of probability. Properties of probability functions. Combinatorics (h 3, training objective 2): Principle of multiplication. Simple permutations. Permutations with repetition. Simple dispositions. Dispositions with repetitition. Simple combinations. Combinations with repetition. Descriptive statistics (h 4, learning objective 5): Qualitative and quantitative characters. Absolute and relative frequency. Frequency distributions. Frequency distributions by classes. Main graphical representations: circular diagram, bar diagram, histogram with classes of equal width and histogram with classes of different widths. Centrality indices: arithmetic mean, median and mode. Quantiles and percentiles. Dispersion indices: variance and standard deviation. Correlation between two characters of a population. Dispersion diagram. Linear relationship. The least squares method. Regression line. Covariance. Linear correlation coefficient. Types of linear correlations. Linear dependence and independence. Conditional probability and independent events (h 5, training objective 3): Conditional probability. Multiplication theorem. Independent and dependent events. The Monty Hall Problem. Total probability theorem. Bayes theorem. Discrete and continuous probability distributions (h 14, learning objective 4): Discrete and continuous random variables. Probability distribution and distribution function of discrete random variables. Bernoulli experiment and Bernoulli variables. Bernoulli process. Mean value, variance and standard deviation of a discrete random variable. Fair Games. Binomial, hypergeometric and geometric distribution. Poisson distribution. Probability density and distribution function of a continuous random variable. Mean value and variance of a continuous random variable. Uniform, exponential and normal distribution. Standard normal distribution. Chebyshev's inequality. Convergence theorems (h 4, educational objective 3): Independent random variables. Sum of random variables. Product of a random variable times a constant. Mean value and variance of the sum of two random variables and the product of a random variable and a constant. Definition of convergence in probability. Multidimensional variables. Law of large numbers. Central limit theorem. Consequences of the central limit theorem. Montecarlo methods. Inferential statistics (h 12, learning objective 6): Punctual estimate. Interval estimate. Estimators and estimates. Sample mean, frequency and variance. Interval estimate of the mean and proportion of a population with known variance. Interval estimate of the mean and proportion of a population with unknown variance. Interval estimate of the variance of a population. Hypothesis test on the mean and on the proportion of a population with known variance. All the topics covered contribute to the achievement of training objectives 1, 7 and 8.

Course Language

Italian

More information

For questions/comments, students are invited to directly contact the teacher by e-mail at the following address pietro.galliani@uninsubria.it. The teacher responds only to e-mails signed and from the domain studenti.uninsubria.it.