ID:
SCV0609
Duration (hours):
48
CFU:
6
SSD:
PROBABILITÀ E STATISTICA MATEMATICA
Located in:
Varese - Università degli Studi dell'Insubria
Year:
2025
Overview
Date/time interval
Primo Semestre (22/09/2025 - 19/12/2025)
Syllabus
Course Objectives
The course enables students to acquire solid knowledge and skills in the main aspects of probability theory and mathematical statistics (both descriptive and inferential). At the end of the course, students will be able to: 1) Understand and use the fundamental language and concepts of probability theory and mathematical statistics. 2) Apply the basic principles of combinatorial calculus to solve simple problems. 3) State and prove some of the main theorems in probability and statistics. 4) Build models of random phenomena using standard probability distributions. 5) Analyze and concisely describe data sets. 6) Estimate parameters in models describing random phenomena. 7) Apply the acquired concepts to solve problems under conditions of uncertainty. 8) Communicate rigorously on issues related to probability and statistics, correctly formalizing and presenting intuitions both orally and in writing. The course also introduces foundational elements that will be useful for further studies in computer science. Acquiring the basic language of probability theory will enable students to independently pursue further study and develop the skills needed to meet professional demands.
Course Prerequisites
The knowledge and skills required for a successful learning experience in this course concern algebra and differential calculus, which are covered in the first-year courses Algebra and Geometry and Mathematical Analysis.
Teaching Methods
Theoretical content is presented primarily through lectures, complemented, where possible, by dialogic teaching moments and brainstorming activities. To stimulate curiosity and foster student engagement, the instructor introduces topics by presenting problems drawn from real-world situations and by consistently providing connections to everyday life, computer science, and the history of mathematics and science. The introduced concepts are then rigorously formalized and discussed using mathematical language. The topics covered are further explored through practical exercises requiring active student participation, allowing them to apply theoretical knowledge to formulate simple probabilistic models and solve problems under conditions of uncertainty.
Assessment Methods
The purpose of the examination is to assess the acquisition of the knowledge and skills described in the section Course Objectives, with particular emphasis on the ability to apply theoretical knowledge—individually and in combination—to solve problems under conditions of uncertainty. The exam consists of a written test lasting two hours, during which students may use the formula sheet provided by the instructor. The test is composed of three exercises. The written exam is passed with a score of at least 18 out of 30. The evaluation criteria adopted by the instructor are as follows: - correctness, completeness, and clarity of both the solution process and the obtained results
Contents
The course consists of a total of 48 hours of instruction, including both the presentation of theoretical concepts and practical exercises. The topics are presented in the chronological order listed below. Introduction to Probability Theory (6 hours, learning objective 3): Historical overview of probability theory. Deterministic and random phenomena. Sample spaces. Events and operations on events. Incompatible events. Classical definition of probability. Frequentist definition of probability. Subjective definition of probability. Axiomatic definition of probability. Properties of probability functions. Combinatorial Calculus (3 hours, learning objective 2): Multiplication principle. Simple permutations. Permutations with repetition. Simple arrangements. Arrangements with repetition. Simple combinations. Combinations with repetition. Descriptive Statistics (4 hours, learning objective 5): Qualitative and quantitative variables. Absolute and relative frequency. Frequency distributions. Frequency distributions by class. Main graphical representations: pie chart, bar chart, histogram with equal-width classes, histogram with unequal-width classes. Measures of central tendency: arithmetic mean, median, and mode. Quantiles and percentiles. Measures of dispersion: variance and standard deviation. Correlation between two variables in a population. Scatter plot. Linear relationship. Least squares method. Regression line. Covariance. Linear correlation coefficient. Types of linear correlation. Linear dependence and independence. Conditional Probability and Independent Events (5 hours, learning objective 3): Conditional probability. Theorem of compound probability. Independent and dependent events. Product rule for independent events. The Monty Hall problem. Law of total probability. Bayes’ theorem. Discrete and Continuous Probability Distributions (14 hours, learning objective 4): Discrete and continuous random variables. Probability distribution and distribution function of discrete random variables. Bernoulli trial and Bernoulli random variables. Bernoulli process (success/failure scheme). Expected value, variance, and standard deviation of a discrete random variable. Fair games. Binomial, hypergeometric, and geometric distributions. Poisson distribution. Probability density and distribution function of a continuous random variable. Expected value and variance of a continuous random variable. Uniform, exponential, and normal distributions. Standard normal distribution. Chebyshev’s inequality. Convergence Theorems (4 hours, learning objective 3): Independent random variables. Sum of random variables. Product of a random variable by a constant. Expected value and variance of the sum of two random variables and of the product of a random variable by a constant. Definition of convergence in probability. Multidimensional random variables. Law of large numbers. Empirical law of chance. Central limit theorem. Consequences of the central limit theorem. Inferential Statistics (12 hours, learning objective 6): Point estimation. Interval estimation. Estimators and estimates. Sample mean, frequency, and variance. Introduction to machine learning. All topics covered contribute to the achievement of learning objectives 1, 7, and 8.
Course Language
Italian
More information
• Reference text (optional): Introduzione alla probabilità con elementi di statistica, Paolo Baldi, McGraw-Hill Education, 2nd Edition, ISBN 9788838667862. • Course materials: lecture notes, slides, and solved exercises provided by the instructor on the course e-learning platform.
Degrees
Degrees
COMPUTER SCIENCE
Bachelor’s Degree
3 years
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