PROBABILITY AND STATISTICS

Course objectives

The aim is that of providing students with some fundamental probabilistic and statistical notions, which are the basis of the logical-mathematical reasoning under uncertainty, with incomplete information. This will stimulate those critical skills which allow to face, besides "routine" problems, new problems too. In particular, students should acquire some basic notions which concern conditional and unconditional probabilities, discrete and continuous probability distributions, and statistical inference.Basic notions and theoretical results on conditional and unconditional probabilities, prevision, variance, correlation coefficient, probability density, cumulative distribution function, joint, marginal and conditional distributions, characteristic function, basic notions on statistical inference.

Channel 1
Giacomo Milizia Lecturers' profile

Program - Frequency - Exams

Course program
Combinatorial analysis: Fundamental principle of combinatorics, mutations, combinations, multinomial coefficients Axioms of probability: sample space and events, equiprobable outcomes, probability as a continuous ensemble function, probability as a measure of confidence; conditional probability, Bayes formula, independent events Discrete random variables; the Binomial, Poisson, geometric, hypergeometric and negative binomial variables Continuous random variables; the uniform, normal and exponential variables (notes on the Gamma variable) Expected value and variance of discrete and continuous v.a. (and their properties) and of functions of v.a. joint laws of v.a., independent v.a., conditional distributions in discrete and continuous cases; covariance of two random variables and correlation coefficient Markov inequality and Chebyshev inequality; central limit theorem and weak law of large numbers (notes on the strong law of large numbers) Statistics; sample mean, median, mode and variance; maximum likelihood estimators; confidence intervals for the mean
Prerequisites
A good knowledge, both conceptual and operational, of the contents of the Mathematical Analysis and Geometry course is required, in particular: limits of sequences, functions of a real variable, derivatives of the functions of a real variable and their applications, calculation of integrals , determinant of a square matrix.
Frequency
Between 20 and 30 students regularly attend the course
Exam mode
The exam consists of a written test with application exercises, and a theoretical test (the student can choose if written or oral) consisting of definitions, statements and demonstrations of theorems, application examples and counterexamples.
Lesson mode
There will be one 5 hours lesson every week in class from 2 pm to 7 pm, until December 18th
  • Lesson code1011710
  • Academic year2025/2026
  • CourseEnvironmental Engineering for Sustainable Development
  • CurriculumIngegneria dell'ambiente per lo sviluppo sostenibile
  • Year2nd year
  • Semester1st semester
  • SSDMAT/06
  • CFU6