Course Topics
- Basic concepts: probability spaces, conditional probability, Bayes' Theorem, independent events - Random variables: distribution, density, expectation, variance, covariance, law of large numbers - Special distributions: Bernoulli, Binomial, Poisson, Exponential, Normal, Chi-Square, t-Distribution - Sampling: sums of random variables, central limit theorem, sample variance - Parameter Estimation: maximum likelihood estimates, interval estimates, confidence intervals - Hypothesis testing: significance levels, test statistics, p-values

Teaching format
The course combines lectures, exercise groups with instructors, and coursework assignments that are corrected and commented on by Teaching Assistants. In the lectures, the instructor introduces new concepts and techniques using board work and projected material, complemented by short in-class exercises. The assignments give students the opportunity to consolidate these concepts by applying them to selected problems. In the exercise groups, students discuss possible approaches to the assignment tasks with the instructors and compare alternative solutions. They also work on additional problems, independent of the assignments, to deepen their understanding of the material covered in the lectures.

Educational objectives
Knowledge and Understanding - D1.1 Have a solid knowledge of mathematical , algebra, numerical calculus, and elementary logic that are in support of computer science. - D1.18 Have a solid knowledge of statistics and probability theory. Applying knowledge and understanding - D2.1 Be able to use the tools of mathematics and logic to solve problems. - D2.21 Be able to apply the tools of statistics and probability theory to solve information technology issues Ability to make judgments - D3.2 Be able to work autonomously according to the own level of knowledge and understanding. - D3.5 Ability to discern between various probability models and capability to find appropriate models for a given application Communication skills - D4.1 Be able to use one of the three languages English, Italian and German, and be able to use technical terms and communication appropriately. Learning skills - D5.1 Have developed learning capabilities to pursue further studies with a high degree of autonomy.

Additional educational objectives and learning outcomes
Use of software tools: Students will be able to use R and Java for basic statistical computations. Application of statistical concepts: Students will be able to apply probabilistic and statistical methods to simple real-world scenarios, such as determining sample sizes for surveys, calculating posterior probabilities for diagnostic tests, or assessing the applicability of the central limit theorem in a given situation.

Assessment
The assessment is based on coursework assignments (30%) and a written final exam (70%). Both assignments and the exam consist of groups of questions built around a hypothetical scenario or a mathematical setting. The questions require students to explore different aspects of the scenario or to investigate properties of the setting. Assignments are intended to help students review and deepen the material covered in the lectures, while the exam assesses whether they have achieved the learning outcomes of Knowledge and understanding, Applying knowledge and understanding, and Making judgments.

Evaluation criteria
Assignments and exams are assessed based on the correctness and clarity of the answers. For students who submit all assignments, the final grade is the weighted average of the exam mark (70%) and the assignment mark (30%). If not all assignments are submitted, the assignment component is reduced in proportion to the number of assignments handed in. In addition, if the mark for a question in an assignment is lower than the corresponding exam mark, the higher exam mark will apply.

Required readings

Sheldon M. Ross. Introduction to Probability and Statistics for Engineers and Scientists. Academic Press, London, England. 6th, 2021. ISBN : 0-12-817747-0

Supplementary readings

Joseph K. Blitzstein, Jessica Hwang. Introduction to Probability. Chapman and Hall/CRC, Boca Raton, USA. 2nd edition, 2019.

ISBN : 978-1-1383-6991-7

Further information
R can be downloaded from: https://www.r-project.org R Studio, the IDE for the R language, can be downloaded from: https://posit.co/download/rstudio-desktop/