Università degli studi di Modena e Reggio Emilia

You are here: Home » Study Plan » Subject

Contents download

Teachers

Luca LA ROCCA

Overview

This course aims to provide basic probabilistic knowledge for the description of random phenomena and basic statistical knowledge for the analysis of datasets, developing the ability to analyze problems, build models, find and evaluate solutions, communicate results and explore topics in autonomy.
For a fuller understanding of the training objectives, see the expected learning outcomes.

Admission requirements

A basic knowledge of the theory of numerical series and of integro-differential calculus for real functions of one real variable, as provided by the propaedeutic Mathematical Analysis course.

Course contents

The contents are structured in three macro-topics as described by the following list:

1. DATA, PROBABILITY AND RANDOM VARIABLES (3 CFU)
Prologue. Data in R. Probability basics and counting. Stochastic simulations. Conditional probability and independence. Probability mass functions and expected value. Binomial and geometric variables. Transformations, variance and independence. Other commonly used discrete variables. Probability density functions and their summaries. Normal variables. Uniform and exponential variables.

2. SIMULATION AND INFERENCE (1CFU)
Estimating probability distributions. Central Limit Theorem. Point estimators. Confidence intervals for the mean.

3. DATA MANIPULATION AND VISUALIZATION (2 CFU)
Introduction to the tidyverse. Data analysis with the tidyverse. Additional information on the tidyverse. The grammar of graphics. Visualizing a single variable. Visualizing two or more variables. Customizing. Epilogue.

The breakdown of CFU by macro-topic and the list of topics in each macro-topic are to be understood as indicative: they may be subject to changes during the lessons, based on contingencies and the feedback received.
For a fuller understanding of the contents, see the reference book.

Teaching methods

Teaching is delivered, face to face, in Italian. Attendance is not compulsory, but it is recommended. Teaching methods include: classroom lectures open to discussion; exercise solving assignments; office hours. Non-attending students are invited to contact the teacher.

Assessment methods

The exam takes place at the end of the lessons, according to the official exam session schedule, subject to enrollment in Esse3 for a specific session (within its deadline). Before taking the exam, students must hand in two PDF documents to the teacher: an individual work in which they present a topic of their choice from those in the program and a group work in which they solve six exercises of their choice from those proposed by each of the first six chapters of the reference book (thirty-six exercises in total). The exam consists of a single oral exam, strictly individual, in which students can consult their favorite reference material (e.g. their notes) as well as use their favorite calculation and writing tools (e.g. their laptop, paper and pen). The oral test is structured into two stages: in the first stage students have a quarter of an hour to illustrate their individual work, demonstrating that they have explored the topic even beyond the boundaries of the lessons and that they are able to communicate it effectively; in the second stage students have half an hour to discuss the solutions of some exercises, chosen by the teacher from those solved in the group work, demonstrating autonomy of judgment and mastery of the models and methods applied. The final grade will be proportional to what students have demonstrated, overall, in the oral exam (without a specific evaluation of the works handed in).

Learning outcomes

Knowledge and understanding: students will know the basic probabilistic models for the description of random phenomena and will understand their main properties; they will also know the basic statistical methods for data analysis and will understand how they work.
Applying knowledge and understanding: students will be able to analyze, describe in mathematical form and computationally solve a problem, making use of appropriate probabilistic models and statistical methods.
Making judgements: students will be able to source information for analysing, describing and solving problems; they will be able to critically assess the results achieved, also based on the choices they made.
Communication: students will be able to effectively present the results of their work.
Lifelong learning skills: students will have learned to explore topics in probability and statistics.

Readings

Darren Speegle & Bryan Clair (2022). Probability, Statistics, and Data: A Fresh Approach Using R. CRC Press, Boca Raton, US-FL.
URL https://mathstat.slu.edu/~speegle/_book/

Materiali a cura del docente: disponibili con più anticipo possibile; da considerare in forma definitiva solo al termine delle lezioni.
URL https://moodle.unimore.it/