Introduction to statistics and data analysis. Elements of probability theory. Random variables.
Introduction to parametric statistical inference. Point estimation. Interval estimation. Hypothesis testing.
G. Cicchitelli, P. D'Urso, M. Minozzo (2022). Statistica: principi e metodi. Pearson, IV edizione
Learning Objectives
The aim of this course is to introduce students to probability theory and to the main parametric inference methods.
Knowledge: Introductory-level concepts of probability and statistics.
Acquired expertise: Students will acquire the ability to organize and analyze a real data set, by adequate statistical methods. Moreover, Students will be able to critically understand features and limits of models and methods, illustrated during the course.
Prerequisites
Courses required: Analysis I: Integral and Differential Calculus.
Teaching Methods
Lectures and exercises sessions.
Further information
Additional teaching material will be provided during the course through the e-learning platform.
Type of Assessment
Written test. The written test consists of exercises on statistical methods introduced during the lectures. In particulars, the written test consists of exercises on
descriptive statistics, probability, and statistical inference (point estimation, interval estimation and hypothesis testing).
The written test will be evaluated using a score in thirtieths with honors if applicable. The written test is successfully passed if the grade awarded is at least 18.
The exercises aim to assess
understanding, acquisition and processing of methods for the analysis of data, the basic concepts of the probability theory and the main parametric inference methods.
Course program
Introduction to statistics
Descriptive statistics: frequency distributions, graphical representations, measures of central tendency and measures of variability.
Elements of probability theory: sample space and events, the algebra of events, axioms of probability, conditional probability.
Random variables: marginal distributions, joint distributions and conditional distributions, expectation and variance of random variables, some discrete distributions, some continuous distributions. Law of large numbers and Central limit Theorem
Introduction to parametric statistical inference: Sample statistics and Central Limit Theorem.
Point estimation: Estimates and estimators, properties of estimators, moment method, Maximum Likelihood method.
Interval estimation: pivotal quantity method for obtaining confidence intervals, confidence intervals for the mean and for the variance of a Normal population, confidence interval for the mean of a non Normal population, confidence intervals for the mean of a Bernoulli population.
Hypothesis testing: basic concepts for obtaining hypothesis tests, test for the mean and for the variance of a Normal population, test for the mean of a non Normal population, test for the mean of a Bernoulli population.