Economics and Finance

1) Introduction: Statistical population, statistical unit, variables and their categories. Unitary and frequency distributions. Cumulative frequencies. Class distributions. Frequency density. Uniform distribution within classes. Bivariate distributions. Graphical representations. Cumulative distribution function for frequency distributions and class distributions, and their graphical representation. 2) Measures of Central Tendency, Variability, and Shape: The arithmetic mean and its properties. Harmonic mean, geometric mean, quadratic mean, and power means. Arithmetic mean for frequency distributions. Arithmetic mean for class distributions. Median for unitary distributions. Properties of the median. Quartiles. Median and quartiles for frequency and class distributions. Central value and mode. Variability. Mean deviation. Mean squared deviation. Variance. Properties of variability measures. Calculating variance for frequency and class distributions. Mean absolute difference. Range. Interquartile range. Concentration. Geometric interpretation of concentration. Heterogeneity. Indices of heterogeneity. Relative variability indices. Coefficient of variation. Concentration in class distributions. Symmetry and skewness. Measures of skewness. Box plot. 3) Bivariate Analysis: Bivariate distributions. Marginal and conditional distributions. Independence. Measures of dependence. Perfect dependence. Mean independence. Measures of mean dependence. Regression. The least squares regression line. Residuals and predictions. Properties of the least squares line. Decomposition of deviance in regression. The r² index for goodness of fit. Correlation. Correlation coefficient and covariance. 4) Probability: Introduction to probability. Definition of probability. Rules of probability. Conditional probability. Partition of a sample space. Bayes' theorem. Elements of combinatorics: permutations and combinations. Definition of independent events. Introduction to random variables. Discrete random variables. Probability distribution of a discrete random variable. Cumulative distribution function of a random variable. Mean and variance of a discrete random variable. Examples of discrete random variables: uniform, Bernoulli, and binomial. Introduction to continuous random variables. The normal random variable. Use of normal distribution tables. Definition of quantile. Quantile calculation for a random variable. Mean and variance of the sum of n random variables. 5) Inference: Population, sample, and sampling distributions. Law of large numbers and central limit theorem. Normal approximation of the binomial distribution. Interval estimation: confidence intervals for the mean of a normal population with known variance. Margin of error. Sampling distribution of the mean when variance is unknown. The t-distribution (Student’s t). Confidence intervals for the mean of a normal population with unknown variance. Confidence intervals for the mean of any population in the case of large samples. Confidence intervals for a proportion.

Basic mathematics knowledge (limits, functions, derivatives, matrices, set theory). It is recommended to have passed the Basic Mathematics course exam.

Cicchitelli, D'Urso, Minozzo. Statistica: principi e metodi. 3a edizione. Pearson editore.

Attendance is not compulsory but is strongly recommended.

The exam will consist of a written exam and a possible oral exam. For students who: -pass the written test (score equal to or greater than 18), the oral exam is at the discretion of the instructor or upon explicit request by the student. -pass the written test with a score equal to or greater than 25, the oral exam is mandatory. If the student chooses not to take the oral exam, the final grade will be set to 25 (for example, if a student scores 28 but decides not to take the oral exam, the recorded grade will be 25). The oral exam will focus on the theoretical aspects covered during the course, including proofs. The oral exam will generally take place at least one week after the written test. The written exam will include: 8 multiple-choice questions 3 exercises: one on descriptive statistics, one on probability, and one on inference. The duration of the written test will range from a minimum of 90 minutes to a maximum of 120 minutes. Students who pass the written exam during the January/February 2026 exam sessions can earn up to 4 additional points on their final grade by successfully completing the optional R programming test.

Lectures will be conducted using a combination of slides and the blackboard. Theoretical, lecture-based sessions will be followed by interactive classes involving exercises and in-class discussions. The course also includes an optional component on the R programming language, which is delivered entirely online.

1) Introduction: Statistical population, statistical unit, variables and their categories. Unitary and frequency distributions. Cumulative frequencies. Class distributions. Frequency density. Uniform distribution within classes. Bivariate distributions. Graphical representations. Cumulative distribution function for frequency distributions and class distributions, and their graphical representation. 2) Measures of Central Tendency, Variability, and Shape: The arithmetic mean and its properties. Harmonic mean, geometric mean, quadratic mean, and power means. Arithmetic mean for frequency distributions. Arithmetic mean for class distributions. Median for unitary distributions. Properties of the median. Quartiles. Median and quartiles for frequency and class distributions. Central value and mode. Variability. Mean deviation. Mean squared deviation. Variance. Properties of variability measures. Calculating variance for frequency and class distributions. Mean absolute difference. Range. Interquartile range. Concentration. Geometric interpretation of concentration. Heterogeneity. Indices of heterogeneity. Relative variability indices. Coefficient of variation. Concentration in class distributions. Symmetry and skewness. Measures of skewness. Box plot. 3) Bivariate Analysis: Bivariate distributions. Marginal and conditional distributions. Independence. Measures of dependence. Perfect dependence. Mean independence. Measures of mean dependence. Regression. The least squares regression line. Residuals and predictions. Properties of the least squares line. Decomposition of deviance in regression. The r² index for goodness of fit. Correlation. Correlation coefficient and covariance. 4) Probability: Introduction to probability. Definition of probability. Rules of probability. Conditional probability. Partition of a sample space. Bayes' theorem. Elements of combinatorics: permutations and combinations. Definition of independent events. Introduction to random variables. Discrete random variables. Probability distribution of a discrete random variable. Cumulative distribution function of a random variable. Mean and variance of a discrete random variable. Examples of discrete random variables: uniform, Bernoulli, and binomial. Introduction to continuous random variables. The normal random variable. Use of normal distribution tables. Definition of quantile. Quantile calculation for a random variable. Mean and variance of the sum of n random variables. 5) Inference: Population, sample, and sampling distributions. Law of large numbers and central limit theorem. Normal approximation of the binomial distribution. Interval estimation: confidence intervals for the mean of a normal population with known variance. Margin of error. Sampling distribution of the mean when variance is unknown. The t-distribution (Student’s t). Confidence intervals for the mean of a normal population with unknown variance. Confidence intervals for the mean of any population in the case of large samples. Confidence intervals for a proportion.

Basic mathematics knowledge (limits, functions, derivatives, matrices, set theory). It is recommended to have passed the Basic Mathematics course exam.

Cicchitelli, D'Urso, Minozzo. Statistica: principi e metodi. 3a edizione. Pearson editore.

Attendance is not compulsory but is strongly recommended.

The exam will consist of a written exam and a possible oral exam. For students who: -pass the written test (score equal to or greater than 18), the oral exam is at the discretion of the instructor or upon explicit request by the student. -pass the written test with a score equal to or greater than 25, the oral exam is mandatory. If the student chooses not to take the oral exam, the final grade will be set to 25 (for example, if a student scores 28 but decides not to take the oral exam, the recorded grade will be 25). The oral exam will focus on the theoretical aspects covered during the course, including proofs. The oral exam will generally take place at least one week after the written test. The written exam will include: 8 multiple-choice questions 3 exercises: one on descriptive statistics, one on probability, and one on inference. The duration of the written test will range from a minimum of 90 minutes to a maximum of 120 minutes. Students who pass the written exam during the January/February 2026 exam sessions can earn up to 4 additional points on their final grade by successfully completing the optional R programming test.

Lectures will be conducted using a combination of slides and the blackboard. Theoretical, lecture-based sessions will be followed by interactive classes involving exercises and in-class discussions. The course also includes an optional component on the R programming language, which is delivered entirely online.

1)Introduction. Frequency distributions e their graphical representation: Cumulative distribution, distribution function and their graphical representation 2)Position and variability indexes. Arithmetic mean. Properties of the arithmetic mean. Median and quantiles. Geometric mean, armonic mean. Variance and other variability indexes. Concentration 3)Bivariate analysis. Dependence and independence for categorical variables. Regresion and correlation. 4) Probability 5) Inference

Basic knowledge of mathemetics. Limits functions and derivatives. Set theory

Cicchitelli, D'Urso, Minozzo. Statistica: principi e metodi. 3a edizione. Pearson editore.

Attendance is not compulsory but is strongly recommended.

The exam will comprise two parts (written and oral). During the written exam the students must solve both data analysis and statistical inference exercises. The written test will be divided into two part. Multiple choice questions will be given in the first part. Exercises ranging from a minimum of 6 points to a maximum of 8 will be given in the second part. The oral examination will deal with the theoretical topics explained throughout the course.

The lessons will be held alternating the use of slides and the blackboard. The proofs of the theorems and the solutions of the exercises will be carried out directly on the blackboard

Detailed course programme 1. Unit and collective; characters and modes 2. Statistical collection and types of statistical data 4. Simple distribution analysis: frequencies. 5. Ratios and index numbers 6. Graphical representations 7. Mean values 8. Variability, concentration and asymmetry 9. From histogram to density 10. Dependency, association and related measures 11. Regression and concordance 12. Combinatorics 13. Introduction to Probability 14. Conditional probability and Bayes' theorem 15. Random variables 16. Sample distributions and the central limit theorem 17. Probability Distributions 18. The statistical model 19. Point and interval estimates

It is strongly suggested to have already passed the Matematica Generale exam

● A. Forcina e B. Liseo (2021) Appunti per il corso di Statistica (available at libro-stat-ott-23.pdf ) ● Other text: Cicchitelli, D'Urso, Minozzo. Statistica: principi e metodi. 3a edizione, Pearson editore. ● Handout from the Instructor

All classes are in presence

The exam evaluation will be carried out by means of a written test relating to the subjects being studied. It is recommended to watch the video lessons and participate in the interactive activities (e-activity) proposed in the course. Participation in the interactive activities will be assessed in a review session. The exam may be taken without any prior notice.