Probability and Statistics
A.Y. 2024/2025
Learning objectives
The goal of the course is to provide notions of descriptive statistics, probability theory and statistical inference that constitute the foundation of applied research in economics. The aim is to develop the proper technical language and to enable students to attend more specialized courses such as "Econometrics" and "Machine Learning for Economics".
Expected learning outcomes
At the end of the course, the student will have acquired the main tools related to descriptive statistics (construction of indices, tables and graphs and interpretation of the same), probability theory (Bayes theorem, probability distribution and random variables) and statistical inference (point estimation, confidence intervals and hypothesis testing).
Students will be able to apply the studied statistical techniques to analyse data and solve common real-life problems. They will be able to interpret the most common statistical indices; calculate and interpret point estimates, and confidence intervals and test the most common statistical hypothesis, such as equality of means and independence between variables. Moreover, they will be able to perform a simple linear regression and interpret the output through statistical software.
Students will be able to apply the studied statistical techniques to analyse data and solve common real-life problems. They will be able to interpret the most common statistical indices; calculate and interpret point estimates, and confidence intervals and test the most common statistical hypothesis, such as equality of means and independence between variables. Moreover, they will be able to perform a simple linear regression and interpret the output through statistical software.
Lesson period: Second trimester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
Second trimester
Course syllabus
Descriptive Statistics:
1) Calculation of a mode, median and sample mean when the data are classified in a frequency table. Properties of the mean.
2) Variability and dispersion indices such as range, interquartile difference, variance and standard deviation.
3) Contingency tables and bivariate analysis. Definition of joint absolute and relative, marginal and conditional frequency distributions; Pearson index for independence; covariance and the correlation coefficient.
Probability and Random variables
1) Introduction to probability theory: classical, frequentist probability definitions, compound, and disjoint events; Bayes theorem; principle of total probabilities.
2) Definition of discrete and continuous random variables: probability distribution and density; distribution function; expected mean and variance of a random variable. Definition of independence between random variables (example of Bernoulli, binomial, and Normal random variables).
3) Central limit theory and the law of large numbers.
Statistical Inference
1) Point estimation: definition of unbiased estimator and standard error. Likelihood function and maximum likelihood estimators.
2) Confidence intervals for the mean and proportion.
3) Statistical hypothesis testing: null vs alternative hypothesis; type 1 and type 2 errors; p-value and rejection region; t-test for comparison between two means; ANOVA test for comparison among multiple means.
4) Definition of a linear regression model; estimation of the parameters (slope and intercept coefficients) with the least square method; goodness of fit and hypothesis testing on the coefficients with some applications.
1) Calculation of a mode, median and sample mean when the data are classified in a frequency table. Properties of the mean.
2) Variability and dispersion indices such as range, interquartile difference, variance and standard deviation.
3) Contingency tables and bivariate analysis. Definition of joint absolute and relative, marginal and conditional frequency distributions; Pearson index for independence; covariance and the correlation coefficient.
Probability and Random variables
1) Introduction to probability theory: classical, frequentist probability definitions, compound, and disjoint events; Bayes theorem; principle of total probabilities.
2) Definition of discrete and continuous random variables: probability distribution and density; distribution function; expected mean and variance of a random variable. Definition of independence between random variables (example of Bernoulli, binomial, and Normal random variables).
3) Central limit theory and the law of large numbers.
Statistical Inference
1) Point estimation: definition of unbiased estimator and standard error. Likelihood function and maximum likelihood estimators.
2) Confidence intervals for the mean and proportion.
3) Statistical hypothesis testing: null vs alternative hypothesis; type 1 and type 2 errors; p-value and rejection region; t-test for comparison between two means; ANOVA test for comparison among multiple means.
4) Definition of a linear regression model; estimation of the parameters (slope and intercept coefficients) with the least square method; goodness of fit and hypothesis testing on the coefficients with some applications.
Prerequisites for admission
To adequately understand the contents of the course, the students must have basic knowledge in Mathematics and basic knowledge in Coding
Teaching methods
Teaching will be delivered through lectures and practical classes. The material will be available on Ariel through lecture notes.
Teaching Resources
-) Abadir, K. M., Heijmans, R. D., Magnus, J. R. (2018) "Statistics" (Editor Cambridge)
-) Agresti, A., Kateri, M. (2021) "Foundations of Statistics for Data Scientists: With R and Python" (Editor Taylor and Francis Ltd)
-) Gelman, A., Hill, J. and Vehtari, A. (2020). "Regression and other stories" (Editor Cambridge)
-) Agresti, A., Kateri, M. (2021) "Foundations of Statistics for Data Scientists: With R and Python" (Editor Taylor and Francis Ltd)
-) Gelman, A., Hill, J. and Vehtari, A. (2020). "Regression and other stories" (Editor Cambridge)
Assessment methods and Criteria
Final written exam (closed book) lasting 90 minutes. It consists of 3 exercises and multiple-choice questions (rated from 0 to 30 points) that will cover all the topics listed in the program.
Professor(s)
Reception:
Each Wednesday 12-14
DEMM, room 31, 3° floor (By appointment, please send an email)