Università Roma Tre

1. Introduction to Probability and Statistics (6h): basic concepts of probability, random variables, and statistical inference. Descriptive statistics: measures of central tendency and dispersion. Introduction to data types and distributions.
2. Probability Distributions (10h): Probability density functions (PDFs) and cumulative distribution functions (CDFs). Conditional probability, joint distributions, and marginal distributions. Bayes' theorem.
3. Key Probability Distributions and Limit Theorems (5h): common probability distributions (e.g., normal, binomial, Poisson). The Law of Large Numbers and its applications. The Central Limit Theorem and its significance.
4. Maximum Likelihood Estimation (8h): Introduction to likelihood functions. Principles and methods of maximum likelihood estimation. Application of maximum likelihood estimation.
5. Chi-Square Tests (8h): Chi-square distribution and its properties. Chi-square goodness-of-fit tests. Chi-square tests for independence.
6. Goodness-of-Fit Testing (8h): Methods for assessing the fit of statistical models to data. Interpretation of goodness-of-fit results. Practical application of goodness of fit tests.
7. Practice (15h)

“A Modern Introduction to Probability and Statistics” – F.M. Dekking, C. Kraaikamp, H.P Lopuhaä, L. E. Meester
“Bayesian Reasoning in Data Analysis” – G. D’Agostini