The course aim at introducing the fundamentals of descriptive statistics, probability and parametric inferential statistics.
Expected learning outcomes
Students will be able to carry out basic explorative analyses and inferences on datasets, they will know the main probability distributions and will be able to understand statistical analyses conducted by others; moreover, they will know simple methods for the problem of binary classification, and will be able to evaluate their performances. The students will also acquire the fundamental competences for studying more sophisticated techniques for data analysis and data modeling.
This course provides an introduction to the fundamental concepts of Probability and Inferential Statistics and points to their most relevant applications in Computer Science. The topics discussed are the following. The course provides an introduction to the fundamental concepts of probability, descriptive statistics and inferential statistics with particular reference to their use in informatics. The topics covered are the following. Set Theoretic definition of Probability Law of large numbers, Monte Carlo simulation methods Set operations with events Probability axioms - Normalization Conditional Probability Product law The birthdays "paradox" Product law for independent events Series-parallel systems Sum Law Guide to the use of product law, sum law and complement law Bayes' Theorem and Inverse Probability The Monty Hall "Goats-and cars" puzzle Bayes' theorem - Role of prior and likelihood Expected value of a bet Introduction to random variables: probability distributions and density The Cumulative Function Position Indicators Amplitude indicators (measures of dispersion) Studying a generic probability density Binomial distribution Geometric distribution Negative Exponential Density Applications of the Negative Exponential in system reliability Poisson distribution Poissonian processes Relations between Binomial, Poissoniana and Gaussian The Gaussian (or Normal) density The three sigma Rule How to use the Gaussian Density Cumulative Tables Normal Approximation to the Binomial Sum of random variables Central Limit Theorem Probability generating functions Moment generating functions Outline of the Generalized Central Limit Theorem Sampling Variables - Sample Minimum and Sample Maximum Distributions Sample Average Distribution Elements of inferential statistics
Prerequisites for admission
Lectures on theoretical foundations and classroom-based problem-solving activities.
The exam consists of a mandatory written test (2 hours, open book), which allows obtaining a grade of up to 30/30 cum laude, structured in open-ended exercises, of an applicative type, with contents and difficulties similar to those faced during the exercises.