Statistics and Data Analysis
A.Y. 2024/2025
Learning objectives
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.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
Course syllabus
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:
- Set theoretic definition of probability
- Law of large numbers, Monte Carlo simulation methods
- Set operations with events
- Probability axioms. Normalization
- Conditional Probability
- Product law
- Product law for independent events
- Series-parallel systems
- Sum law
- Bayes' theorem and inverse probability
- Bayes' theorem: Role of prior and likelihood
- Expected value of a bet
- Introduction to random variables: probability distributions and probability density
- The cumulative function
- Position Indicators
- Amplitude indicators (measures of dispersion)
- Studying a generic probability density
- Binomial distribution
- Geometric distribution
- Negative exponential density
- Poisson distribution
- Poissonian processes
- Relations between binomial, Poissonian and Gaussian
- The Gaussian (or normal) density
- The three sigma rule
- Normal approximation to the binomial
- Sum of random variables
- Central limit theorem
- Probability generating functions
- Moment generating functions
- Sampling variables. Sample minimum and sample maximum distributions
- Sample average distribution
- Elements of inferential statistics
- Set theoretic definition of probability
- Law of large numbers, Monte Carlo simulation methods
- Set operations with events
- Probability axioms. Normalization
- Conditional Probability
- Product law
- Product law for independent events
- Series-parallel systems
- Sum law
- Bayes' theorem and inverse probability
- Bayes' theorem: Role of prior and likelihood
- Expected value of a bet
- Introduction to random variables: probability distributions and probability density
- The cumulative function
- Position Indicators
- Amplitude indicators (measures of dispersion)
- Studying a generic probability density
- Binomial distribution
- Geometric distribution
- Negative exponential density
- Poisson distribution
- Poissonian processes
- Relations between binomial, Poissonian and Gaussian
- The Gaussian (or normal) density
- The three sigma rule
- Normal approximation to the binomial
- Sum of random variables
- Central limit theorem
- Probability generating functions
- Moment generating functions
- Sampling variables. Sample minimum and sample maximum distributions
- Sample average distribution
- Elements of inferential statistics
Prerequisites for admission
Calculus
Teaching methods
Lectures on theoretical foundations and classroom-based problem-solving activities.
Teaching Resources
Sheldon M. Ross, Introduction to probability and statistics for engineers and scientists, Academic Press, sixth ed., 2020
Assessment methods and Criteria
The exam consists of a mandatory two-hours written test, which allows obtaining a grade of up to 30/30 cum laude, structured in open-ended theory questions and exercises, similar for content and difficulty to those proposed in class. During the written test, the student is allowed to use statistical tables and the compendium of main formulas made available by the instructor. Use of a hand-held calculator is permitted
INF/01 - INFORMATICS - University credits: 6
Practicals: 36 hours
Lessons: 24 hours
Lessons: 24 hours
Professor:
Rocchesso Davide
Professor(s)