Statistics and Data Analysis
A.Y. 2023/2024
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: Third four month period
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
Lesson period
Third four month period
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. 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
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
Continuum mathematics
Teaching methods
Lectures on theoretical foundations and classroom-based problem-solving activities.
Teaching Resources
Web site: http://ggianinicpsm.ariel.ctu.unimi.it/
Assessment methods and Criteria
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.
INF/01 - INFORMATICS - University credits: 6
Lessons: 48 hours
Professor:
Gianini Gabriele