Hello and Welcome to this introductory Lecture in Probability!

These Course Notes are a complement to the Lecture Probability I.

## Contents

The Lecture is divided in the following Chapters, and each Chapter contains several themes.

Number Name Themes Status
1 Introduction Intro, Mathematics reminder and Combinatorics. โ๏ธ
2 Elements of Set Theory For Probability Random variables, Trees, Venn diagram, Conditional probability, Independence & Bayesโ theorem. โ๏ธ
3 Axiomatic Foundations of Probability Probability Axioms, Illustrations of use โ๏ธ
4 Discrete random variables Definitions, Expected value and variance, Binomial, Poisson, Negative binomial and Hypergeometric ๐ง
5 Continuous random variables Definitions, Expected value and variance, Cumulative distribution function (cdf) and Probability density function (pdf), Some important examples: Uniform, Exponential, Gamma, Normal, logNormal, Studentโs t, Relationships ๐ง
6 Limit Theorems Weak Law of Large Numbers (WLLN) and Central Limit Theorem (CLT) ๐
7 Bivariate Discrete Random Variables ๐
8 Elements of Simulation Numerical methods for the simulation of random variable with a given CDF. ๐
• โ๏ธ = Ready (almost surely with typos).
• ๐ง = Fine-tuning.
• ๐ = Writing.

## Practical information

### Who we are

##### Daniel FLORES AGREDA
###### Data Science Course Developer and Instructor
Daniel.Flores@unige.ch
##### Edoardo VIGNOTTO
###### Teaching and Research Assistant
Edoardo.Vignotto@unige.ch

### Lectures

The Lectures will take place over Zoom on Thursdays from 12h to 14h.

• Lectures will consist on a presentation of the contents of the class.

• During the class, there will be some exercises. You are invited to download the app Wooclap

### Exercises

• Q&A sessions on the exercises will take place on Thursdays from 16 to 18 over Zoom. We will soon be making available a platform to raise and vote on your questions.

• The problem set and their solutions will be posted on-line one week before. You must are warmly reminded to try the exercises by yourselves before looking at the solution. If you are blocked in a point, or you donโt understand a step, you can raise your questions to the T.A.

• Problem sets are not graded.

### Tools

• Moodle. All the resources of the class will be available in this page.

• Wooclap A Web application allowing to choose among a wide range of questions (multiple choice, word cloud, visual questions)

#### Reference

Aside from these Course Notes, you can check:

We will not be following the content of this book beat-by-beat, but it is available for reference and/or in case you want a different explanation or go deeper in the context of the Course.