# 🃏 Probability I

*Course Notes*

# About this lecture

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. | ☑️ |

2 | Elements of Set Theory For Probability |
Random variables, Trees, Venn diagram, Conditional probability, Independence & Bayes’ theorem. | ☑️ |

3 | Axiomatic Foundations of Probability |
Probability Axioms, Illustrations of use | ☑️ |

4 | Discrete random variables |
Definitions, Expected value and variance, Binomial, Poisson, Negative binomial and Hypergeometric | 🔧 |

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, Student’s t, Relationships | 🔧 |

6 | Limit Theorems |
Weak Law of Large Numbers (WLLN) and Central Limit Theorem (CLT) | 📝 |

7 | Bivariate Discrete Random Variables |
📝 | |

8 | Elements of Simulation |
Numerical methods for the simulation of random variable with a given CDF. | 📝 |

- ☑️ = Ready (almost surely with typos).
- 🔧 = Fine-tuning.
- 📝 = Writing.

## Practical information

### Who we are

### 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 don’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:

*A first course in probability*, S. Ross (any edition), Ed: Pearson New International Edition, cited as Ross (2014).

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.