# 🃏 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

##### Davide LA VECCHIA

###### Associate Professor at Geneva School of Economics and Management

Davide.Lavecchia@unige.ch##### Manon FELIX

###### Teaching and Research Assistant, PhD. student at Geneva School of Economics and Management

Manon.Felix@unige.ch##### Alice Scattolin

###### Teaching and Research Assistant, PhD. student at Geneva School of Economics and Management

Alice.Scattolin@unige.ch### Instructors

**Davide La Vecchia**, Associate Professor at Geneva School of Economics and Management**M. Manon Felix**, Teaching and Research Assistant, PhD. student at Geneva School of Economics and Management**M. Alice Scattolin**, Teaching and Research Assistant, PhD. student at Geneva School of Economics and Management

### Lectures

The Lectures will take place in the room MR280 on Thursday from 12h15 to 14h00. For those students who cannot attend the lectures, a recording will be available on **Mediaserver**.

### Exercises

Seminars will take place on Thursday from 16h15 to 18h00 in the room MS130. The seminars are not recorded.

### Tutorials

Every two week (starting from the third one), tutorials will take place on Wednesday from 16h15 to 18h00 in the room MS160. The tutorials are not recorded.

### Tools

You have access to a new forum on **SpeakUp** to submit your potential 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.

### References

*A First Course in Probability*. Pearson.