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
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.