Hello and Welcome to this introductory Lecture in Probability!
These Course Notes are a complement to the Lecture Probability I.
The Lecture is divided in the following Chapters, and each Chapter contains several themes.
|1||Introduction||Intro, Mathematics reminder and Combinatorics.||☑️|
|2||Elements of Set Theory For Probability||Sets, Venn diagram, Fundamental theorems, Basic definition of probability||☑️|
|3||Axiomatic Foundations of Probability||Probability Axioms, Illustrations of use, Conditional probability, Independence & Bayes’ theorem||☑️|
|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||Table for discrete and bivariate random variables: joint probability, expected value (unconditional and conditional), variance, covariance and independence||📝|
|8||Elements of Simulation||Numerical methods for the simulation of random variable with a given CDF.||📝|
- ☑️ = Ready (almost surely with typos).
- 🔧 = Fine-tuning.
- 📝 = Writing.
Daniel FLORES AGREDA
Data Science Course Developer and InstructorDaniel.Flores@unige.ch
Teaching and Research AssistantEdoardo.Vignotto@unige.ch
Davide LA VECCHIA
Associate Professor at Geneva School of Economics and ManagementDavide.Lavecchia@unige.ch
Teaching and Research Assistant, PhD. student at Geneva School of Economics and ManagementManon.Felix@unige.ch
- 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
- Mr. Hervégil Voegeli, Master student in Statistics at Geneva School of Economics and Management
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.
Seminars will take place on Thursday from 16h15 to 18h00 in the room MS130. For those students who cannot attend the seminars, a recording will be available on Mediaserver.
Every week, you have access to a new forum on SpeakUp to submit your potential questions. The assistant only reads and answers the SpeakUp room related to the current week; the links to the previous weeks remain visible, but will not be consulted (and updated) any more by the assistant. Your questions are also submitted to the assistant for validation before being published.
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.