Objectives

This crash course objective is to synthesize the essential probability concepts which will be needed for the curriculum. This is not a substitute to a first course of probability but as a refresher for students. The level of the course does not go far beyond the prerequisite of a senior undergraduate course of probability at the level of "Probability and statistics for machine learning" (A. Dasgupta)

 

Syllabus

  • Foundations of probability : probability Axioms, Sample Spaces, Events, Mutually Exclusive Events, Law of Total Probability
  • Random variables : definitions, cumulative distribution function, probability density functions, classical laws, moment generating functions
  • Random vectors: joint distribution, marginal distribution, independent random variables, joint moments
  • Conditional probability, conditional expectation, Bayes’ Rule

Functions of random variables: one-to-one transformation, sums of random variables

Langue du cours : Anglais