Probability

Objectives

This course will enable students to master the basic concepts of probability calculation, which will be central to all statistics courses taught at ENSAI. In particular, students will be able to: Calculate probability laws and mathematical expectations using appropriate techniques, whether in a one- or multi-dimensional framework; Understand and use the basic formalism of probability to model a discrete or continuous random event; Identify the usual probability laws and their characteristic properties; Determine and use the properties of independence between several random variables.

Course outline

Random variables: definition, notion of probability law, discrete or density laws, mathematical expectation, transfer theorem. Moments and Lp spaces, distribution function, Laplace transform, characteristic function. Methods for calculating probability laws and probabilistic inequalities. Random vectors and multivariate laws: notion of probabilistic independence, characterization of independence, convolution. Notion of covariance, correlation. Gaussian vectors.

Prerequisites

Integral calculus and measure theory, linear algebra, discrete probabilities