General Probability

Objectifs

Be familiar with probability calculations in one or more dimensions,

Be able to identify distributions, and in particular usual distributions,

Master the notion of Gaussian vector.

Plan

Random variables and real laws: definition, distribution function, density laws, moments, transfer theorem. Markov, Chebyshev, Jensen and Chernoff inequalities. Laplace transform, characteristic function, dumb function method. Quantiles. Density laws.

Random vectors and multivariate laws: definition, distribution function. Reminder of integration. Density laws, practical independence criterion, convolution product. Transfer theorem, expectation, covariance matrix, correlation coefficient, dumb function method. Characteristic function. Gaussian vectors.

Prérequis

Integral calculus and measure theory, notions of linear algebra, discrete probabilities.