General Probability

Objectives

Be able to routinely perform probability calculations, whether in a one- or multi-dimensional framework; Know how to identify distributions and in particular usual distributions; Master the concept of Gaussian vector.

Course outline

Random variables and real distributions: definition, distribution function, density distributions, moments, transfer theorem. Markov, Chebyshev, Jensen and Chernoff inequalities. Laplace transform, characteristic function, dummy function method. Quantiles. Usual density distributions. Random vectors and multivariate distributions: definition, distribution function. Integration reminders. Density distributions, practical independence criterion, convolution product. Transfer theorem, expectation, covariance matrix, correlation coefficient, dummy function method. Characteristic function. Gaussian vectors.rn

Prerequisites

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