Probability Theory

Credits

Prerequisites

Probability and Statistics, Mathematical Analysis 1.

Examination method

Passing an oral exam that includes solving an exercise

Learning
objectives

To consider the fundamental elements of measure theory in a probabilistic context and to present some of the enrichments that have been developed in this field.

Uniqueness and extension theorems. The Lebesgue measure. The completion of a probability space. Random variables and measurable functions. Joint distributions. The concept of stochastic independence and 0-1 laws. Integration of measurable functions and moments. Notable inequalities (Markov, Jensen, Schwarz, Hölder, Chebyshev) and their interpretation via moments. Independence and product measure. n-dimensional extension. Conditional expectation with respect to sigma-algebras.

Academic Year
2018/2019

Lecturer: Bruno TOALDO.

Semester: second.

Probability Theory