Probability: a brief introduction

Abstract

Different approaches to probability: classical, empirical, subjective and axiomatic. The notion of (Borel measurable) random number and its moments. Moment generating function. The von Neumann-Mogenstern utility model: expected utility and certainty equivalent. The notion of risk aversion. Random vectors: stochastic independence and linear correlation between two random numbers. Linear function of a random vector: expected value and variance