Review of Probability Theory

Abstract

Outline • Probability definitions. • Axiomatic definition of probability. • Joint probability. • Marginal probability. • Bayes theorem. 2 3 Random Signals • Some physical signals (noise) cannot be expressed as an explicit mathematical formula. • Noise: typically unwanted and to eliminate it we need to understand it quantitatively. • Must be described in probabilistic terms. • We need probability theory. 4 Classical (Intuitive) Definition of Probability • Assume all outcomes are equally likely number of ways event can occur total number of possible outcomes