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Lecture Notes on Probability Theory and Random Processes

Lecture Notes on Probability Theoryand Random ProcessesJean WalrandDepartment of Electrical Engineering and Computer SciencesUniversity of CaliforniaBerkeley, CA 94720 August 25, 20042 Table of ContentsTable of Contents3 Abstract9 Introduction11 Modelling Models and Physical Reality.. Concepts and Calculations.. Function of Hidden Variable.. A Look Back.. References.. 122 Probability Choosing At Random .. Events.. Countable Additivity.. Probability Space.. Examples.. Choosing uniformly in{1,2, .. , N}.. Choosing uniformly in [0,1].

Probability Theory is a mathematical model of uncertainty. In these notes, we introduce examples of uncertainty and we explain how the theory models them. It is important to appreciate the difierence between uncertainty in the physical world and the models of Probability Theory. That difierence is similar to that between laws of

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