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TABLE OF CONTENTS PROBABILITY THEORY Lecture – 1 Basics

TABLE OF CONTENTS PROBABILITY THEORY Lecture – 1 Basics Lecture – 2 Independence and Bernoulli Trials Lecture – 3 Random Variables Lecture – 4 Binomial Random Variable Applications, Conditional

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TABLE OF CONTENTS PROBABILITY THEORY Lecture – 1 Basics

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  1. TABLE OF CONTENTS PROBABILITY THEORY Lecture – 1 Basics Lecture – 2 Independence and Bernoulli Trials Lecture – 3 Random Variables Lecture – 4 Binomial Random Variable Applications, Conditional Probability Density Function and Stirling’s Formula. Lecture – 5 Function of a Random Variable Lecture – 6 Mean, Variance, Moments and Characteristic Functions Lecture – 7 Two Random Variables Lecture – 8 One Function of Two Random Variables Lecture – 9 Two Functions of Two Random Variables Lecture – 10 Joint Moments and Joint Characteristic Functions Lecture – 11 Conditional Density Functions and Conditional Expected Values Lecture – 12 Principles of Parameter Estimation Lecture – 13 The Weak Law and the Strong Law of Large numbers

  2. STOCHASTIC PROCESSES Lecture – 14 Stochastic Processes - Introduction Lecture – 15 Poisson Processes Lecture – 16 Mean Square Estimation Lecture – 17 Long Term Trends and Hurst PhenomenaKalman Filters Lecture – 18 Power Spectrum and its Estimation Lecture – 19 Series Representation of Stochastic Processes Lecture – 20 Extinction Probability for Queues and Martingales Note: These lecture notes are revised periodically with new materials and examples added from time to time. Lectures 1 11 are used at Polytechnic for a first level graduate course on “Probability theory and Random Variables”. Parts of lectures 14 19 are used at Polytechnic for a “Stochastic Processes” course. These notes are intended for unlimited worldwide use. However the user must acknowledge the present website www.mhhe.com/papoulis as the source of information. Any feedback may be addressed to pillai@hora.poly.edu

  3. Participants Andrea Pisculli <andreapisculli@libero.it>, Antonio Agresta <ant.agr@gmail.com>, David Sassun <david-s@hotmail.it>, Federico Bunkheila <fbunkheila@gmail.com>, Giovanna Gargiulo <adamas.hs@libero.it>, Marco Leonardi <marco.leonardi@uniroma1.it>, Melissa Arras <melissa.arras@uniroma1.it>, Paolo D'Addio <paolodaddio@msn.com>, Tanya Scalia <tanya_1974@libero.it>, Alessandro Longo <alessandro.longo@uniroma1.it>, Fabio Marra <f.marra86@gmail.com>, Gianluca Facchini <gianluca.facchini@uniroma1.it>, Marzia Parisi <marzia.parisi@uniroma1.it>, Stefania Gemma <stefania.gemma@uniroma1.it>, Giacomo Rossi <rossigiacomo82@gmail.com>, Marco Eugeni <marco.eugeni@uniroma1.it>, Michele Pasquali <michele.pasquali@uniroma1.it> Marco Gregnanin <marco.gregnanin@uniroma1.it>

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