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

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2 STOCHASTIC PROCESSES Lecture – 14Stochastic Processes - Introduction Lecture – 15 Poisson Processes Lecture – 16Mean Square Estimation Lecture – 17Long Term Trends and Hurst Phenomena Kalman Filters Lecture – 18Power Spectrum and its Estimation Lecture – 19Series 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 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 as the source of information. Any feedback may be addressed to

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Participants 3 Andrea Pisculli, Antonio Agresta, David Sassun, Federico Bunkheila, Giovanna Gargiulo, Marco Leonardi, Melissa Arras, Paolo D'Addio, Tanya Scalia, Alessandro Longo, Fabio Marra, Gianluca Facchini, Marzia Parisi, Stefania Gemma, Giacomo Rossi, Marco Eugeni, Michele Pasquali Marco Gregnanin

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