TABLE OF CONTENTS
PROBABILITY THEORY
Lecture – 1
Lecture – 2
Lecture – 3
Lecture – 4
Lecture – 5
Lecture – 6
Lecture – 7
Lecture – 8
Lecture – 9
Lecture – 10
Lecture – 11
Lecture – 12
Lecture – 13
Basics
Independence and Bernoulli Trials
Random Variables
Binomial Random Variable Applications, Conditional
Probability Density Function and Stirling’s Formula.
Function of a Random Variable
Mean, Variance, Moments and Characteristic Functions
Two Random Variables
One Function of Two Random Variables
Two Functions of Two Random Variables
Joint Moments and Joint Characteristic Functions
Conditional Density Functions and Conditional Expected Values
Principles of Parameter Estimation
The Weak Law and the Strong Law of Large numbers
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STOCHASTIC PROCESSES
Lecture – 14
Lecture – 15
Lecture – 16
Lecture – 17
Lecture – 18
Lecture – 19
Lecture – 20
Stochastic Processes - Introduction
Poisson Processes
Mean Square Estimation
Long Term Trends and Hurst Phenomena Kalman Filters
Power Spectrum and its Estimation
Series Representation of Stochastic Processes
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
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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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