Transcript Course Outline

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
1
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 [email protected]
2
Participants
Andrea Pisculli <[email protected]>,
Antonio Agresta <[email protected]>,
David Sassun <[email protected]>,
Federico Bunkheila <[email protected]>,
Giovanna Gargiulo <[email protected]>,
Marco Leonardi <[email protected]>,
Melissa Arras <[email protected]>,
Paolo D'Addio <[email protected]>,
Tanya Scalia <[email protected]>,
Alessandro Longo <[email protected]>,
Fabio Marra <[email protected]>,
Gianluca Facchini <[email protected]>,
Marzia Parisi <[email protected]>,
Stefania Gemma <[email protected]>,
Giacomo Rossi <[email protected]>,
Marco Eugeni <[email protected]>,
Michele Pasquali <[email protected]>
Marco Gregnanin <[email protected]>
3