Intuitive Probability And Random Processes Using Matlab,9780387241579

Intuitive Probability And Random Processes Using Matlab

by
ISBN13: 9780387241579
ISBN10: 0387241574
Format: Hardcover
Pub. Date: 2005-12-30
Publisher(s): SPRINGER - VERLAG
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Summary

This book covers:- The use of MATLAB examples to provide motivation for the theory to come.- The incorporation of MATLAB code to allow students to understand how the theory is applied in practice.- Numerous computer exercises to familiarize the student with MATLAB and how it is used to solve real problems.- The incorporation of "real-world" problems from various disciplines in each chapter to illlustrate the application of the chapter concepts.- Discussion of discrete random variables first, followed by continuous random variables to minimize confusion.

Author Biography

Steven M. Kay is a Professor of Electrical Engineering at the University of Rhode Island.

Table of Contents

Preface vii
Introduction
1(12)
What Is Probability?
1(2)
Types of Probability Problems
3(1)
Probabilistic Modeling
4(3)
Analysis versus Computer Simulation
7(1)
Some Notes to the Reader
8(5)
References
9(1)
Problems
10(3)
Computer Simulation
13(24)
Introduction
13(1)
Summary
13(1)
Why Use Computer Simulation?
14(3)
Computer Simulation of Random Phenomena
17(1)
Determining Characteristics of Random Variables
18(6)
Real-World Example -- Digital Communications
24(7)
References
26(1)
Problems
26(5)
Brief Introduction to MATLAB
31(6)
Basic Probability
37(36)
Introduction
37(1)
Summary
37(1)
Review of Set Theory
38(5)
Assigning and Determining Probabilities
43(5)
Properties of the Probability Function
48(4)
Probabilities for Continuous Sample Spaces
52(2)
Probabilities for Finite Sample Spaces -- Equally Likely Outcomes
54(1)
Combinatorics
55(7)
Binomial Probability Law
62(2)
Real-World Example -- Quality Control
64(9)
References
66(1)
Problems
66(7)
Conditional Probability
73(32)
Introduction
73(1)
Summary
73(1)
Joint Events and the Conditional Probability
74(9)
Statistically Independent Events
83(3)
Bayes' Theorem
86(3)
Multiple Experiments
89(8)
Real-World Example -- Cluster Recognition
97(8)
References
100(1)
Problems
100(5)
Discrete Random Variables
105(28)
Introduction
105(1)
Summary
105(1)
Definition of Discrete Random Variable
106(2)
Probability of Discrete Random Variables
108(3)
Important Probability Mass Functions
111(2)
Approximation of Binomial PMF by Poisson PMF
113(2)
Transformation of Discrete Random Variables
115(2)
Cumulative Distribution Function
117(5)
Computer Simulation
122(2)
Real-World Example -- Servicing Customers
124(9)
References
128(1)
Problems
128(5)
Expected Values for Discrete Random Variables
133(34)
Introduction
133(1)
Summary
133(1)
Determining Averages from the PMF
134(3)
Expected Values of Some Important Random Variables
137(3)
Expected Value for a Function of a Random Variable
140(3)
Variance and Moments of a Random Variable
143(4)
Characteristic Functions
147(6)
Estimating Means and Variances
153(2)
Real-World Example -- Data Compression
155(8)
References
157(1)
Problems
158(5)
Derivation of E[g(X)] Formula
163(2)
MATLAB Code Used to Estimate Mean and Variance
165(2)
Multiple Discrete Random Variables
167(48)
Introduction
167(1)
Summary
168(1)
Jointly Distributed Random Variables
169(5)
Marginal PMFs and CDFs
174(4)
Independence of Multiple Random Variables
178(3)
Transformations of Multiple Random Variables
181(5)
Expected Values
186(3)
Joint Moments
189(3)
Prediction of a Random Variable Outcome
192(6)
Joint Characteristic Functions
198(2)
Computer Simulation of Random Vectors
200(2)
Real-World Example Assessing Health Risks
202(11)
References
204(1)
Problems
204(9)
Derivation of the Cauchy-Schwarz Inequality
213(2)
Conditional Probability Mass Functions
215(32)
Introduction
215(1)
Summary
216(1)
Conditional Probability Mass Function
217(3)
Joint, Conditional, and Marginal PMFs
220(5)
Simplifying Probability Calculations using Conditioning
225(4)
Mean of the Conditional PMF
229(6)
Computer Simulation Based on Conditioning
235(2)
Real-World Example -- Modeling Human Learning
237(10)
References
240(1)
Problems
240(7)
Discrete N-Dimensional Random Variables
247(38)
Introduction
247(1)
Summary
247(1)
Random Vectors and Probability Mass Functions
248(3)
Transformations
251(4)
Expected Values
255(10)
Joint Moments and the Characteristic Function
265(1)
Conditional Probability Mass Functions
266(3)
Computer Simulation of Random Vectors
269(3)
Real-World Example -- Image Coding
272(13)
References
277(1)
Problems
277(8)
Continuous Random Variables
285(58)
Introduction
285(1)
Summary
286(1)
Definition of a Continuous Random Variable
287(6)
The PDF and Its Properties
293(2)
Important PDFs
295(8)
Cumulative Distribution Functions
303(8)
Transformations
311(6)
Mixed Random Variables
317(7)
Computer Simulation
324(4)
Real-World Example -- Setting Clipping Levels
328(11)
References
331(1)
Problems
331(8)
Derivation of PDF of a Transformed Continuous Random Variable
339(2)
MATLAB Subprograms to Compute Q and Inverse Q Functions
341(2)
Expected Values for Continuous Random Variables
343(34)
Introduction
343(1)
Summary
343(1)
Determining the Expected Value
344(5)
Expected Values for Important PDFs
349(2)
Expected Value for a Function of a Random Variable
351(4)
Variance and Moments
355(4)
Characteristic Functions
359(2)
Probability, Moments, and the Chebyshev Inequality
361(2)
Estimating the Mean and Variance
363(1)
Real-World Example -- Critical Software Testing
364(11)
References
367(1)
Problems
367(8)
Partial Proof of Expected Value of Function of Continuous Random Variable
375(2)
Multiple Continuous Random Variables
377(56)
Introduction
377(1)
Summary
378(1)
Jointly Distributed Random Variables
379(8)
Marginal PDFs and the Joint CDF
387(5)
Independence of Multiple Random Variables
392(2)
Transformations
394(10)
Expected Values
404(8)
Joint Moments
412(1)
Prediction of Random Variable Outcome
412(2)
Joint Characteristic Functions
414(1)
Computer Simulation
415(4)
Real-World Example - Optical Character Recognition
419(14)
References
423(1)
Problems
423(10)
Conditional Probability Density Functions
433(24)
Introduction
433(1)
Summary
433(1)
Conditional PDF
434(6)
Joint, Conditional, and Marginal PDFs
440(4)
Simplifying Probability Calculations Using Conditioning
444(2)
Mean of Conditional PDF
446(1)
Computer Simulation of Jointly Continuous Random Variables
447(2)
Real-World Example -- Retirement Planning
449(8)
References
452(1)
Problems
452(5)
Continuous N-Dimensional Random Variables
457(28)
Introduction
457(1)
Summary
457(1)
Random Vectors and PDFs
458(5)
Transformations
463(2)
Expected Values
465(2)
Joint Moments and the Characteristic Function
467(4)
Conditional PDFs
471(1)
Prediction of a Random Variable Outcome
471(4)
Computer Simulation of Gaussian Random Vectors
475(1)
Real-World Example -- Signal Detection
476(9)
References
479(1)
Problems
479(6)
Probability and Moment Approximations Using Limit Theorems
485(30)
Introduction
485(1)
Summary
486(1)
Convergence and Approximation of a Sum
486(1)
Law of Large Numbers
487(5)
Central Limit Theorem
492(11)
Real-World Example -- Opinion Polling
503(8)
References
506(1)
Problems
507(4)
MATLAB Program to Compute Repeated Convolution of PDFs
511(2)
Proof of Central Limit Theorem
513(2)
Basic Random Processes
515(32)
Introduction
515(1)
Summary
516(1)
What Is a Random Process?
517(3)
Types of Random Processes
520(3)
The Important, Property of Stationarity
523(5)
Some More Examples
528(5)
Joint Moments
533(5)
Real-World Example - Statistical Data Analysis
538(9)
References
542(1)
Problems
542(5)
Wide Sense Stationary Random Processes
547(50)
Introduction
547(1)
Summary
548(1)
Definition of WSS Random Process
549(3)
Autocorrelation Sequence
552(10)
Ergodicity and Temporal Averages
562(5)
The Power Spectral Density
567(9)
Estimation of the ACS and PSD
576(4)
Continuous-Time WSS Random Processes
580(6)
Real-World Example - Random Vibration Testing
586(11)
References
589(1)
Problems
590(7)
Linear Systems and Wide Sense Stationary Random Processes
597(44)
Introduction
597(1)
Summary
598(1)
Random Process at Output of Linear System
598(9)
Interpretation of the PSD
607(2)
Wiener Filtering
609(14)
Continuous-Time Definitions and Formulas
623(3)
Real-World Example -- Speech Synthesis
626(11)
References
630(1)
Problems
631(6)
Solution for Infinite Length Predictor
637(4)
Multiple Wide Sense Stationary Random Processes
641(32)
Introduction
641(1)
Summary
642(1)
Jointly Distributed WSS Random Processes
642(5)
The Cross-Power Spectral Density
647(5)
Transformations of Multiple Random Processes
652(5)
Continuous-Time Definitions and Formulas
657(4)
Cross-Correlation Sequence Estimation
661(2)
Real-World Example -- Brain Physiology Research
663(10)
References
667(1)
Problems
667(6)
Gaussian Random Processes
673(38)
Introduction
673(2)
Summary
675(1)
Definition of the Gaussian Random Process
676(5)
Linear Transformations
681(2)
Nonlinear Transformations
683(3)
Continuous-Time Definitions and Formulas
686(3)
Special Continuous-Time Gaussian Random Processes
689(7)
Computer Simulation
696(2)
Real-World Example -- Estimating Fish Populations
698(11)
References
701(1)
Problems
702(7)
MATLAB Listing for Figure 20.2
709(2)
Poisson Random Processes
711(28)
Introduction
711(2)
Summary
713(1)
Derivation of Poisson Counting Random Process
714(4)
Interarrival Times
718(3)
Arrival Times
721(2)
Compound Poisson Random Process
723(4)
Computer Simulation
727(1)
Real-World Example -- Automobile Traffic Signal Planning
728(9)
References
732(1)
Problems
732(5)
Joint PDF for Interarrival Times
737(2)
Markov Chains
739(38)
Introduction
739(5)
Summary
744(1)
Definitions
744(4)
Computation of State Probabilities
748(8)
Ergodic Markov Chains
756(3)
Further Steady-State Characteristics
759(3)
K-State Markov Chains
762(2)
Computer Simulation
764(1)
Real-World Example -- Strange Markov Chain Dynamics
765(10)
References
767(1)
Problems
767(8)
Solving for the Stationary PMF
775(2)
A. Glossary of Symbols and Abbrevations
777(6)
B. Assorted Math Facts and Formulas
783(6)
B.1 Proof by Induction
783(1)
B.2 Trigonometry
784(1)
B.3 Limits
784(1)
B.4 Sums
785(1)
B.5 Calculus
786(3)
C. Linear and Matrix Algebra
789(6)
C.1 Definitions
789(2)
C.2 Special Matrices
791(1)
C.3 Matrix Manipulation and Formulas
792(1)
C.4 Some Properties of PD (PSD) Matrices
793(1)
C.5 Eigendecomposition of Matrices
793(2)
D. Summary of Signals, Linear Transforms, and Linear Systems
795(14)
D.1 Discrete-Time Signals
795(1)
D.2 Linear Transforms
796(4)
D.3 Discrete-Time Linear Systems
800(4)
D.4 Continuous-Time Signals
804(1)
D.5 Linear Transforms
805(2)
D.6 Continuous-Time Linear Systems
807(2)
E. Answers to Selected Problems
809(14)
Index 823

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