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## Probability and random processes for electrical engineering / Alberto Leon-Garcia.

Editor: Reading, Mass. : Addison-Wesley, c1994Edición: 2nd edDescripción: xii, 596 p. : ill. ; 24 cmISBN: 020150037XOtra clasificación: *CODIGO*
Contenidos:
```CHAPTER 1 Probability Models in Electrical and Computer Engineering  --
1.1 Mathematical Models as Tools in Analysis and Design  --
1.2 Deterministic Models  --
1.3 Probability Models  --
Statistical Regularity  --
Properties of Relative Frequency  --
The Axiomatic Approach to a Theoty of Probability  --
Building a Probability Model  --
1.4 A Detailed Example: A Packet Voice Transmission System  --
1.5 Other Examples  --
Communication over Unreliable Channels  --
Processing of Random Signals  --
Resource S haring Systems  --
Reliability of Systems  --
1.6 Overview of Book  --
SUMMARY  --
PROBLEMS  --
CHAPTER 2 Basic Concepts of Probability Theory --
2.1 Specifying Random Experiments  --
The Sample Space  --
Events  --
Set Operations  --
2.2 The Axioms of Probability  --
Discrete Sample Spaces  --
Continuous Sample Spaces  --
*2.3 Computing Probabilities Using Counting Methods  --
Sampling with Replacement and with Ordering  --
Sampling without Replacement and with Ordering  --
Permutations of n Distinct Objects  --
Sampling without Replacement and without Ordering  --
Sampling with Replacement and without Ordering  --
2.4 Conditional Probability  --
Bayes’ Rule  --
2.5 Independence of Events  --
2.6 Sequential Experiments  --
Sequences of Independent Experiments  --
The Binomial Probability Law  --
The Multinomial Probability Law  --
The Geometric Probability Law 66 Sequences of Dependent Experiments  --
2.7 A Computer Method for Synthesizing Randomness: Random Number Generators  --
SUMMARY  --
PROBLEMS  --
CHAPTER 3 Random Variables  --
3.1 The Notion of a Random Variable  --
3.2 The Cumulative Distribution Function  --
The Three Types of Random Variables  --
3.3 The Probability Density Function  --
Conditional cdf’s and pdf's  --
3.4 Some Important Random Variables  --
Discrete Random Variables  --
Continuous Random Variables  --
3.5 Functions of a Random Variable  --
3.6 The Expected Value of Random Variables  --
The Expected Value of X  --
The Expected Value ofY = g(X)  --
Variance of X  --
3.7 The Markov and Chebyshev Inequalities  --
3.8 Testing the Fit of a Distribution to Data  --
3.9 Transform Methods  --
The Characteristic Function  --
The Probability Generating Function  --
The Laplace Transform of the pdf I49 --
3.10 Basic Reliability Calculations  --
The Failure Rate Function  --
Reliability of Systems  --
3.11 Computer Methods for Generating Random Variables  --
The Transformation Method  --
The Rejection Method  --
Generation of Functions of a Random Variable  --
Generating M ixtures of Random Variables --
3.12 Entropy  --
The Entropy of a Random Variable  --
Entropy as a M easure of Information  --
The Method of Maximum Entropy  --
SUMMARY  --
PROBLEMS  --
CHAPTER 4 Multiple Random Variables  --
4.1 Vector Random Variables  --
Events and Probabilities  --
Independence  --
4.2 Pairs of Random Variables --
Pairs of Discrete Random Variables 195  --
The Joint cdf of X and Y  --
7 he Joint pdf of Two Jointly Continuous Random Variables  --
Random Variables That Differ in Type  --
4.3 Independence of Two Random Variables  --
4.4 Conditional Probability and Conditional Expectation  --
Conditional Probability  --
Conditional Expectation  --
4.5 Multiple Random Variables  --
Joint Distributions  --
Independence  --
4.6 Functions of Several Random Variables  --
One Function of Several Random Variables 22  --
Transformations of Random Vectors  --
pdf of Linear Transformations  --
*pdf of General Transformations  --
4.7 Expected Value of Functions of Random Variables  --
The Correlation and Covariance of Two Random Variables  --
*Joint Characteristic Function  --
4.8 Jointly Gaussian Random Variables  --
n Jointly Gaussian Random Variables  --
* Linear Transformation of Gaussian Random Variables  --
* Joint Characteristic Function of Gaussian Random Variables  --
4.9 Mean Square Estimation  --
* Linear Prediction  --
4.10 Generating Correlated Vector Random Variables  --
Generating Vectors of Random Variables with Specified Covariances  --
Generating Vectors of Jointly Gaussian Random Variables  --
SUMMARY  --
PROBLEMS  --
CHAPTER 5 Sums of Random Variables and Long-Term Averages  --
5.1 Sums of Random Variables  --
Mean and Variance of Sums of Random Variables  --
pdf of Sums of Independent Random Variables  --
*Sum of a Random Number of Random Variables  --
5.2 The Sample Mean and the Laws of Large Numbers  --
5.3 The Central Limit Theorem  --
Gaussian Approximation for Binomial Probabilities  --
* Proof of the Central Limit Theorem  --
5.4 Confidence Intervals  --
Case 1: Xfs Gaussian; Unknown Mean and Known Variance  --
Case 2: X/s Gaussian; Mean and Variance Unknown  --
Case 3: Xfs Non-Gaussian; Mean and Variance Unknown  --
5.5 Convergence of Sequences of Random Variables  --
5.6 Long-Term Arrival Rates and Associated Averages  --
Long-Term Time Averages  --
5.7 A Computer Method for Evaluating the Distribution of a Random --
Variable Using the Discrete Fourier Transform  --
Discrete Random Variables  --
Continuous Random Variables  --
SUMMARY  --
PROBLEMS  --
APPENDIX 5.1: Subroutine FFT(A,M,N)  --
CHAPTER 6 Random Processes  --
6.1 Definition of a Random Process  --
6.2 Specifying a Random Process  --
Joint Distributions of Time Samples  --
The Mean, Autocorrelation, and Autocovariance Functions  --
Gaussian Random Processes  --
Multiple Random Processes  --
6.3 Examples of Discrete-Time Random Processes  --
iid Random Processes  --
Sum Processes'. The Binomial Counting and Random Walk Processes  --
6.4 Examples of Continuous-Time Random Processes  --
Poisson Process  --
Random Telegraph Signal and Other Processes Derived from the Poisson Process  --
Wiener Process and Brownian Motion  --
6.5 Stationary Random Processes  --
Wide-Sense Slationary Random Processes 35  --
Wide-Sense Stationary Gaussian Random Processes  --
Cyclostationary Random Processes  --
6.6 Continuity, Derivatives, and Integrals of Random Processes  --
Mean Square Continuity  --
Mean Square Derivatives  --
Mean Square Integrals  --
Response of a Linear System to Random Input  --
6.7 Time Averages of Random Processes and Ergodic Theorems  --
6.8 Fourier Series and Karhunen-Loeve Expansion  --
Karhunen-Loeve Expansion  --
SUMMARY  --
PROBLEMS  --
CHAPTER 7 Analysis and Processing of Random Signals  --
7.1 Power Spectral Density  --
Continuous-Time Random Processes  --
Discrete-Time Random Processes  --
Power Spectral Density as a Time Average  --
7.2 Response of Linear Systems to Random Signals  --
Continuous-Time Systems  --
Discrete-Time Systems  --
7.3 Amplitude Modulation by Random Signals  --
7.4 Optimum Linear Systems  --
The Orthogonality Condition  --
Prediction  --
Estimation Using the Entire Realization of the Observed Process  --
*Estimation Using Causal Filters  --
7.5 The Kalman Filter  --
7.6 Estimating the Power Spectral Density  --
Variance of Periodogram Estimate  --
Smoothing of Periodogram Estimate  --
SUMMARY  --
PROBLEMS  --
CHAPTER 8 Markov Chains  --
8.1 Markov Processes  --
8.2 Discrete-Time Markov Chains  --
The n-step Transition Probabilities  --
The State Probabilities  --
8.3 Continuous-Time Markov Chains  --
State Occupancy Times  --
Transition Rates and Time-Dependent State Probabilities  --
Steady State Probabilities and Global Balance Equations  --
8.4 Classes of States, Recurrence Properties, and Limiting Probabilities  --
Classes of States  --
Recurrence Properties  --
Limiting Probabilities  --
Limiting Probabilities for Continuous-Time Markov Chains  --
8.5 Time-Reversed Markov Chains  --
Time-Reversible Markov Chains  --
Time-Reversible Continuous-Time Markov Chains  --
SUMMARY  --
PROBLEMS  --
CHAPTER 9 Introduction to Queueing Theory  --
9.1 The Elements of a Queueing System  --
9.2 Little’s Formula  --
9.3 The M/M/1 Queue  --
Distribution of Number in the System  --
Delay Distribution in M /M /1 System and Arriving Customer's Distribution  --
The M /M /1 System with Finite Capacity  --
9.4 Multi-Server Systems: M/M/c, M/M/c/c, and M/M/<»  --
Distribution of Number in the M /M/c System  --
Waiting Time Distribution for M /M /c  --
The M/M/c/c Queueing System  --
The M /M /°° Queueing System  --
9.5 Finite-Source Queueing Systems  --
Arriving Customer's Distribution  --
9.6 M/G/l Queueing Systems  --
The Residual Service Time  --
Mean Delay in M /G /1 Systems  --
Mean Delay in M/G/1 Systems with Priority Service Discipline  --
9.7 M/G/l Analysis Using Embedded Markov Chains  --
The Embedded Markov Chain  --
The Number of Customers in an M/G/1 System  --
Delay and Waiting Time Distribution in an M/G/1 System  --
9.8 Burke’s Theorem: Departures from M/M/c Systems  --
Proof of Burke's Theorem Using Time Reversibility  --
9.9 Networks of Queues: Jackson’s Theorem  --
Open Networks of Queues  --
Proof of Jackson's Theorem  --
Closed Networks of Queues  --
Mean Value Analysis  --
Proof of the Arrival Theorem  --
SUMMARY  --
PROBLEMS  --
APPENDIXES --
A. Mathematical Tables  --
B. Tables of Fourier Transforms  --
C. Computer Programs for Generating Random Variables  --
Answers to Selected Problems  --
Index  --``` Average rating: 0.0 (0 votes)
Item type Home library Shelving location Call number Materials specified Status Date due Barcode Libros
Libros ordenados por tema 60 L579-2 (Browse shelf) Available A-9349
##### Browsing Instituto de Matemática, CONICET-UNS shelves, Shelving location: Libros ordenados por tema Close shelf browser
 60 L314 A philosophical essay on probabilities / 60 L434 Extremes and related properties of random sequences and processes / 60 L496 Les systèmes avec ou sans attente et les processus sotchastiques. 60 L579-2 Probability and random processes for electrical engineering / 60 L629 Heads or tails : 60 L645 Chaînes de Markov sur les permutations / 60 L668 Processus stochastiques et mouvement brownien /

Includes index.

CHAPTER 1 Probability Models in Electrical and Computer Engineering  --
1.1 Mathematical Models as Tools in Analysis and Design  --
1.2 Deterministic Models  --
1.3 Probability Models  --
Statistical Regularity  --
Properties of Relative Frequency  --
The Axiomatic Approach to a Theoty of Probability  --
Building a Probability Model  --
1.4 A Detailed Example: A Packet Voice Transmission System  --
1.5 Other Examples  --
Communication over Unreliable Channels  --
Processing of Random Signals  --
Resource S haring Systems  --
Reliability of Systems  --
1.6 Overview of Book  --
SUMMARY  --
PROBLEMS  --
CHAPTER 2 Basic Concepts of Probability Theory --
2.1 Specifying Random Experiments  --
The Sample Space  --
Events  --
Set Operations  --
2.2 The Axioms of Probability  --
Discrete Sample Spaces  --
Continuous Sample Spaces  --
*2.3 Computing Probabilities Using Counting Methods  --
Sampling with Replacement and with Ordering  --
Sampling without Replacement and with Ordering  --
Permutations of n Distinct Objects  --
Sampling without Replacement and without Ordering  --
Sampling with Replacement and without Ordering  --
2.4 Conditional Probability  --
Bayes’ Rule  --
2.5 Independence of Events  --
2.6 Sequential Experiments  --
Sequences of Independent Experiments  --
The Binomial Probability Law  --
The Multinomial Probability Law  --
The Geometric Probability Law 66 Sequences of Dependent Experiments  --
2.7 A Computer Method for Synthesizing Randomness: Random Number Generators  --
SUMMARY  --
PROBLEMS  --
CHAPTER 3 Random Variables  --
3.1 The Notion of a Random Variable  --
3.2 The Cumulative Distribution Function  --
The Three Types of Random Variables  --
3.3 The Probability Density Function  --
Conditional cdf’s and pdf's  --
3.4 Some Important Random Variables  --
Discrete Random Variables  --
Continuous Random Variables  --
3.5 Functions of a Random Variable  --
3.6 The Expected Value of Random Variables  --
The Expected Value of X  --
The Expected Value ofY = g(X)  --
Variance of X  --
3.7 The Markov and Chebyshev Inequalities  --
3.8 Testing the Fit of a Distribution to Data  --
3.9 Transform Methods  --
The Characteristic Function  --
The Probability Generating Function  --
The Laplace Transform of the pdf I49 --
3.10 Basic Reliability Calculations  --
The Failure Rate Function  --
Reliability of Systems  --
3.11 Computer Methods for Generating Random Variables  --
The Transformation Method  --
The Rejection Method  --
Generation of Functions of a Random Variable  --
Generating M ixtures of Random Variables --
3.12 Entropy  --
The Entropy of a Random Variable  --
Entropy as a M easure of Information  --
The Method of Maximum Entropy  --
SUMMARY  --
PROBLEMS  --
CHAPTER 4 Multiple Random Variables  --
4.1 Vector Random Variables  --
Events and Probabilities  --
Independence  --
4.2 Pairs of Random Variables --
Pairs of Discrete Random Variables 195  --
The Joint cdf of X and Y  --
7 he Joint pdf of Two Jointly Continuous Random Variables  --
Random Variables That Differ in Type  --
4.3 Independence of Two Random Variables  --
4.4 Conditional Probability and Conditional Expectation  --
Conditional Probability  --
Conditional Expectation  --
4.5 Multiple Random Variables  --
Joint Distributions  --
Independence  --
4.6 Functions of Several Random Variables  --
One Function of Several Random Variables 22  --
Transformations of Random Vectors  --
pdf of Linear Transformations  --
*pdf of General Transformations  --
4.7 Expected Value of Functions of Random Variables  --
The Correlation and Covariance of Two Random Variables  --
*Joint Characteristic Function  --
4.8 Jointly Gaussian Random Variables  --
n Jointly Gaussian Random Variables  --
* Linear Transformation of Gaussian Random Variables  --
* Joint Characteristic Function of Gaussian Random Variables  --
4.9 Mean Square Estimation  --
* Linear Prediction  --
4.10 Generating Correlated Vector Random Variables  --
Generating Vectors of Random Variables with Specified Covariances  --
Generating Vectors of Jointly Gaussian Random Variables  --
SUMMARY  --
PROBLEMS  --
CHAPTER 5 Sums of Random Variables and Long-Term Averages  --
5.1 Sums of Random Variables  --
Mean and Variance of Sums of Random Variables  --
pdf of Sums of Independent Random Variables  --
*Sum of a Random Number of Random Variables  --
5.2 The Sample Mean and the Laws of Large Numbers  --
5.3 The Central Limit Theorem  --
Gaussian Approximation for Binomial Probabilities  --
* Proof of the Central Limit Theorem  --
5.4 Confidence Intervals  --
Case 1: Xfs Gaussian; Unknown Mean and Known Variance  --
Case 2: X/s Gaussian; Mean and Variance Unknown  --
Case 3: Xfs Non-Gaussian; Mean and Variance Unknown  --
5.5 Convergence of Sequences of Random Variables  --
5.6 Long-Term Arrival Rates and Associated Averages  --
Long-Term Time Averages  --
5.7 A Computer Method for Evaluating the Distribution of a Random --
Variable Using the Discrete Fourier Transform  --
Discrete Random Variables  --
Continuous Random Variables  --
SUMMARY  --
PROBLEMS  --
APPENDIX 5.1: Subroutine FFT(A,M,N)  --
CHAPTER 6 Random Processes  --
6.1 Definition of a Random Process  --
6.2 Specifying a Random Process  --
Joint Distributions of Time Samples  --
The Mean, Autocorrelation, and Autocovariance Functions  --
Gaussian Random Processes  --
Multiple Random Processes  --
6.3 Examples of Discrete-Time Random Processes  --
iid Random Processes  --
Sum Processes'. The Binomial Counting and Random Walk Processes  --
6.4 Examples of Continuous-Time Random Processes  --
Poisson Process  --
Random Telegraph Signal and Other Processes Derived from the Poisson Process  --
Wiener Process and Brownian Motion  --
6.5 Stationary Random Processes  --
Wide-Sense Slationary Random Processes 35  --
Wide-Sense Stationary Gaussian Random Processes  --
Cyclostationary Random Processes  --
6.6 Continuity, Derivatives, and Integrals of Random Processes  --
Mean Square Continuity  --
Mean Square Derivatives  --
Mean Square Integrals  --
Response of a Linear System to Random Input  --
6.7 Time Averages of Random Processes and Ergodic Theorems  --
6.8 Fourier Series and Karhunen-Loeve Expansion  --
Karhunen-Loeve Expansion  --
SUMMARY  --
PROBLEMS  --
CHAPTER 7 Analysis and Processing of Random Signals  --
7.1 Power Spectral Density  --
Continuous-Time Random Processes  --
Discrete-Time Random Processes  --
Power Spectral Density as a Time Average  --
7.2 Response of Linear Systems to Random Signals  --
Continuous-Time Systems  --
Discrete-Time Systems  --
7.3 Amplitude Modulation by Random Signals  --
7.4 Optimum Linear Systems  --
The Orthogonality Condition  --
Prediction  --
Estimation Using the Entire Realization of the Observed Process  --
*Estimation Using Causal Filters  --
7.5 The Kalman Filter  --
7.6 Estimating the Power Spectral Density  --
Variance of Periodogram Estimate  --
Smoothing of Periodogram Estimate  --
SUMMARY  --
PROBLEMS  --
CHAPTER 8 Markov Chains  --
8.1 Markov Processes  --
8.2 Discrete-Time Markov Chains  --
The n-step Transition Probabilities  --
The State Probabilities  --
8.3 Continuous-Time Markov Chains  --
State Occupancy Times  --
Transition Rates and Time-Dependent State Probabilities  --
Steady State Probabilities and Global Balance Equations  --
8.4 Classes of States, Recurrence Properties, and Limiting Probabilities  --
Classes of States  --
Recurrence Properties  --
Limiting Probabilities  --
Limiting Probabilities for Continuous-Time Markov Chains  --
8.5 Time-Reversed Markov Chains  --
Time-Reversible Markov Chains  --
Time-Reversible Continuous-Time Markov Chains  --
SUMMARY  --
PROBLEMS  --
CHAPTER 9 Introduction to Queueing Theory  --
9.1 The Elements of a Queueing System  --
9.2 Little’s Formula  --
9.3 The M/M/1 Queue  --
Distribution of Number in the System  --
Delay Distribution in M /M /1 System and Arriving Customer's Distribution  --
The M /M /1 System with Finite Capacity  --
9.4 Multi-Server Systems: M/M/c, M/M/c/c, and M/M/<»  --
Distribution of Number in the M /M/c System  --
Waiting Time Distribution for M /M /c  --
The M/M/c/c Queueing System  --
The M /M /°° Queueing System  --
9.5 Finite-Source Queueing Systems  --
Arriving Customer's Distribution  --
9.6 M/G/l Queueing Systems  --
The Residual Service Time  --
Mean Delay in M /G /1 Systems  --
Mean Delay in M/G/1 Systems with Priority Service Discipline  --
9.7 M/G/l Analysis Using Embedded Markov Chains  --
The Embedded Markov Chain  --
The Number of Customers in an M/G/1 System  --
Delay and Waiting Time Distribution in an M/G/1 System  --
9.8 Burke’s Theorem: Departures from M/M/c Systems  --
Proof of Burke's Theorem Using Time Reversibility  --
9.9 Networks of Queues: Jackson’s Theorem  --
Open Networks of Queues  --
Proof of Jackson's Theorem  --
Closed Networks of Queues  --
Mean Value Analysis  --
Proof of the Arrival Theorem  --
SUMMARY  --
PROBLEMS  --
APPENDIXES --
A. Mathematical Tables  --
B. Tables of Fourier Transforms  --
C. Computer Programs for Generating Random Variables  --
Answers to Selected Problems  --
Index  --

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