Probability and random processes for electrical engineering / Alberto Leon-Garcia.
Editor: Reading, Mass. : Addison-Wesley, c1994Edición: 2nd edDescripción: xii, 596 p. : ill. ; 24 cmISBN: 020150037XTema(s): Electrical engineering -- Mathematics | Probabilities | Stochastic processesOtra clasificación: *CODIGO*CHAPTER 1 Probability Models in Electrical and Computer Engineering [1] -- 1.1 Mathematical Models as Tools in Analysis and Design [2] -- 1.2 Deterministic Models [4] -- 1.3 Probability Models [4] -- Statistical Regularity [5] -- Properties of Relative Frequency [6] -- The Axiomatic Approach to a Theoty of Probability [8] -- Building a Probability Model [9] -- 1.4 A Detailed Example: A Packet Voice Transmission System [9] -- 1.5 Other Examples [13] -- Communication over Unreliable Channels [13] -- Processing of Random Signals [14] -- Resource S haring Systems [14] -- Reliability of Systems [17] -- 1.6 Overview of Book [18] -- SUMMARY [19] -- PROBLEMS [20] -- CHAPTER 2 Basic Concepts of Probability Theory -- 2.1 Specifying Random Experiments [23] -- The Sample Space [24] -- Events [27] -- Set Operations [28] -- 2.2 The Axioms of Probability [31] -- Discrete Sample Spaces [35] -- Continuous Sample Spaces [38] -- *2.3 Computing Probabilities Using Counting Methods [42] -- Sampling with Replacement and with Ordering [43] -- Sampling without Replacement and with Ordering [43] -- Permutations of n Distinct Objects [44] -- Sampling without Replacement and without Ordering [45] -- Sampling with Replacement and without Ordering [48] -- 2.4 Conditional Probability [48] -- Bayes’ Rule [53] -- 2.5 Independence of Events [54] -- 2.6 Sequential Experiments [60] -- Sequences of Independent Experiments [61] -- The Binomial Probability Law [61] -- The Multinomial Probability Law [65] -- The Geometric Probability Law 66 Sequences of Dependent Experiments [66] -- 2.7 A Computer Method for Synthesizing Randomness: Random Number Generators [69] -- SUMMARY [71] -- PROBLEMS [73] -- CHAPTER 3 Random Variables [84] -- 3.1 The Notion of a Random Variable [84] -- 3.2 The Cumulative Distribution Function [87] -- The Three Types of Random Variables [92] -- 3.3 The Probability Density Function [93] -- Conditional cdf’s and pdf's [98] -- 3.4 Some Important Random Variables [99] -- Discrete Random Variables [99] -- Continuous Random Variables [110] -- 3.5 Functions of a Random Variable [119] -- 3.6 The Expected Value of Random Variables [126] -- The Expected Value of X [127] -- The Expected Value ofY = g(X) [130] -- Variance of X [133] -- 3.7 The Markov and Chebyshev Inequalities [137] -- 3.8 Testing the Fit of a Distribution to Data [138] -- 3.9 Transform Methods [144] -- The Characteristic Function [145] -- The Probability Generating Function [148] -- The Laplace Transform of the pdf I49 -- 3.10 Basic Reliability Calculations [150] -- The Failure Rate Function [150] -- Reliability of Systems [153] -- 3.11 Computer Methods for Generating Random Variables [155] -- The Transformation Method [155] -- The Rejection Method [158] -- Generation of Functions of a Random Variable [161] -- Generating M ixtures of Random Variables -- 3.12 Entropy [162] -- The Entropy of a Random Variable [162] -- Entropy as a M easure of Information [167] -- The Method of Maximum Entropy [170] -- SUMMARY [172] -- PROBLEMS [174] -- CHAPTER 4 Multiple Random Variables [191] -- 4.1 Vector Random Variables [191] -- Events and Probabilities [192] -- Independence [194] -- 4.2 Pairs of Random Variables -- Pairs of Discrete Random Variables 195 [195] -- The Joint cdf of X and Y [197] -- 7 he Joint pdf of Two Jointly Continuous Random Variables [201] -- Random Variables That Differ in Type [206] -- 4.3 Independence of Two Random Variables [207] -- 4.4 Conditional Probability and Conditional Expectation [210] -- Conditional Probability [210] -- Conditional Expectation [215] -- 4.5 Multiple Random Variables [217] -- Joint Distributions [217] -- Independence [220] -- 4.6 Functions of Several Random Variables [221] -- One Function of Several Random Variables 22 [1] -- Transformations of Random Vectors [224] -- pdf of Linear Transformations [225] -- *pdf of General Transformations [227] -- 4.7 Expected Value of Functions of Random Variables [232] -- The Correlation and Covariance of Two Random Variables [233] -- *Joint Characteristic Function [235] -- 4.8 Jointly Gaussian Random Variables [237] -- n Jointly Gaussian Random Variables [240] -- * Linear Transformation of Gaussian Random Variables [242] -- * Joint Characteristic Function of Gaussian Random Variables [245] -- 4.9 Mean Square Estimation [246] -- * Linear Prediction [249] -- 4.10 Generating Correlated Vector Random Variables [251] -- Generating Vectors of Random Variables with Specified Covariances [251] -- Generating Vectors of Jointly Gaussian Random Variables [253] -- SUMMARY [255] -- PROBLEMS [256] -- CHAPTER 5 Sums of Random Variables and Long-Term Averages [269] -- 5.1 Sums of Random Variables [270] -- Mean and Variance of Sums of Random Variables [270] -- pdf of Sums of Independent Random Variables [271] -- *Sum of a Random Number of Random Variables [274] -- 5.2 The Sample Mean and the Laws of Large Numbers [275] -- 5.3 The Central Limit Theorem [280] -- Gaussian Approximation for Binomial Probabilities [285] -- * Proof of the Central Limit Theorem [287] -- 5.4 Confidence Intervals [288] -- Case 1: Xfs Gaussian; Unknown Mean and Known Variance [289] -- Case 2: X/s Gaussian; Mean and Variance Unknown [290] -- Case 3: Xfs Non-Gaussian; Mean and Variance Unknown [293] -- 5.5 Convergence of Sequences of Random Variables [293] -- 5.6 Long-Term Arrival Rates and Associated Averages [303] -- Long-Term Time Averages [306] -- 5.7 A Computer Method for Evaluating the Distribution of a Random -- Variable Using the Discrete Fourier Transform [309] -- Discrete Random Variables [309] -- Continuous Random Variables [314] -- SUMMARY [316] -- PROBLEMS [317] -- APPENDIX 5.1: Subroutine FFT(A,M,N) [327] -- CHAPTER 6 Random Processes [329] -- 6.1 Definition of a Random Process [330] -- 6.2 Specifying a Random Process [333] -- Joint Distributions of Time Samples [333] -- The Mean, Autocorrelation, and Autocovariance Functions [334] -- Gaussian Random Processes [336] -- Multiple Random Processes [337] -- 6.3 Examples of Discrete-Time Random Processes [338] -- iid Random Processes [339] -- Sum Processes'. The Binomial Counting and Random Walk Processes [341] -- 6.4 Examples of Continuous-Time Random Processes [346] -- Poisson Process [346] -- Random Telegraph Signal and Other Processes Derived from the Poisson Process [350] -- Wiener Process and Brownian Motion [354] -- 6.5 Stationary Random Processes [356] -- Wide-Sense Slationary Random Processes 35 [8] -- Wide-Sense Stationary Gaussian Random Processes [362] -- Cyclostationary Random Processes [363] -- 6.6 Continuity, Derivatives, and Integrals of Random Processes [366] -- Mean Square Continuity [366] -- Mean Square Derivatives [369] -- Mean Square Integrals [373] -- Response of a Linear System to Random Input [376] -- 6.7 Time Averages of Random Processes and Ergodic Theorems [378] -- 6.8 Fourier Series and Karhunen-Loeve Expansion [381] -- Karhunen-Loeve Expansion [383] -- SUMMARY [387] -- PROBLEMS [389] -- CHAPTER 7 Analysis and Processing of Random Signals [403] -- 7.1 Power Spectral Density [403] -- Continuous-Time Random Processes [404] -- Discrete-Time Random Processes [409] -- Power Spectral Density as a Time Average [411] -- 7.2 Response of Linear Systems to Random Signals [413] -- Continuous-Time Systems [413] -- Discrete-Time Systems [419] -- 7.3 Amplitude Modulation by Random Signals [421] -- 7.4 Optimum Linear Systems [426] -- The Orthogonality Condition [427] -- Prediction [431] -- Estimation Using the Entire Realization of the Observed Process [433] -- *Estimation Using Causal Filters [435] -- 7.5 The Kalman Filter [438] -- 7.6 Estimating the Power Spectral Density [443] -- Variance of Periodogram Estimate [444] -- Smoothing of Periodogram Estimate [447] -- SUMMARY [449] -- PROBLEMS [450] -- CHAPTER 8 Markov Chains [459] -- 8.1 Markov Processes [459] -- 8.2 Discrete-Time Markov Chains [462] -- The n-step Transition Probabilities [464] -- The State Probabilities [464] -- Steady State Probabilities [466] -- 8.3 Continuous-Time Markov Chains [468] -- State Occupancy Times [469] -- Transition Rates and Time-Dependent State Probabilities [470] -- Steady State Probabilities and Global Balance Equations [474] -- 8.4 Classes of States, Recurrence Properties, and Limiting Probabilities [477] -- Classes of States [478] -- Recurrence Properties [480] -- Limiting Probabilities [482] -- Limiting Probabilities for Continuous-Time Markov Chains [485] -- 8.5 Time-Reversed Markov Chains [487] -- Time-Reversible Markov Chains [490] -- Time-Reversible Continuous-Time Markov Chains [492] -- SUMMARY [493] -- PROBLEMS [494] -- CHAPTER 9 Introduction to Queueing Theory [499] -- 9.1 The Elements of a Queueing System [499] -- 9.2 Little’s Formula [501] -- 9.3 The M/M/1 Queue [504] -- Distribution of Number in the System [504] -- Delay Distribution in M /M /1 System and Arriving Customer's Distribution [509] -- The M /M /1 System with Finite Capacity [510] -- 9.4 Multi-Server Systems: M/M/c, M/M/c/c, and M/M/<» [514] -- Distribution of Number in the M /M/c System [514] -- Waiting Time Distribution for M /M /c [518] -- The M/M/c/c Queueing System [519] -- The M /M /°° Queueing System [520] -- 9.5 Finite-Source Queueing Systems [521] -- Arriving Customer's Distribution [524] -- 9.6 M/G/l Queueing Systems [526] -- The Residual Service Time [526] -- Mean Delay in M /G /1 Systems [528] -- Mean Delay in M/G/1 Systems with Priority Service Discipline [529] -- 9.7 M/G/l Analysis Using Embedded Markov Chains [533] -- The Embedded Markov Chain [533] -- The Number of Customers in an M/G/1 System [534] -- Delay and Waiting Time Distribution in an M/G/1 System [539] -- 9.8 Burke’s Theorem: Departures from M/M/c Systems [541] -- Proof of Burke's Theorem Using Time Reversibility [544] -- 9.9 Networks of Queues: Jackson’s Theorem [545] -- Open Networks of Queues [546] -- Proof of Jackson's Theorem [548] -- Closed Networks of Queues [550] -- Mean Value Analysis [554] -- Proof of the Arrival Theorem [557] -- SUMMARY [558] -- PROBLEMS [560] -- APPENDIXES -- A. Mathematical Tables [571] -- B. Tables of Fourier Transforms [574] -- C. Computer Programs for Generating Random Variables [576] -- Answers to Selected Problems [580] -- Index [589] --
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Includes index.
CHAPTER 1 Probability Models in Electrical and Computer Engineering [1] --
1.1 Mathematical Models as Tools in Analysis and Design [2] --
1.2 Deterministic Models [4] --
1.3 Probability Models [4] --
Statistical Regularity [5] --
Properties of Relative Frequency [6] --
The Axiomatic Approach to a Theoty of Probability [8] --
Building a Probability Model [9] --
1.4 A Detailed Example: A Packet Voice Transmission System [9] --
1.5 Other Examples [13] --
Communication over Unreliable Channels [13] --
Processing of Random Signals [14] --
Resource S haring Systems [14] --
Reliability of Systems [17] --
1.6 Overview of Book [18] --
SUMMARY [19] --
PROBLEMS [20] --
CHAPTER 2 Basic Concepts of Probability Theory --
2.1 Specifying Random Experiments [23] --
The Sample Space [24] --
Events [27] --
Set Operations [28] --
2.2 The Axioms of Probability [31] --
Discrete Sample Spaces [35] --
Continuous Sample Spaces [38] --
*2.3 Computing Probabilities Using Counting Methods [42] --
Sampling with Replacement and with Ordering [43] --
Sampling without Replacement and with Ordering [43] --
Permutations of n Distinct Objects [44] --
Sampling without Replacement and without Ordering [45] --
Sampling with Replacement and without Ordering [48] --
2.4 Conditional Probability [48] --
Bayes’ Rule [53] --
2.5 Independence of Events [54] --
2.6 Sequential Experiments [60] --
Sequences of Independent Experiments [61] --
The Binomial Probability Law [61] --
The Multinomial Probability Law [65] --
The Geometric Probability Law 66 Sequences of Dependent Experiments [66] --
2.7 A Computer Method for Synthesizing Randomness: Random Number Generators [69] --
SUMMARY [71] --
PROBLEMS [73] --
CHAPTER 3 Random Variables [84] --
3.1 The Notion of a Random Variable [84] --
3.2 The Cumulative Distribution Function [87] --
The Three Types of Random Variables [92] --
3.3 The Probability Density Function [93] --
Conditional cdf’s and pdf's [98] --
3.4 Some Important Random Variables [99] --
Discrete Random Variables [99] --
Continuous Random Variables [110] --
3.5 Functions of a Random Variable [119] --
3.6 The Expected Value of Random Variables [126] --
The Expected Value of X [127] --
The Expected Value ofY = g(X) [130] --
Variance of X [133] --
3.7 The Markov and Chebyshev Inequalities [137] --
3.8 Testing the Fit of a Distribution to Data [138] --
3.9 Transform Methods [144] --
The Characteristic Function [145] --
The Probability Generating Function [148] --
The Laplace Transform of the pdf I49 --
3.10 Basic Reliability Calculations [150] --
The Failure Rate Function [150] --
Reliability of Systems [153] --
3.11 Computer Methods for Generating Random Variables [155] --
The Transformation Method [155] --
The Rejection Method [158] --
Generation of Functions of a Random Variable [161] --
Generating M ixtures of Random Variables --
3.12 Entropy [162] --
The Entropy of a Random Variable [162] --
Entropy as a M easure of Information [167] --
The Method of Maximum Entropy [170] --
SUMMARY [172] --
PROBLEMS [174] --
CHAPTER 4 Multiple Random Variables [191] --
4.1 Vector Random Variables [191] --
Events and Probabilities [192] --
Independence [194] --
4.2 Pairs of Random Variables --
Pairs of Discrete Random Variables 195 [195] --
The Joint cdf of X and Y [197] --
7 he Joint pdf of Two Jointly Continuous Random Variables [201] --
Random Variables That Differ in Type [206] --
4.3 Independence of Two Random Variables [207] --
4.4 Conditional Probability and Conditional Expectation [210] --
Conditional Probability [210] --
Conditional Expectation [215] --
4.5 Multiple Random Variables [217] --
Joint Distributions [217] --
Independence [220] --
4.6 Functions of Several Random Variables [221] --
One Function of Several Random Variables 22 [1] --
Transformations of Random Vectors [224] --
pdf of Linear Transformations [225] --
*pdf of General Transformations [227] --
4.7 Expected Value of Functions of Random Variables [232] --
The Correlation and Covariance of Two Random Variables [233] --
*Joint Characteristic Function [235] --
4.8 Jointly Gaussian Random Variables [237] --
n Jointly Gaussian Random Variables [240] --
* Linear Transformation of Gaussian Random Variables [242] --
* Joint Characteristic Function of Gaussian Random Variables [245] --
4.9 Mean Square Estimation [246] --
* Linear Prediction [249] --
4.10 Generating Correlated Vector Random Variables [251] --
Generating Vectors of Random Variables with Specified Covariances [251] --
Generating Vectors of Jointly Gaussian Random Variables [253] --
SUMMARY [255] --
PROBLEMS [256] --
CHAPTER 5 Sums of Random Variables and Long-Term Averages [269] --
5.1 Sums of Random Variables [270] --
Mean and Variance of Sums of Random Variables [270] --
pdf of Sums of Independent Random Variables [271] --
*Sum of a Random Number of Random Variables [274] --
5.2 The Sample Mean and the Laws of Large Numbers [275] --
5.3 The Central Limit Theorem [280] --
Gaussian Approximation for Binomial Probabilities [285] --
* Proof of the Central Limit Theorem [287] --
5.4 Confidence Intervals [288] --
Case 1: Xfs Gaussian; Unknown Mean and Known Variance [289] --
Case 2: X/s Gaussian; Mean and Variance Unknown [290] --
Case 3: Xfs Non-Gaussian; Mean and Variance Unknown [293] --
5.5 Convergence of Sequences of Random Variables [293] --
5.6 Long-Term Arrival Rates and Associated Averages [303] --
Long-Term Time Averages [306] --
5.7 A Computer Method for Evaluating the Distribution of a Random --
Variable Using the Discrete Fourier Transform [309] --
Discrete Random Variables [309] --
Continuous Random Variables [314] --
SUMMARY [316] --
PROBLEMS [317] --
APPENDIX 5.1: Subroutine FFT(A,M,N) [327] --
CHAPTER 6 Random Processes [329] --
6.1 Definition of a Random Process [330] --
6.2 Specifying a Random Process [333] --
Joint Distributions of Time Samples [333] --
The Mean, Autocorrelation, and Autocovariance Functions [334] --
Gaussian Random Processes [336] --
Multiple Random Processes [337] --
6.3 Examples of Discrete-Time Random Processes [338] --
iid Random Processes [339] --
Sum Processes'. The Binomial Counting and Random Walk Processes [341] --
6.4 Examples of Continuous-Time Random Processes [346] --
Poisson Process [346] --
Random Telegraph Signal and Other Processes Derived from the Poisson Process [350] --
Wiener Process and Brownian Motion [354] --
6.5 Stationary Random Processes [356] --
Wide-Sense Slationary Random Processes 35 [8] --
Wide-Sense Stationary Gaussian Random Processes [362] --
Cyclostationary Random Processes [363] --
6.6 Continuity, Derivatives, and Integrals of Random Processes [366] --
Mean Square Continuity [366] --
Mean Square Derivatives [369] --
Mean Square Integrals [373] --
Response of a Linear System to Random Input [376] --
6.7 Time Averages of Random Processes and Ergodic Theorems [378] --
6.8 Fourier Series and Karhunen-Loeve Expansion [381] --
Karhunen-Loeve Expansion [383] --
SUMMARY [387] --
PROBLEMS [389] --
CHAPTER 7 Analysis and Processing of Random Signals [403] --
7.1 Power Spectral Density [403] --
Continuous-Time Random Processes [404] --
Discrete-Time Random Processes [409] --
Power Spectral Density as a Time Average [411] --
7.2 Response of Linear Systems to Random Signals [413] --
Continuous-Time Systems [413] --
Discrete-Time Systems [419] --
7.3 Amplitude Modulation by Random Signals [421] --
7.4 Optimum Linear Systems [426] --
The Orthogonality Condition [427] --
Prediction [431] --
Estimation Using the Entire Realization of the Observed Process [433] --
*Estimation Using Causal Filters [435] --
7.5 The Kalman Filter [438] --
7.6 Estimating the Power Spectral Density [443] --
Variance of Periodogram Estimate [444] --
Smoothing of Periodogram Estimate [447] --
SUMMARY [449] --
PROBLEMS [450] --
CHAPTER 8 Markov Chains [459] --
8.1 Markov Processes [459] --
8.2 Discrete-Time Markov Chains [462] --
The n-step Transition Probabilities [464] --
The State Probabilities [464] --
Steady State Probabilities [466] --
8.3 Continuous-Time Markov Chains [468] --
State Occupancy Times [469] --
Transition Rates and Time-Dependent State Probabilities [470] --
Steady State Probabilities and Global Balance Equations [474] --
8.4 Classes of States, Recurrence Properties, and Limiting Probabilities [477] --
Classes of States [478] --
Recurrence Properties [480] --
Limiting Probabilities [482] --
Limiting Probabilities for Continuous-Time Markov Chains [485] --
8.5 Time-Reversed Markov Chains [487] --
Time-Reversible Markov Chains [490] --
Time-Reversible Continuous-Time Markov Chains [492] --
SUMMARY [493] --
PROBLEMS [494] --
CHAPTER 9 Introduction to Queueing Theory [499] --
9.1 The Elements of a Queueing System [499] --
9.2 Little’s Formula [501] --
9.3 The M/M/1 Queue [504] --
Distribution of Number in the System [504] --
Delay Distribution in M /M /1 System and Arriving Customer's Distribution [509] --
The M /M /1 System with Finite Capacity [510] --
9.4 Multi-Server Systems: M/M/c, M/M/c/c, and M/M/<» [514] --
Distribution of Number in the M /M/c System [514] --
Waiting Time Distribution for M /M /c [518] --
The M/M/c/c Queueing System [519] --
The M /M /°° Queueing System [520] --
9.5 Finite-Source Queueing Systems [521] --
Arriving Customer's Distribution [524] --
9.6 M/G/l Queueing Systems [526] --
The Residual Service Time [526] --
Mean Delay in M /G /1 Systems [528] --
Mean Delay in M/G/1 Systems with Priority Service Discipline [529] --
9.7 M/G/l Analysis Using Embedded Markov Chains [533] --
The Embedded Markov Chain [533] --
The Number of Customers in an M/G/1 System [534] --
Delay and Waiting Time Distribution in an M/G/1 System [539] --
9.8 Burke’s Theorem: Departures from M/M/c Systems [541] --
Proof of Burke's Theorem Using Time Reversibility [544] --
9.9 Networks of Queues: Jackson’s Theorem [545] --
Open Networks of Queues [546] --
Proof of Jackson's Theorem [548] --
Closed Networks of Queues [550] --
Mean Value Analysis [554] --
Proof of the Arrival Theorem [557] --
SUMMARY [558] --
PROBLEMS [560] --
APPENDIXES --
A. Mathematical Tables [571] --
B. Tables of Fourier Transforms [574] --
C. Computer Programs for Generating Random Variables [576] --
Answers to Selected Problems [580] --
Index [589] --
MR, REVIEW #
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