دانلود کتاب Probability and Statistics with Reliability, Queuing, and Computer Science Applications

فهرست مطالب :

Cover......Page 1
Title Page......Page 5
Copyright......Page 6
Contents......Page 7
Preface to the Paperback Edition......Page 11
Preface to the Second Edition......Page 13
Preface to the First Edition......Page 15
Acronyms......Page 17
About the Companion Website......Page 21
1.1 Motivation......Page 23
1.2 Probability Models......Page 24
1.3 Sample Space......Page 25
1.4 Events......Page 28
1.5 Algebra of Events......Page 29
1.6 Graphical Methods of Representing Events......Page 33
1.7 Probability Axioms......Page 35
1.8 Combinatorial Problems......Page 41
1.8.1 Ordered Samples of Size k, with Replacement......Page 43
1.8.3 Unordered Samples of Size k, without Replacement......Page 44
1.9 Conditional Probability......Page 46
1.10 Independence of Events......Page 48
1.11 Bayes\' Rule......Page 60
1.12 Bernoulli Trials......Page 69
2.1 Introduction......Page 87
2.2 Random Variables and Their Event Spaces......Page 88
2.3 The Probability Mass Function......Page 90
2.4 Distribution Functions......Page 92
2.5 Special Discrete Distributions......Page 94
2.5.1 The Bernoulli pmf......Page 95
2.5.2 The Binomial pmf......Page 96
2.5.3 The Geometric pmf......Page 104
2.5.4 The Negative Binomial pmf......Page 107
2.5.5 The Poisson pmf......Page 109
2.5.6 The Hypergeometric pmf......Page 113
2.5.7 The Discrete Uniform pmf......Page 115
2.5.9 Indicator Random Variable......Page 116
2.6 Analysis of Program MAX......Page 119
2.7 The Probability Generating Function......Page 123
2.8 Discrete Random Vectors......Page 126
2.9 Independent Random Variables......Page 132
3.1 Introduction......Page 143
3.2 The Exponential Distribution......Page 147
3.3 The Reliability and Failure Rate......Page 152
3.4.1 Hypoexponential Distribution......Page 157
3.4.2 Erlang and Gamma Distribution......Page 159
3.4.3 Hyperexponential Distribution......Page 161
3.4.4 Weibull Distribution......Page 163
3.4.5 Log-Logistic Distribution......Page 164
3.4.6 Normal or Gaussian Distribution......Page 165
3.4.7 The Uniform or Rectangular Distribution......Page 171
3.4.8 Pareto Distribution......Page 172
3.4.9 Defective Distribution......Page 174
3.5 Functions of a Random Variable......Page 176
3.6 Jointly Distributed Random Variables......Page 181
3.7 Order Statistics......Page 185
3.8 Distribution of Sums......Page 196
3.9 Functions of Normal Random Variables......Page 212
4.1 Introduction......Page 223
4.2 Moments......Page 227
4.3 Expectation Based on Multiple Random Variables......Page 231
4.4 Transform Methods......Page 238
4.5.1 Discrete Uniform Distribution......Page 248
4.5.3 Binomial Distribution......Page 249
4.5.4 Geometric Distribution......Page 250
4.5.5 Poisson pmf......Page 251
4.5.6 Continuous Uniform Distribution......Page 252
4.5.8 Gamma Distribution......Page 253
4.5.9 Hypoexponential Distribution......Page 254
4.5.10 Hyperexponential Distribution......Page 255
4.5.12 Log-logistic Distribution......Page 257
4.5.13 Pareto Distribution......Page 258
4.5.14 The Normal Distribution......Page 259
4.6 Computation of Mean Time to Failure......Page 260
4.6.1 Series System......Page 261
4.6.2 Parallel System......Page 262
4.6.3 Standby Redundancy......Page 263
4.6.4 TMR and TMR/Simplex Systems......Page 264
4.6.6 The Hybrid k-out-of-n System......Page 265
4.7 Inequalities and Limit Theorems......Page 269
5.1 Introduction......Page 279
5.2 Mixture Distributions......Page 288
5.3 Conditional Expectation......Page 295
5.4 Imperfect Fault Coverage and Reliability......Page 302
5.5 Random Sums......Page 312
6.1 Introduction......Page 323
6.2 Classification of Stochastic Processes......Page 329
6.3 The Bernoulli Process......Page 335
6.4 The Poisson Process......Page 339
6.5 Renewal Processes......Page 349
6.6 Availability Analysis......Page 354
6.7 Random Incidence......Page 364
6.8 Renewal Model of Program Behavior......Page 368
7.1 Introduction......Page 373
7.2 Computation of n-step Transition Probabilities......Page 378
7.3 State Classification and Limiting Probabilities......Page 384
7.4 Distribution of Times Between State Changes......Page 393
7.5 Markov Modulated Bernoulli Process......Page 395
7.6.1 Memory Interference in Multiprocessor Systems......Page 398
7.6.2.1 The Independent Reference Model......Page 402
7.6.2.2 Performance Analysis of Cache Memories......Page 404
7.6.2.3 The LRU Stack Model......Page 406
7.6.3 Slotted Aloha Model......Page 410
7.6.4 Performance Analysis of an ATM Multiplexer......Page 411
7.7 * The M/G/ 1 Queuing System......Page 413
7.8 Discrete-Time Birth-Death Processes......Page 422
7.9 Finite Markov Chains with Absorbing States......Page 429
8.1 Introduction......Page 443
8.2 The Birth-Death Process......Page 450
8.2.1 The M/M/1 Queue......Page 453
8.2.2 The M/M/m Queue......Page 460
8.2.3 Finite State Space......Page 467
8.2.3.1 Machine Repairman Model......Page 478
8.2.3.2 Wireless Handoff Performance Model......Page 485
8.3.1 The Pure Birth Process......Page 487
8.3.2.1 Death Process with a Constant Rate......Page 492
8.3.2.2 Death Process with a Linear Rate......Page 493
8.4.1 Availability Models......Page 496
8.4.2 Performance Models......Page 518
8.4.2.3 The MMPP/M/1 Queue......Page 523
8.4.3 Performance and Availability Combined......Page 526
8.5 Markov Chains with Absorbing States......Page 541
8.6 Solution Techniques......Page 563
8.6.1.1 Power Method......Page 564
8.6.1.2 Successive Overrelaxation (SOR)......Page 566
8.6.2.1 Fully Symbolic Method......Page 568
8.6.2.2 Numerical Methods......Page 569
8.7.1 Petri Nets......Page 574
8.7.2 Stochastic Petri Nets......Page 577
8.7.3 Generalized Stochastic Petri Nets......Page 580
8.7.4 Stochastic Reward Nets......Page 584
9.1 Introduction......Page 599
9.2 Open Queuing Networks......Page 604
9.3 Closed Queuing Networks......Page 612
9.4 General Service Distribution and Multiple Job Types......Page 642
9.5 Non-product-form Networks......Page 650
9.6.1 Response Time Distribution in Open Networks......Page 663
9.6.1.1 Response Time Blocks......Page 666
9.6.2 Response Time Distribution in Closed Networks......Page 670
9.7 Summary......Page 676
10.1 Introduction......Page 683
10.2 Parameter Estimation......Page 685
10.2.1 The Method of Moments......Page 692
10.2.2 Maximum-Likelihood Estimation......Page 694
10.2.3 Confidence Intervals......Page 703
10.2.3.1 Sampling from the Normal Distribution......Page 705
10.2.3.2 Sampling from the Exponential Distribution......Page 711
10.2.3.3 Sampling from the Weibull Distribution......Page 715
10.2.3.4 Sampling from the Bernoulli Distribution......Page 716
10.2.4.1 Discrete-Time Markov Chains......Page 724
10.2.4.2 Estimating Parameters of an M/M/1 Queue......Page 725
10.2.4.3 Estimation of Availability......Page 727
10.2.4.4 Estimation for a Semi-Markov Process......Page 730
Cluster analysis......Page 731
The transition probability matrix......Page 732
Sojourn time distributions......Page 733
Model validation......Page 734
10.2.5 Estimation with Dependent Samples......Page 736
10.3 Hypothesis Testing......Page 740
10.3.1 Tests on the Population Mean......Page 741
10.3.2 Hypotheses Concerning Two Means......Page 754
10.3.3 Hypotheses Concerning Variances......Page 760
10.3.4 Goodness-of-fit Tests......Page 762
11.1 Introduction......Page 775
11.2 Least-squares Curve Fitting......Page 780
11.3 The Coefficients of Determination......Page 784
11.4 Confidence Intervals in Linear Regression......Page 787
11.5.1 Mann-Kendall Test......Page 790
11.5.2 Sen\'s Slope Estimator......Page 792
11.6 Correlation Analysis......Page 793
11.7 Simple Nonlinear Regression......Page 796
11.8 Higher-dimensional Least-squares Fit......Page 797
11.9 Analysis of Variance......Page 800
A.1.1 Probability Theory......Page 813
A.1.2 Stochastic Processes......Page 814
A.1.3 Queuing Theory......Page 815
A.1.4 Reliability Theory......Page 816
A.1.5 Statistics......Page 817
A.2.1 Computer Performance Evaluation......Page 818
A.2.2 Communications......Page 820
A.2.4 Simulation......Page 821
A.2.5 Computer-Communication Networks......Page 822
A.2.7 Fault-Tolerant Computing......Page 823
A.2.9 Numerical Solutions......Page 824
AppendixB Properties of Distributions......Page 826
AppendixC Statistical Tables......Page 829
AppendixD Laplace Transforms......Page 850
Appendix E Program Performance Analysis......Page 857
Author Index......Page 859
Subject Index......Page 867
EULA......Page 880