Probability and Statistics with Reliability, Queuing and Computer Science Applications 2e

<p>Preface to the Paperback Edition ix</p>
<p>Preface to the Second Edition xi</p>
<p>Preface to the First Edition xiii</p>
<p>Acronyms xv</p>
<p>About the Companion Website xix</p>
<p>1 Introduction 1</p>
<p>1.1 Motivation&nbsp; 1</p>
<p>1.2 Probability Models&nbsp; 2</p>
<p>1.3 Sample Space 3</p>
<p>1.4 Events 6</p>
<p>1.5 Algebra of Events 7</p>
<p>1.6 Graphical Methods of Representing Events&nbsp; 11</p>
<p>1.7 Probability Axioms&nbsp; 13</p>
<p>1.8 Combinatorial Problems 19</p>
<p>1.9 Conditional Probability 24</p>
<p>1.10 Independence of Events 26</p>
<p>1.11 Bayes Rule&nbsp; 38</p>
<p>1.12 Bernoulli Trials&nbsp; 47</p>
<p>2 Discrete Random Variables 65</p>
<p>2.1 Introduction&nbsp; 65</p>
<p>2.2 Random Variables and Their Event Spaces&nbsp; 66</p>
<p>2.3 The Probability Mass Function 68</p>
<p>2.4 Distribution Functions&nbsp; 70</p>
<p>2.5 Special Discrete Distributions&nbsp; 72</p>
<p>2.6 Analysis of Program MAX&nbsp; 97</p>
<p>2.7 The Probability Generating Function&nbsp; 101</p>
<p>2.8 Discrete Random Vectors&nbsp; 104</p>
<p>2.9 Independent Random Variables 110</p>
<p>3 Continuous Random Variables 121</p>
<p>3.1 Introduction&nbsp; 121</p>
<p>3.2 The Exponential Distribution&nbsp; 125</p>
<p>3.3 The Reliability and Failure Rate&nbsp; 130</p>
<p>3.4 Some Important Distributions&nbsp; 135</p>
<p>3.5 Functions of a Random Variable&nbsp; 154</p>
<p>3.6 Jointly Distributed Random Variables 159</p>
<p>3.7 Order Statistics&nbsp; 163</p>
<p>3.8 Distribution of Sums 174</p>
<p>3.9 Functions of Normal Random Variables&nbsp; 190</p>
<p>4 Expectation 201</p>
<p>4.1 Introduction&nbsp; 201</p>
<p>4.2 Moments 205</p>
<p>4.3 Expectation Based on Multiple Random Variables&nbsp; 209</p>
<p>4.4 Transform Methods&nbsp; 216</p>
<p>4.5 Moments and Transforms of Some Distributions&nbsp; 226</p>
<p>4.6 Computation of Mean Time to Failure 238</p>
<p>4.7 Inequalities and Limit Theorems&nbsp; 247</p>
<p>5 Conditional Distribution and Expectation 257</p>
<p>5.1 Introduction&nbsp; 257</p>
<p>5.2 Mixture Distributions&nbsp; 266</p>
<p>5.3 Conditional Expectation 273</p>
<p>5.4 Imperfect Fault Coverage and Reliability&nbsp; 280</p>
<p>5.5 Random Sums&nbsp; 290</p>
<p>6 Stochastic Processes 301</p>
<p>6.1 Introduction&nbsp; 301</p>
<p>6.2 Classification of Stochastic Processes&nbsp; 307</p>
<p>6.3 The Bernoulli Process&nbsp; 313</p>
<p>6.4 The Poisson Process 317</p>
<p>6.5 Renewal Processes&nbsp; 327</p>
<p>6.6 Availability Analysis 332</p>
<p>6.7 Random Incidence&nbsp; 342</p>
<p>6.8 Renewal Model of Program Behavior&nbsp; 346</p>
<p>7 Discrete–Time Markov Chains 351</p>
<p>7.1 Introduction&nbsp; 351</p>
<p>7.2 Computation of n–step Transition Probabilities&nbsp; 356</p>
<p>7.3 State Classification and Limiting Probabilities 362</p>
<p>7.4 Distribution of Times Between State Changes 371</p>
<p>7.5 Markov Modulated Bernoulli Process&nbsp; 373</p>
<p>7.6 Irreducible Finite Chains with Aperiodic States&nbsp; 376</p>
<p>7.7 ∗ The M /G/ 1 Queuing System&nbsp; 391</p>
<p>7.8 Discrete–Time Birth Death Processes&nbsp; 400</p>
<p>7.9 Finite Markov Chains with Absorbing States 407</p>
<p>8 Continuous–Time Markov Chains 421</p>
<p>8.1 Introduction&nbsp; 421</p>
<p>8.2 The Birth Death Process&nbsp; 428</p>
<p>8.3 Other Special Cases of the Birth Death Model&nbsp; 465</p>
<p>8.4 Non–Birth Death Processes 474</p>
<p>8.5 Markov Chains with Absorbing States 519</p>
<p>8.6 Solution Techniques 541</p>
<p>8.7 Automated Generation&nbsp; 552</p>
<p>9 Networks of Queues 577</p>
<p>9.1 Introduction&nbsp; 577</p>
<p>9.2 Open Queuing Networks 582</p>
<p>9.3 Closed Queuing Networks&nbsp; 590</p>
<p>9.4 General Service Distribution and Multiple Job Types 620</p>
<p>9.5 Non–product–form Networks 628</p>
<p>9.6 Computing Response Time Distribution&nbsp; 641</p>
<p>9.7 Summary 654</p>
<p>10 Statistical Inference 661</p>
<p>10.1 Introduction&nbsp; 661</p>
<p>10.2 Parameter Estimation&nbsp; 663</p>
<p>10.3 Hypothesis Testing&nbsp; 718</p>
<p>11 Regression and Analysis of Variance 753</p>
<p>11.1 Introduction&nbsp; 753</p>
<p>11.2 Least–squares Curve Fitting 758</p>
<p>11.3 The Coefficients of Determination&nbsp; 762</p>
<p>11.4 Confidence Intervals in Linear Regression 765</p>
<p>11.5 Trend Detection and Slope Estimation 768</p>
<p>11.6 Correlation Analysis 771</p>
<p>11.7 Simple Nonlinear Regression 774</p>
<p>11.8 Higher–dimensional Least–squares Fit&nbsp; 775</p>
<p>11.9 Analysis of Variance 778</p>
<p>A Bibliography 791</p>
<p>A.1 Theory 791</p>
<p>A.2 Applications&nbsp; 796</p>
<p>B Properties of Distributions 804</p>
<p>C Statistical Tables 807</p>
<p>D Laplace Transforms 828</p>
<p>E Program Performance Analysis 835</p>
<p>Author Index 837</p>
<p>Subject Index 845</p>