Preface to the Fifth Edition |
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xi | |
Preface to the Sixth Edition |
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xiii | |
Preface to the Seventh Edition |
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xv | |
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Introduction to Probability Theory |
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1 | (22) |
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1 | (1) |
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1 | (3) |
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Probabilities Defined on Events |
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4 | (2) |
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Conditional Probabilities |
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6 | (4) |
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10 | (2) |
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12 | (11) |
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15 | (6) |
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21 | (2) |
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23 | (70) |
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23 | (4) |
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Discrete Random Variables |
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27 | (6) |
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The Bernoulli Random Variable |
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27 | (1) |
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The Binomial Random Variable |
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28 | (3) |
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The Geometric Random Variable |
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31 | (1) |
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The Poisson Random Variable |
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31 | (2) |
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Continuous Random Variables |
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33 | (4) |
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The Uniform Random Variable |
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34 | (1) |
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Exponential Random Variables |
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35 | (1) |
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35 | (1) |
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36 | (1) |
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Expectation of a Random Variable |
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37 | (9) |
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37 | (3) |
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40 | (2) |
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Expectation of a Function of a Random Variable |
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42 | (4) |
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Jointly distributed Random Variables |
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46 | (16) |
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Joint Distribution Functions |
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46 | (4) |
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Independent Random Variables |
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50 | (1) |
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Covariance and Variance of Sums of Random Variables |
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51 | (8) |
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Joint Probability Distribution of Functions of Random Variables |
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59 | (3) |
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Moment Generating Functions |
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62 | (11) |
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The Joint Distribution of the Sample Mean and Sample Variance from a Normal Population |
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70 | (3) |
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73 | (6) |
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79 | (14) |
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82 | (10) |
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92 | (1) |
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Conditional Probability and Conditional Expectation |
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93 | (70) |
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93 | (1) |
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93 | (5) |
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98 | (3) |
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Computing Expectations by Conditioning |
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101 | (13) |
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Computing Probabilities by Conditioning |
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114 | (14) |
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128 | (35) |
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128 | (1) |
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129 | (8) |
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Uniform Priors, Polya's Urn Model, and Bose-Einstein Statistics |
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137 | (4) |
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The k-Record Values of Discrete Random Variables |
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141 | (4) |
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145 | (18) |
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163 | (78) |
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163 | (3) |
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Chapman-Kolmogorov Equations |
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166 | (2) |
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168 | (10) |
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178 | (10) |
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188 | (12) |
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The Gambler's Ruin Problem |
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188 | (4) |
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A Model for Algorithmic Efficiency |
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192 | (2) |
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Using a Random Walk to analyze a Probabilistic Algorithm for the Satisfiability Problem |
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194 | (6) |
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Mean Time Spent in Transient States |
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200 | (2) |
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202 | (3) |
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Time Reversible Markov Chains |
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205 | (11) |
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Markov Chain Monte Carlo Methods |
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216 | (6) |
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Markov Decision Processes |
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222 | (19) |
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226 | (14) |
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240 | (1) |
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The Exponential distribution and the Poisson Process |
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241 | (72) |
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241 | (1) |
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The Exponential Distribution |
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242 | (14) |
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242 | (1) |
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Properties of the exponential Distribution |
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243 | (5) |
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Further Properties of the Exponential Distribution |
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248 | (5) |
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Convolutions of Exponential Random Variables |
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253 | (3) |
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256 | (28) |
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256 | (2) |
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Definition of the Poisson Process |
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258 | (3) |
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Interarrival and Waiting Time Distributions |
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261 | (3) |
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Further Properties of Poisson Processes |
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264 | (6) |
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Conditional Distribution of the Arrival Times |
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270 | (11) |
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Estimating software Reliability |
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281 | (3) |
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Generalizations of the Poisson Process |
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284 | (29) |
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Nonhomogeneous Poisson Process |
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284 | (5) |
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289 | (6) |
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295 | (16) |
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311 | (2) |
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Continuous-Time Markov Chains |
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313 | (50) |
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313 | (1) |
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Continuous-Time Markov Chains |
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314 | (2) |
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Birth and Death Processes |
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316 | (7) |
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The Transition Probability Function Pij(t) |
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323 | (8) |
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331 | (7) |
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338 | (8) |
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346 | (3) |
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Computing the Transition Probabilities |
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349 | (14) |
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352 | (9) |
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361 | (2) |
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Renewal Theory and Its Applications |
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363 | (64) |
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363 | (2) |
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365 | (3) |
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Limit Theorems and Their Applications |
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368 | (9) |
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377 | (9) |
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386 | (9) |
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Alternating Renewal Processes |
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389 | (6) |
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395 | (3) |
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398 | (2) |
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Computing the Renewal Function |
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400 | (3) |
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403 | (24) |
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Patterns of Discrete Random Variables |
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404 | (6) |
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The Expected Time to a Maximal Run of distinct Values |
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410 | (2) |
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Increasing runs of Continuous Random Variables |
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412 | (1) |
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413 | (12) |
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425 | (2) |
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427 | (72) |
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427 | (1) |
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428 | (4) |
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429 | (1) |
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Steady-State Probabilities |
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430 | (2) |
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432 | (15) |
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A Single-Server Exponential Queueing System |
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432 | (6) |
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A Single-Server Exponential Queueing System Having Finite Capacity |
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438 | (4) |
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442 | (2) |
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A Queueing System with Bulk Service |
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444 | (3) |
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447 | (11) |
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447 | (5) |
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452 | (6) |
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458 | (3) |
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Preliminaries: Work and Another Cost Identity |
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458 | (1) |
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Application of Work to M/G/1 |
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459 | (1) |
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460 | (1) |
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461 | (9) |
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The M/G/1 with Random-Sized Batch Arrivals |
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461 | (2) |
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463 | (3) |
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An M/G/1 Optimization Example |
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466 | (4) |
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470 | (5) |
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The G/M/1 Busy and Idle Periods |
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475 | (1) |
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475 | (4) |
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479 | (20) |
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479 | (2) |
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481 | (1) |
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481 | (2) |
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483 | (1) |
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484 | (12) |
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496 | (3) |
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499 | (50) |
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499 | (1) |
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500 | (6) |
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Minimal Path and Minimal Cut Sets |
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502 | (4) |
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Reliability of Systems of Independent Components |
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506 | (4) |
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Bounds on the Reliability Function |
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510 | (11) |
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Method of Inclusion and Exclusion |
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511 | (8) |
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Second Method for Obtaining Bounds on r(p) |
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519 | (2) |
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System Life as a Function of Component Lives |
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521 | (8) |
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529 | (6) |
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An Upper Bound on the Expected Life of a Parallel System |
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533 | (2) |
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535 | (14) |
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A Series Model with Suspended Animation |
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539 | (3) |
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542 | (6) |
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548 | (1) |
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Brownian Motion and Stationary Processes |
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549 | (36) |
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549 | (4) |
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Hitting Times, Maximum Variable, and the Gambler's Ruin Problem |
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553 | (1) |
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Variations on Brownian Motion |
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554 | (2) |
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Brownian Motion with Drift |
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554 | (1) |
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Geometric Brownian Motion |
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555 | (1) |
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556 | (11) |
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An Example in Options Pricing |
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556 | (2) |
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558 | (3) |
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The Black - Scholes Option Pricing Formula |
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561 | (6) |
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567 | (2) |
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569 | (3) |
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Stationary and Weakly Stationary Processes |
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572 | (5) |
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Harmonic Analysis of Weakly Stationary Processes |
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577 | (8) |
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579 | (5) |
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584 | (1) |
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585 | (64) |
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585 | (5) |
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General Techniques for Simulating Continuous Random Variables |
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590 | (8) |
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The Inverse Transformation Method |
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590 | (1) |
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591 | (4) |
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595 | (3) |
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Special Techniques for Simulating Continuous Random Variables |
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598 | (8) |
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598 | (4) |
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602 | (1) |
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The Chi-Squared Distribution |
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602 | (1) |
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The Beta (n, m) Distribution |
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603 | (1) |
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The Exponential Distribution--The von Neumann Algorithm |
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604 | (2) |
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Simulating from Discrete Distributions |
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606 | (7) |
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610 | (3) |
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613 | (11) |
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Simulating a Nonhomogeneous Poisson Process |
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615 | (6) |
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Simulating a Two-Dimensional Poisson Process |
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621 | (3) |
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Variance Reduction Techniques |
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624 | (15) |
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Use of Antithetic Variables |
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625 | (4) |
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Variance Reduction by Conditioning |
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629 | (4) |
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633 | (1) |
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634 | (5) |
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Determining the Number of Runs |
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639 | (10) |
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640 | (8) |
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648 | (1) |
Appendix: Solutions to Starred Exercises |
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649 | (38) |
Index |
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687 | |