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Ross S.M. — Introduction to probability models
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Íàçâàíèå: Introduction to probability modelsÀâòîð: Ross S.M. Àííîòàöèÿ: The sixth edition of the successful Introduction to Probability Models introduces elementary probability theory and the stochastic processes and is particularly well-suited to those applying probability theory to the study of phenomena in engineering, management science, the physical and social sciences, and operations research. Skillfully organized, Introduction to Probability Models covers all essential topics. Sheldon Ross, a talented and prolific textbook author, distinguishes this carefully and substantially revised book by his effort to develop in students an intuitive, and therefore lasting, grasp of probability theory. The seventh edition includes many new examples and exercises, with the majority of the new exercises being less demanding of the student. In addition, the text introduces stochastic processes, stressing applications, in an easily understood manner. There is a comprehensive introduction to the applied models of probability that stresses intuition. Both students and professors will agree that this is the most solid and widely used text for probability theory.
ßçûê: Ðóáðèêà: Ìàòåìàòèêà /Âåðîÿòíîñòü /Ñòîõàñòè÷åñêèå ïðîöåññû /Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö ed2k: ed2k stats Èçäàíèå: sixth editionÃîä èçäàíèÿ: 1997Êîëè÷åñòâî ñòðàíèö: 669Äîáàâëåíà â êàòàëîã: 10.06.2005Îïåðàöèè: Ïîëîæèòü íà ïîëêó |
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413—414 414 Absorbing state of a Markov chain 160 Accessibility of states 163 Age of a renewal process 371 375—376 405 Alias method 584—587 Aloha protocol 170—171 Alternating renewal process 374—375 Antithetic variables 599 622 Aperiodic state of a Markov chain 173 Arbitrage 532 Arbitrage theorem 533 Arrival theorem 439 Assignment problem 244 Autoregressive process 549 Availability 511—512 Balance equations 323 418 Ballot problem 117—118 152 Bayes formula 14 Bernoulli random variable 26 Bernoulli random variable, simulation of 582 Best prize problem 114—115 Beta random variable 567 577 Beta random variable, simulation of 577—578 Binomial random variables 26—27 81 87 93 94 Binomial random variables, simulation of 582 Binomial random variables, sums of independent 66 Birth and death process 303 306—313 323—324 331 Bivariate exponential distribution 299 Bivariate normal distribution 142—143 Black — Scholes formula 536—539 Bonferroni's inequality 15 Boole's inequality 16 Bose — Einstein distribution 136 Box — Muller method of simulating normal random variables 574 Branching process 197—200 230 Bridge structure 480 490 Brownian bridge 543—544 557 Brownian motion 524 Brownian motion with drift 529 Brownian motion with drift as limit of random walks 554 Brownian motion, continued standard 525 Brownian motion, continued standard as a Gaussian process 543 Brownian motion, integrated 545—546 Brownian motion, maximum variable 528 Busy period 284—285 444—445 Cayley's theorem 493 Central limit theorem 74 Chapman — Kolmogorov equations in continuous time 317 Chapman — Kolmogorov equations in discrete time 160 Chebyshev's inequality 72 Chi-squared random variables 69 574 Chi-squared random variables, moment generating function of 69—70 Chi-squared random variables, simulation of 576—577 Class of a Markov chain 163 Closed class 222 Communication of states 163 Complement of an event 4 Compound Poisson process 281—282 286—287 Conditional expectation 92 95 97 99 Conditional probability 7 Conditional probability, density function 96 Conditional probability, distribution function 92 Conditional probability, mass function 91—92 Conditional variance formula 147 283 312 313 Connected graph 126 205 Control variates 606—608 Convolutions 55 Counting process 249 Coupon collecting problem 261—262 Covariance 49—51 148 Coxian random variables 248—249 Craps 16 Cumulative distribution function 24 Decreasing failure rate (DFR) 498—499 Delayed renewal process 387 400 Dependent events 10 Dirichlet distribution 135 Distribution function see “Cumulative distribution function” Doubly stochastic 223 Ehrenfest urn model 204 228 Elementary renewal theorem 358 401—402 Equilibrium distribution 406 Ergodic Markov chain 323 Ergodic state 173 Erlang's loss system 456—458 Event 2 Excess of a renewal process 363 372 376 Expectation see “Expected value” Expected value 36 Expected value of Bernoulli random variables 37 Expected value of Binomial random variables 37 46—47 62 Expected value of continuous random variables 39 Expected value of discrete random variables 36 Expected value of exponential random variables 39 63 236 Expected value of functions of random variables 40—42 45—46 Expected value of geometric random variables 37—38 101—102 Expected value of normal random variables 39—40 64 Expected value of Poisson random variables 38 62 Expected value of sums of a random number of random variables 101 Expected value of sums of random variables 46 Expected value of uniform random variables 39 Expected value, tables of 65 Exponential random variable 34 236 291 508—509 Exponential random variable, simulation of 565 578—580 Failure rate function 239—240 498 Gambler's ruin problem 183—184 185 229 Gamma function 34 Gamma random variables 34 58—59 499 Gamma random variables as interarrival distribution 399 407 Gamma random variables, relation to exponential 59 Gamma random variables, simulation of 576 615 Gaussian process 543 General renewal process see “Delayed renewal process” Geometric Brownian motion 529—530 Geometric random variable 29 141 Geometric random variable, simulation of 581 Gibbs sampler 214—217 441—442 Graph 126 347 Greedy algorithms 244—245 Hardy — Weinberg law 176—177 Hastings — Metropolis algorithm 212—214 Hazard function 503 Hazard rate function see “Failure rate function” Hazard rate, method of simulation 569—570 Hazard rate, method of simulation for discrete random variables 616 Hit-miss method 620 Hyperexponential random variables 241—242 Hypergeometric random variables 54 94 Hypoexponential random variables 245—249 Idle period 284 444 Ignatov's theorem 122 138 Importance sampling 608—613 Impulse response function 551 Inclusion-exclusion bounds 487—489 Increasing failure rate (IFR) 498—499 502 519 520 521 Increasing failure rate on average (IFRA) 503 505 Independent events 10 11 Independent increments 250 Independent random variables 48—49 56 Independent trials 11 Indicator random variables 23 Inspection paradox 382—383 Instantaneous ransition rates 316 Interarrival times 255 Intersection of events 3 Inventory model 377—378 Inverse transformation method 564 Irreducible Markov chain 164 Joint cumulative probability distribution function 44 Joint moment generating function 67 Joint probability density function 45 Joint probability mass function 44 Jointly continuous random variables 45 k-of-n structure 477 482—483 502—503 522 Kolmogorov's equations, backward 318 Kolmogorov's equations, forward 320 Laplace's rule of succession 134 Limiting probabilities of a Markov chain 173—174 322—323 Linear filter 551 Linear growth model 307—309 325 Linear programming 187 220 533—534 List problem 124—125 207—209 226 Markov chain, continuous time 304—305 Markov chain, discrete time 157 Markov chain, Monte Carlo methods 211—217 Markov decision process 217—221 232—233 Markov's inequality 71—72 Markovian property 304 Martingale stopping theorem 555 556 Martingales 541 555 Matching problem 9 47 116—117 Matching rounds problem 103—105 Mean of a random variable see “Expected value” Mean value, analysis 439—440 Mean value, function of a renewal process see “Renewal function” Memoryless random variable 237 238 Minimal cut set 480 481 Minimal path set 478 479 Mixture of distributions 501 Moment generating function 60—61 Moment generating function of binomial random variables 61—62 Moment generating function of exponential random variables 63 Moment generating function of normal random variables 63—64 Moment generating of Poisson random variables 62 Moment generating of the sum of independent random variables 64 Moment generating, tables of 65 Moments 42—43 Monte Carlo simulation 212 560 Multinomial distribution 81 Multivariate normal distribution 67—69 Mutually exclusive events 3 Negative binomial distribution 82 Nonhomogeneous Poisson process 277—281 298 619 Nonhomogeneous Poisson process mean value function 278 Nonhomogeneous Poisson process, simulation of 589—595 Nonstationary Poisson process see “Nonhomogeneous Poisson process” Normal process see “Gaussian Process” Normal random variables 34—37 Normal random variables as approximations to the binomial 74—75 Normal random variables, simulation of 567—569 572—576 Normal random variables, sums of independent 66—67 Null event 3 Null recurrent state 173 Occupation time 337—338 349 Odds 534—535 options 530—532 535—539 Order statistics 57 Order statistics, simulation of 617—618 Ornstein — Uhlenbeck process 548—549 Parallel system 476 482 512 Parallel system upper bound on expected system life 509—511 Patterns 387—398 Patterns mean time until appearance 181—182 360—362 387—398 Patterns of increasing runs of specified size 397—398 Patterns of maximum run of distinct values 395—396 Patterns variance of time until appearance 387—392 Period of a stale of a Markov hain 173 Poisson process 250—252 Poisson process, conditional distribution of the arrival times 265 Poisson process, interarrival times 255 Poisson process, rate 250—251 252 Poisson process, simulation of 588 Poisson random variable sums of independent 56 66 Poisson random variable, approximation to the binomial 3 Poisson random variable, maximum probability 83 Poisson random variable, simulation of 582—583 Poisson random variables 30 93 Polar method of simulating normal random variables 574—576 Pollaczek — Khintchine fomula 444 Polya's urn model 134 Positive recurrent state 173 323 Power spectral density 552 Probability density function 31 32 Probability density function, relation to cumulative distribution function 32 Probability of a union of events 5 6 Probability of an event 4 Probability, mass function 25 Probability, model 1 Pure birth process 303 314 Queues, bulk service 429—432 Queues, function cost equations 412—413 Queues, G/M/k 458—460 Queues, G/M/l 451—455 Queues, G/M/l busy and idle periods 455—456 Queues, infinite server 266—268 Queues, infinite server loss systems 456 Queues, infinite server output process 280—281 Queues, M/C/k 460—461 Queues, M/G/l 442—445 470 Queues, M/G/l busy and idle periods 444—445 470—471 Queues, M/G/l network of queues 432—442 Queues, M/G/l network of queues analysis via the Gibbs sampler 441—442 Queues, M/G/l network of queues closed systems 437—442 Queues, M/G/l network of queues mean value analysis 439—440 Queues, M/G/l network of queues open systems 432—437 Queues, M/G/l output process 331 Queues, M/G/l single server exponential queue (M/M/1) 309—310 326 416—423 Queues, M/G/l single server exponential queue with finite capacity 334 423—426 Queues, M/G/l steady state probabilities 414—416 Queues, M/G/l tandem queues 346 432 Queues, M/G/l with batch arrivals 446—448 Queues, M/G/l with priorities 448—451 471 472 Queues, multiserver exponential queue (M/M/s) 310 325 346 458 462 Queues, multiserver exponential queue departure process 331 468—469 Quick-sort algorithm 107—109 Random graph 126—132 491—495 Random numbers 560 Random permutations 561—562 Random subset 563 619 Random telegraph signal process 547 Random variables 21 Random variables continuous 24 31 Random variables discrete 24 25 Random walk 159 167—168 189—193 202—204 223 Rate of a renewal process 358 Rate of exponential random variable 240 Records 89 298—299 Records, k-Record index 139 Records, k-Record values 137 Recurrent state 164 165 166 Regenerative process 373 Rejection method in simulation 565—566 567 Rejection method in simulation for discrete random variables 616 Reliability function 482 484 485 486 504 Reliability function, bounds for 489 495—497 519 Renewal equation 356 Renewal function 354 Renewal function estimation by simulation 604—606 Renewal function, computation of 384—387 Renewal process 351 Renewal process, central limit theorem for 365 Renewal reward process 366 395 Residual life of a renewal process see “Excess life” Reverse chain 201 210—211 231 330 Sample mean 51 71 Sample space 1 Sample variance 68—69 71 Satisfiability problem 193—195 Second order stationary process 548 550
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