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Ross S.M. — Introduction to probability models

Ross S.M. — Introduction to probability models

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Название: Introduction to probability models

Автор: Ross S.M.

Аннотация:

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.

Язык:

Рубрика: Математика/Вероятность/Стохастические процессы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: sixth edition

Год издания: 1997

Количество страниц: 669

Добавлена в каталог: 10.06.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$L = \lambda_a W$       413—414
$L_Q = \lambda_a W_Q$       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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