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Ross S.M. Ч Introduction to probability models
Ross S.M. Ч Introduction to probability models

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Ќазвание: Introduction to probability models

јвтор: Ross S.M.


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: en

–убрика: ћатематика/¬еро€тность/—тохастические процессы/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

»здание: sixth edition

√од издани€: 1997

 оличество страниц: 669

ƒобавлена в каталог: 10.06.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
ѕредметный указатель
$L = \lambda_a W$      413Ч414
$L_Q = \lambda_a W_Q$      414
Absorbing state of a Markov chain      160
Accessibility of states      163
Age of a renewal process      371 375Ч376 405
Alias method      584Ч587
Aloha protocol      170Ч171
Alternating renewal process      374Ч375
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      511Ч512
Balance equations      323 418
Ballot problem      117Ч118 152
Bayes formula      14
Bernoulli random variable      26
Bernoulli random variable, simulation of      582
Best prize problem      114Ч115
Beta random variable      567 577
Beta random variable, simulation of      577Ч578
Binomial random variables      26Ч27 81 87 93 94
Binomial random variables, simulation of      582
Binomial random variables, sums of independent      66
Birth and death process      303 306Ч313 323Ч324 331
Bivariate exponential distribution      299
Bivariate normal distribution      142Ч143
Black Ч Scholes formula      536Ч539
Bonferroni's inequality      15
Boole's inequality      16
Bose Ч Einstein distribution      136
Box Ч Muller method of simulating normal random variables      574
Branching process      197Ч200 230
Bridge structure      480 490
Brownian bridge      543Ч544 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      545Ч546
Brownian motion, maximum variable      528
Busy period      284Ч285 444Ч445
Cayley's theorem      493
Central limit theorem      74
Chapman Ч Kolmogorov equations in continuous time      317
Chapman Ч Kolmogorov equations in discrete time      160
Chebyshev's inequality      72
Chi-squared random variables      69 574
Chi-squared random variables, moment generating function of      69Ч70
Chi-squared random variables, simulation of      576Ч577
Class of a Markov chain      163
Closed class      222
Communication of states      163
Complement of an event      4
Compound Poisson process      281Ч282 286Ч287
Conditional expectation      92 95 97 99
Conditional probability      7
Conditional probability, density function      96
Conditional probability, distribution function      92
Conditional probability, mass function      91Ч92
Conditional variance formula      147 283 312 313
Connected graph      126 205
Control variates      606Ч608
Convolutions      55
Counting process      249
Coupon collecting problem      261Ч262
Covariance      49Ч51 148
Coxian random variables      248Ч249
Craps      16
Cumulative distribution function      24
Decreasing failure rate (DFR)      498Ч499
Delayed renewal process      387 400
Dependent events      10
Dirichlet distribution      135
Distribution function      see УCumulative distribution functionФ
Doubly stochastic      223
Ehrenfest urn model      204 228
Elementary renewal theorem      358 401Ч402
Equilibrium distribution      406
Ergodic Markov chain      323
Ergodic state      173
Erlang's loss system      456Ч458
Event      2
Excess of a renewal process      363 372 376
Expectation      see УExpected valueФ
Expected value      36
Expected value of Bernoulli random variables      37
Expected value of Binomial random variables      37 46Ч47 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      40Ч42 45Ч46
Expected value of geometric random variables      37Ч38 101Ч102
Expected value of normal random variables      39Ч40 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 508Ч509
Exponential random variable, simulation of      565 578Ч580
Failure rate function      239Ч240 498
Gambler's ruin problem      183Ч184 185 229
Gamma function      34
Gamma random variables      34 58Ч59 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 УDelayed renewal processФ
Geometric Brownian motion      529Ч530
Geometric random variable      29 141
Geometric random variable, simulation of      581
Gibbs sampler      214Ч217 441Ч442
Graph      126 347
Greedy algorithms      244Ч245
Hardy Ч Weinberg law      176Ч177
Hastings Ч Metropolis algorithm      212Ч214
Hazard function      503
Hazard rate function      see УFailure rate functionФ
Hazard rate, method of simulation      569Ч570
Hazard rate, method of simulation for discrete random variables      616
Hit-miss method      620
Hyperexponential random variables      241Ч242
Hypergeometric random variables      54 94
Hypoexponential random variables      245Ч249
Idle period      284 444
Ignatov's theorem      122 138
Importance sampling      608Ч613
Impulse response function      551
Inclusion-exclusion bounds      487Ч489
Increasing failure rate (IFR)      498Ч499 502 519 520 521
Increasing failure rate on average (IFRA)      503 505
Independent events      10 11
Independent increments      250
Independent random variables      48Ч49 56
Independent trials      11
Indicator random variables      23
Inspection paradox      382Ч383
Instantaneous ransition rates      316
Interarrival times      255
Intersection of events      3
Inventory model      377Ч378
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 482Ч483 502Ч503 522
Kolmogorov's equations, backward      318
Kolmogorov's equations, forward      320
Laplace's rule of succession      134
Limiting probabilities of a Markov chain      173Ч174 322Ч323
Linear filter      551
Linear growth model      307Ч309 325
Linear programming      187 220 533Ч534
List problem      124Ч125 207Ч209 226
Markov chain, continuous time      304Ч305
Markov chain, discrete time      157
Markov chain, Monte Carlo methods      211Ч217
Markov decision process      217Ч221 232Ч233
Markov's inequality      71Ч72
Markovian property      304
Martingale stopping theorem      555 556
Martingales      541 555
Matching problem      9 47 116Ч117
Matching rounds problem      103Ч105
Mean of a random variable      see УExpected valueФ
Mean value, analysis      439Ч440
Mean value, function of a renewal process      see УRenewal functionФ
Memoryless random variable      237 238
Minimal cut set      480 481
Minimal path set      478 479
Mixture of distributions      501
Moment generating function      60Ч61
Moment generating function of binomial random variables      61Ч62
Moment generating function of exponential random variables      63
Moment generating function of normal random variables      63Ч64
Moment generating of Poisson random variables      62
Moment generating of the sum of independent random variables      64
Moment generating, tables of      65
Moments      42Ч43
Monte Carlo simulation      212 560
Multinomial distribution      81
Multivariate normal distribution      67Ч69
Mutually exclusive events      3
Negative binomial distribution      82
Nonhomogeneous Poisson process      277Ч281 298 619
Nonhomogeneous Poisson process mean value function      278
Nonhomogeneous Poisson process, simulation of      589Ч595
Nonstationary Poisson process      see УNonhomogeneous Poisson processФ
Normal process      see УGaussian ProcessФ
Normal random variables      34Ч37
Normal random variables as approximations to the binomial      74Ч75
Normal random variables, simulation of      567Ч569 572Ч576
Normal random variables, sums of independent      66Ч67
Null event      3
Null recurrent state      173
Occupation time      337Ч338 349
Odds      534Ч535
options      530Ч532 535Ч539
Order statistics      57
Order statistics, simulation of      617Ч618
Ornstein Ч Uhlenbeck process      548Ч549
Parallel system      476 482 512
Parallel system upper bound on expected system life      509Ч511
Patterns      387Ч398
Patterns mean time until appearance      181Ч182 360Ч362 387Ч398
Patterns of increasing runs of specified size      397Ч398
Patterns of maximum run of distinct values      395Ч396
Patterns variance of time until appearance      387Ч392
Period of a stale of a Markov hain      173
Poisson process      250Ч252
Poisson process, conditional distribution of the arrival times      265
Poisson process, interarrival times      255
Poisson process, rate      250Ч251 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      582Ч583
Poisson random variables      30 93
Polar method of simulating normal random variables      574Ч576
Pollaczek Ч 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      429Ч432
Queues, function cost equations      412Ч413
Queues, G/M/k      458Ч460
Queues, G/M/l      451Ч455
Queues, G/M/l busy and idle periods      455Ч456
Queues, infinite server      266Ч268
Queues, infinite server loss systems      456
Queues, infinite server output process      280Ч281
Queues, M/C/k      460Ч461
Queues, M/G/l      442Ч445 470
Queues, M/G/l busy and idle periods      444Ч445 470Ч471
Queues, M/G/l network of queues      432Ч442
Queues, M/G/l network of queues analysis via the Gibbs sampler      441Ч442
Queues, M/G/l network of queues closed systems      437Ч442
Queues, M/G/l network of queues mean value analysis      439Ч440
Queues, M/G/l network of queues open systems      432Ч437
Queues, M/G/l output process      331
Queues, M/G/l single server exponential queue (M/M/1)      309Ч310 326 416Ч423
Queues, M/G/l single server exponential queue with finite capacity      334 423Ч426
Queues, M/G/l steady state probabilities      414Ч416
Queues, M/G/l tandem queues      346 432
Queues, M/G/l with batch arrivals      446Ч448
Queues, M/G/l with priorities      448Ч451 471 472
Queues, multiserver exponential queue (M/M/s)      310 325 346 458 462
Queues, multiserver exponential queue departure process      331 468Ч469
Quick-sort algorithm      107Ч109
Random graph      126Ч132 491Ч495
Random numbers      560
Random permutations      561Ч562
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 167Ч168 189Ч193 202Ч204 223
Rate of a renewal process      358
Rate of exponential random variable      240
Records      89 298Ч299
Records, k-Record index      139
Records, k-Record values      137
Recurrent state      164 165 166
Regenerative process      373
Rejection method in simulation      565Ч566 567
Rejection method in simulation for discrete random variables      616
Reliability function      482 484 485 486 504
Reliability function, bounds for      489 495Ч497 519
Renewal equation      356
Renewal function      354
Renewal function estimation by simulation      604Ч606
Renewal function, computation of      384Ч387
Renewal process      351
Renewal process, central limit theorem for      365
Renewal reward process      366 395
Residual life of a renewal process      see УExcess lifeФ
Reverse chain      201 210Ч211 231 330
Sample mean      51 71
Sample space      1
Sample variance      68Ч69 71
Satisfiability problem      193Ч195
Second order stationary process      548 550
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