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| Авторизация |
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| Feller W. — Introduction to probability theory and its applications (volume 1) |
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| Предметный указатель |
Morse code 54
moving averages 422 426
Multinomial coefficients 37
Multinomial distribution 167 215 239
Multinomial distribution generating function 279
Multinomial distribution maximal term 171 194
Multinomial distribution randomized 216 301
Multiple Bernoulli trials 168 171 238
Multiple classification 27
Multiple coin games 316 338
Multiple Poisson distribution 172
Multiplets 27
Murphy, G.M. and Margenau, H. 41
Mutations 295
M’Kendrick, A.G. 450
Negation 15
Negative binomial distribution 164ff. 238
Negative binomial distribution as limit of Bose — Einstein statistics 61
Negative binomial distribution as limit of Bose — Einstein statistics and of Polya distr. 143
Negative binomial distribution expectation 224
Negative binomial distribution generating function 268
Negative binomial distribution in birth and death processes 450
Negative binomial distribution infinite divisibility 289
Negative binomial distribution, bivariate 285
Negative binomial distribution, Poisson limit of 166 281
Nelson, E. 96
Newman, D.J. 210 367
Newton, I. 55
Newton’s binomial formula 51
Neyman, J. 163 285
Non-Markovian processes 293 421 426
Non-Markovian processes satisfying Chapman — Kolmogorov equation 423 471
Normal approximation for binomial distribution 76 179ff.
Normal approximation for binomial distribution large deviations 192 195
Normal approximation for changes of sign 86
Normal approximation for combinatorial runs 194
Normal approximation for first passages 90
Normal approximation for hypergeometric distribution 194
Normal approximation for permutations 256
Normal approximation for Poisson distribution 190 194 245
Normal approximation for recurrent events 321
Normal approximation for returns to origin 90
Normal approximation for success runs 324 (cf. “Central limit theorem”)
Normal density and distribution 174
Normal density and distribution tail estimates 179 193
Normalized random variables 229
Nuclear chain reaction 294
Null state 388
Number theoretical interpretations 208
Occupancy numbers 38
Occupancy problems 38ff. 58ff. 101ff. 241
Occupancy problems empirical interpretations 9
Occupancy problems multiply occupied cells 112
Occupancy problems negative binomial limit 61
Occupancy problems Poisson limit 59 105
Occupancy problems treatment by Markov chains 379 435
Occupancy problems treatment by Markov chains and by randomization 301
Occupancy problems waiting times 47 225
Occupancy problems waiting times, elementary problems 27 32 35 55 141 237 “Bose “Collector’s
Optional stopping 186 241
Orderings 29 36 “Runs combinatorial”)
Ore, O. 56
Orey, S. 413
Pairs 26
Palm, C. 460 462
Panse, V.G. and Sukhatme, P.V. 150
Parapsychology 56 407
Parapsychology Guessing 107
Parking lots 55 479
Parking tickets 55
Partial derivatives 39
Partial fraction expansions 275ff. 285
Partial fraction expansions explicit calculations for reflecting barrier 436ff.
Partial fraction expansions for finite Markov chains 428ff.
Partial fraction expansions for ruin problem 349ff.
Partial fraction expansions for ruin problem and for success runs 322ff.
Partial fraction expansions numerical calculations 278 325 334
Particular solutions, method of 344 347 365
Partitioning of polygons 283
Partitioning of stochastic matrices 386
Partitions, combinatorial 34ff.
Pascal, B. 56
Pascal’s distribution 166
Pathria, R.K. 32
Paths in random walks 68
Pearson, K. 173 256
Pedestrians as non-Markovian process 422
Pedestrians crossing the street 170
Pepys, S. 55
Periodic Markov chains (states) 387 404ff.
Periodic recurrent events 310
permutations 29 406
Permutations represented by independent trials 132 256ff.
Persistent recurrent event 310
Persistent recurrent event limit theorem 335
Persistent state 388
Petersburg Paradox 251
Petri plate 163
Phase space 13
Photographic emulsions 11 59
Poisson approximation or limit for Bernoulli trials with variable probabilities 282
Poisson approximation or limit for binomial distr. 153ff 172 190
Poisson approximation or limit for density fluctuations 425
Poisson approximation or limit for hyper-geometric distr. 172
Poisson approximation or limit for long success runs 341
Poisson approximation or limit for matching 108
Poisson approximation or limit for negative binomial 172 281
Poisson approximation or limit for normal distr. 190 245
Poisson approximation or limit for occupancy problems 105 153
Poisson approximation or limit for stochastic processes 461 462 480 481
Poisson distribution (the ordinary) 156ff.
Poisson distribution convolutions 173 266
Poisson distribution empirical observations 159ff.
Poisson distribution generating function 268
Poisson distribution integral representation 173
Poisson distribution moments 224 228
Poisson distribution normal approximation 190 194 245
Poisson distributions bivariate 172 279
Poisson distributions compound 288ff. 474
Poisson distributions generalized 474
Poisson distributions multiple 172
Poisson distributions spatial 159
Poisson distributions spatial combined with binomial distr. 171 287 301
Poisson process 292 446ff.
Poisson process backward and forward equs. 469—470
Poisson process generalized 474
Poisson traffic 459
Poisson trials (= Bernoulli trials with variable probabilities) 218 230 282
Poisson, S.D. 153
Poker definition 8
Poker tabulation 487
Poker, Elementary problems 35 58 169
Pollard, H. 312
Polya process 480
Polya urn model 120 142 240 262 480
Polya urn model as non-Markovian process 421
Polya’s distribution 142 143 166 172
Polygons, partitions of 283
Polymers 11 240
Population 34ff.
Population growth 334—335 450 456
Population in renewal theory 334—335 340
Population, stratified 117
Positive state 389
power supply problems 149 467
Product measure 131
Product spaces 128ff.
Progeny (in branching processes) 298ff.
Prospective equations cf. “Forward equations”
Quality control 42 (cf. “Inspection sampling”)
| Queue discipline 479
Queuing and queues 306 315 460ff. 479
Queuing and queues a Markov chain in queuing theory 425
Queuing and queues as branching process 295 299—301
Queuing and queues general limit theorem 320
Radiation cf. “Cosmic rays” “Irradiation”
Radioactive disintegrations 157 159 328
Radioactive disintegrations, differential equations for 449
Raff, M.S. 240
Raisins, distribution of 156 169
Random chains 240
Random choice 30
Random digits (= random sampling numbers) 10 31
Random digits normal approximation 189
Random digits Poisson approximation 155
Random digits, Elementary problems 55 169
Random digits, references to 21 61
Random mating 134
Random placement of balls into cells cf. “Occupancy problems”
Random sampling cf. “Sampling”
Random sums 286ff.
Random variables 212ff.
Random variables, defective 273 309
Random variables, integral valued 264ff.
Random variables, normalized 229 (cf. “Independent Random variables”)
Random walks 67ff. 342ff.
Random walks cyclical 377 434
Random walks invariant measure 408
Random walks Markov chain treatment 373 376—377 425 436ff.
Random walks renewal method 370
Random walks reversibility 415
Random walks with variable probabilities 402 (cf. “Absorbing barrier” “Arc “Changes “Diffusion” “Duration “First “Leads” “Maxima” “Reflecting “Returns “Ruin
Random walks, dual 91
Random walks, generalized 363ff. 368
Randomization method in occupancy problems 301
Randomization method in sampling 216 (cf. “Random sums”)
Randomness in sequences 204
Randomness in sequences, tests for 42 61
RANGE 213
Rank order test 69 94
Ratio limit theorem 407 413
Realization of events, simultaneous 16 99 106 109 142
Recapture in trapping experiments 45
Recessive genes 133
Recessive genes sex-linked 139
Recurrence times 388
Recurrence times in Markov chains 388 (cf. “Renewal theorem”)
Recurrent events 310ff.
Recurrent events reversibility 415 (cf. “Renewal theorem”)
Recurrent events, delayed 316ff.
Recurrent events, Markov chain treatment of 381—382 398 403
Recurrent events, number of occurrences of a 320ff.
Reduced number of successes 186
Reflecting barriers 343 367ff.
Reflecting barriers invariant distribution 397 424
Reflecting barriers two dimensions 425
Reflecting barriers, Markov chain for 376 436ff.
Reflection principle 72 369
Reflection principle, Repeated reflections 96 369ff.
Rencontre (= matches) 100 107
Renewal argument 331
Renewal method for random walks 370
Renewal of aggregates and populations 311 334—335 340 381
Renewal Theorem 329
Renewal theorem, estimates to 340
Renewal theorem, estimates to, for Markov chains 443
Repairs of machines 462ff.
Repeated averaging 333 425
replacement cf. “Renewal” “Sampling”
Residual waiting time 332 381
Retrospective equations cf. “Backward equations”
Return process 477
Returns to origin first return 76—78 273 313
Returns to origin in higher dimensions 360
Returns to origin nth return 90 274
Returns to origin through negative values 314 339
Returns to origin visits prior to first 376 (cf. “Changes of sign” “First
Returns to origin, number of 96
Reuter, G.E. and Ledermann, W. 455
Reversed Markov chains 414ff.
Riordan, J. 73 299 306
Robbins, H.E. 53
Romig, H.C. 148
Ruin problem 342ff.
Ruin problem in generalized random walk 363ff.
Ruin problem renewal method 370
Ruin problem with ties permitted 367
Rumors 56
Runs, combinatorial 42 62
Runs, combinatorial moments 240
Runs, combinatorial normal approximation 194 (cf. “Success runs”)
Rutherford — Chadwick — Ellis 160
Rutherford, E. 170
Sacks, L. and Li, C.C. 144
Safety campaign 121
Sample point 9
Sample space 4 9 13ff.
Sample space discrete 17ff.
Sample space for repeated trials and experiments 128ff.
Sample space in terms of random variables 217
Sampling 28ff. 59 132 232
Sampling required sample size 189 245
Sampling waiting times 224 239
Sampling waiting times, Elementary problems 10 12 56 117 194 “Inspection
Sampling, randomized 216
Sampling, sequential 344 363
Sampling, stratified 240
Savage, L.J. 4 346
Schell, E.D. 55
Schensted, I.V. 379
Schroedinger, E. 294
Schwarz’ inequality 242
Seeds Poisson distribution 159
Seeds survival 295
Segregation, subnuclear 379
Selection (genetic) 139 143 295
Selection principle 336
Self-renewing aggregates 311 334 340
Senator problem 35 44
Sequential sampling 344 363
Sequential tests 171
Sera, testing of 150
Servers cf. “Queuing” “Trunking
Service times 457ff.
Service times as branching process 288
Servicing factor 463
Servicing problems 460 479
Seven-way lamps 27
Sex distribution within families 11 117 118 126 169 288
Sex-linked characters 136
Shewhart, W.A. 42
Shoe problems 57 111
Shuffling 406
Shuffling, composite 422
Simulation of a perfect coin 238
Small numbers, law of 159
Smirnov, N. 70 71
Smith, B. and Kendall, M.G. 154
Sobel, M. and Groll, P.A. 239
Sojourn times 82 453
Sparre-Andersen, E. 82
Spent waiting time 382
Spores 226 379
Spurious contagion 121
Stable distribution of order one half 90
Stakes (effect of changing) 346
Standard deviation 228
Stars (Poisson distribution) 159 170
States in a Markov chain 374 446
States in a Markov chain absorbing 384
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