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| Feller W. — Introduction to probability theory and its applications (volume 1) |
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| Предметный указатель |
Ehrenfest model steady state 397
Ehrenfest, P. and T. 121
Eigenvalue = characteristic value 429
Einstein — Bose statistics 5 20 40 61 113
Einstein — Bose statistics negative binomial limit 62
Eisenhart, C. and Swed, F.S. 42.
Elastic barrier 343 368 377
Elastic force, diffusion under 378
Elevator problem 11 32 58
Elevator problem complete table 486
Ellis, R.E. 354
Empirical distribution 71
Entrance boundary 419
Epoch 73 300 306 444
Equalization cf. “Changes of sign” “Returns
Equidistribution theorems 94 97
Equilibrium, macroscopic 395ff. 456
Equilibrium, return to cf. “Returns to origin”
Erdoes, P. 82 211 312
Ergodic properties in Markov chains 393ff. 443
Ergodic properties in stochastic processes 455 482
Ergodic states 389
Erlang, A.K. 460
Erlang’s loss formula 464
Error function 179
ESP 55 407
Essential states 389
Estimation from recaptures and trapping 45 170
Estimation from samples 189 226 238
Estimator, unbiased 242
Events 8 13ff.
Events in product spaces 128ff.
Events independent 125ff.
Events, compatible 98
Events, simultaneous realization of 16 99 106 109
Evolution process (Yule) 450 (cf. “Genes”)
Exit boundary 416
Expectation 220ff.
Expectation from generating functions 265
Expectation infinite 265
Expectation of normal distribution 179
Expectation of products 227
Expectation of reciprocals 238 242
Expectation of sums 222
Expectation, conditional 223
Experiments compound and repeated 131
Experiments conceptual 9ff.
Exponential characterization by a functional equ. 459
Exponential distribution 446
Exponential holding times 458ff.
Exponential sojourn times 453
Extinction in birth and death processes 457
Extinction in bivariate branching processes 302
Extinction in branching processes 295ff.
Extinction of family names 294
Extinction of genes 136 295 400
Extra Sensory Perception 55 407
Factorials 29
Factorials gamma function 66
Factorials Stirling’s formula 52 66
Fair games 248ff. 346
Fair games with infinite expectation 252
Fair games, unfavorable 249 262
Faltung “Convolution”
Families dishwashing 56
Families, sex distribution in 117 118 126 141 288
Family names, survival of 294
Family relations 144
Family size, geometric distribution for 141 294 295
Ferguson, T.S. 237
Fermi — Dirac statistics 5 40
Fermi — Dirac statistics for misprints 42 58
Finucan, H.M. 28 239
Fire cf. “Accidents”
Firing at targets 10 169
First passage times in Bernoulli trials and random walks 88 271 274 343ff.
First passage times in Bernoulli trials and random walks Explicit formulas 89 274 275 351 353 368
First passage times in Bernoulli trials and random walks limit theorems 90 360 “Returns “Waiting
First passage times in diffusion 359 368 370
First passage times in Markov chains 388
First passage times in stochastic processes 481 (cf. “Absorption probabilities”)
Fish catches 45
Fisher, R.A. 6 46 149 380
Fission 294
Flags, display of 28 36
Flaws in material 159 170
Flying bomb hits 160
Fokker — Planck equation 358
Forward equations 358 469 473 482
Frame, J.S. 367
Frechet, M. 98 111 375
Freedman, D. 78
Frequency function 179
Friedman, B. (urn model) 119 121 378
Fry, T.C. 460
Fuerth, R. 422
Fuerth’s formula 359
Furry, W.H. 451
G. — M. Counters cf. Geiger counters
Galton, F. 70 256 294
Galton’s rank order test 69 94
Gambling systems 198ff. 345
Gamma function 66
Gauss (= normal) distribution 179
Geiger counters 11
Geiger counters as Markov chain 425
Geiger counters general types 339
Geiger counters type I 306 315
Geiringer, H. 6
Generalized Poisson process 474
Generating functions 264
Generating functions, bivariate 279
Generating functions, moment 285 301
Genes 132ff.
Genes evolution of frequencies 135ff. 380 400
Genes inheritance 256
Genes mutations 295
Genes Yule process 450
Genetics 132ff.
Genetics branching process 295
Genetics Yule process 450
Genetics, Markov chains in 379 380 400
Geometric distribution 216
Geometric distribution as limit for Bose — Einstein statistics 61
Geometric distribution as negative binomial 166 224
Geometric distribution characterization 237 328
Geometric distribution convolutions 269
Geometric distribution exponential limit 458
Geometric distribution generating function 268
Gnedenko, B.V. 71
Goncarov, V. 258
Good, I.J. 298 300
Greenwood, J.A. and Stuart, E.E. 56 407
Greenwood, R.E. 61
Groll, P.A. and Sobel, M. 239
Grouping of states 426
Grouping, tests of 42
guessing 107
Gumbel, E.J. 156
Halstroem, H.L. 460
Hamel equation 459
Hardy, G.H. and Littlewood, J.E. 209
Hardy’s law 135
Hardy’s law nonapplicability to pairs 144
Harris, T.E. 297 426
Hausdorff, F. 204 209
Heat flow cf. “Diffusion” “Ehrenfest
Heterozygotes 133
Higher sums 421
Hitting probabilities 332 339
| Hodges, J.L. 69
Hoeffding, W. 231
Holding times 458ff.
Holding times as branching process 286
Homogeneity, test for 43
Homozygotes 133
Hybrids 133
Hypergeometric distribution 43ff.
Hypergeometric distribution approximation by binomial and by Poisson 59 172
Hypergeometric distribution approximation by normal distr. 194
Hypergeometric distribution as limit in Bernoulli — Laplace model 397
Hypergeometric distribution moments 232
Hypergeometric distribution, multiple 47
Hypothesis for conditional probability 115
hypothesis, statistical cf. “Estimation” “Tests”
Images, method of 72 369
Implication 16
Improper (= defective) random variable 273 309
Independence, stochastic 125ff.
Independence, stochastic pair-wise but not mutual 127 143
Independent experiments 131
Independent increments 292
Independent random variables 217 241
Independent random variables pairwise but not mutually 220
Independent trials 128ff.
Indistinguishable elements in problems of occupancy and arrangements 38ff. 58
Indistinguishable elements in problems of occupancy and arrangements elementary examples 11 20 36
Infinite moments 246 265
Infinite moments limit theorems involving 90 252 262 313 322
Infinitely divisible distributions 289
Infinitely divisible distributions factorization 291
inheritance 256 (cf. “Genetics”)
Initials 54
Insect litters and survivors 171 288
Inspection sampling 44 169 238
Inspection sampling, sequential 363 368
Intersection of events 16
Invariant distributions and measures (in Markov chains) 392ff. 407ff.
Invariant distributions and measures periodic chains 406 (cf. “Stationary distributions”)
Inverse probabilities (in Markov chains) 414
Inversions (in combinations) 256
Irradiation, harmful 10 55 112
Irradiation, harmful Poisson distribution 161 287
Irreducible chains 384 390ff.
Ising’s model 43
Iterated logarithm, law of the 186 204ff.
Iterated logarithm, law of the stronger form 211
Iterated logarithm, law of the stronger form, Number theoretical interpretation 208
Kac, M. 55 82 121 378 438
Karlin, S. and McGregor, J.L. 455
Kelvin’s method of images 72 369
Kendall, D.G. 288 295 456
Kendall, M.G. and Smith, B. 154
Key problems 48 55 141 239
Khintchine, A. 195 205 209 244
Kolmogorov — Smirnov type tests 70
Kolmogorov, A. 6 208 312 354 375 389 419 461
Kolmogorov’s criterion 259
Kolmogorov’s criterion converse 263
Kolmogorov’s differential equations 475
Kolmogorov’s inequality 234 (cf. “Chapman — Kolmogorov equation”)
Koopman, B.O. 4
Kronecker symbols 428
Ladder variables 305 315
Lagrange, J.L. 285 353
Laplace, P.S. 100 179 264
Laplace’s law of succession 124 (cf. “Bernoulli — Laplace model” “DeMoivre
Large numbers, strong law of 258 262
Large numbers, strong law of, for Bernoulli trials 203
Large numbers, weak law of 243ff. 254
Large numbers, weak law of generalized form (with infinite expectations) 246 252
Large numbers, weak law of, for Bernoulli trials 152 195 261
Large numbers, weak law of, for dependent variables 261
Large numbers, weak law of, for permutations 256
Largest observation, estimation from 226 238
Last visits (arc sine law) 79
Leads, distribution of 78ff. 94
Leads, distribution of, experimental illustration 86ff.
Leads, distribution of, experimental illustration, Galton’s rank order test 69
Ledermann, W. and Reuter, G.E. 455
Lefthanders 169
Levy, Paul 82 290
Li, C.C. and Sacks, L. 144
Lightning, damage from 289 292
Lindeberg, J.W. 244 254 261
Linear growth process 456 480
Little wood, J.E. 209
Ljapunov, A. 244 261
Logarithm, expansion for 51
Logarithmic distribution 291
Long chain molecules 11 240
Long leads in random walks 78ff.
Loss formula, Erlang’s 464
Loss, coefficient of 466
Lotka, A.J. 141 294
Lunch counter example 42
Lundberg, O. 480
Machine servicing 462ff. (cf. “Power supply”)
Macroscopic equilibrium 395ff. 456
Malecot, G. 380
Mallows, C.L. and Barton, D.E. 69
Marbe, K. 147
Margenau, H. and Murphy, G.M. 41
Marginal distribution 215
Markov chains 372ff.
Markov chains of infinite order 426
Markov chains, mixing of 426
Markov chains, superposition of 422
Markov process 419ff.
Markov process with continuous time 444ff. 470ff.
Markov process with continuous time, Markov property 329
Markov, A. 244 375
Martin, R.S. (boundary) 419
Martingales 399
Match box problem 166 170 238
Matches = coincidences 100 107
Matching of cards 107ff. 231
Matching of cards, multiple 112
Mating (assortative and random) 134
Mating brother-sister mating 143 380 441
Maxima in random walks distribution 369
Maxima in random walks position 91ff. 96
Maxima in random walks position arc sine laws 93
Maximal solution (in Markov chains) 401
Maximum likelihood 46
Maxwell, C. 72 (cf. “Boltzmann — Maxwell statistics”)
McCrea, W.H. and Whipple, F.J.W. 360 362
McGregor, J. and Karlin, S. 455
Mean cf. “Expectation”
Median 49 220
Memory in waiting times 328 458
Mendel, G. 132
Miller, K.W. and Adler, H.A. 467
Minimal solution for Kolmogorov differential equations 475
Minimal solution in Markov chains 403
Mises relating to occupancy problems 32 105 106 341
Misprints 11
Misprints estimation 170
Misprints Poisson distribution 156 169
Misprints, Fermi — Dirac distribution for 42 58
Mixtures of distributions 301
Mixtures of Markov chains 426
Mixtures of populations 117 121
Molina, E.C. 155 191
Moment generating function 285 301
Moments 227
Moments, infinite 246 265
Montmort, P.R. 100
Mood, A.M. 194
Moran, P.A.P. 170
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