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Feller W. Introduction to probability theory and its applications (volume 1)
Feller W.  Introduction to probability theory and its applications (volume 1)









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: Introduction to probability theory and its applications (volume 1)

: Feller W.

:

Major changes in this edition include the substitution of probabilistic arguments for combinatorial artifices, and the addition of new sections on branching processes, Markov chains, and the De Moivre-Laplace theorem.


: en

: //

:

ed2k: ed2k stats

: third edition

: 1967

: 509

: 29.05.2005

: | | ID
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$(n)_\tau$      29
$p(k;\lambda)$      157
$\mathfrak{n}$ and $\mathfrak{R}$      174
$\pi$, distribution of decimals      31 61
$\varepsilon$ for recurrent events      303 308
Absolute probabilities      116
Absolute probabilities in Markov chains      384
Absorbing barrier in random walks      342 368 369 376
Absorbing barrier in random walks in higher dimensions      361
Absorbing boundaries      477
Absorbing states (in Markov chains)      384
Absorption probabilities in birth and death processes      455 457
Absorption probabilities in diffusion      358 367
Absorption probabilities in Markov chains      399ff. 418 424 425 438ff.
Absorption probabilities in random walk      342ff. 362 367 Extinction First Ruin
Acceptance      cf. Inspection sampling
Accidents as Bernoulli trials with variable probabilities      282
Accidents bomb hits      160
Accidents distribution of damages      288
Accidents occupancy model      10
Accidents Poisson distribution      158 292
Accidents urn models      119 121
Adler, H.A. and Miller, K.W.      467
Aftereffect urn models      119 122
Aftereffect, lack of      329 458
Age distribution in renewal theory      335 340
Age distribution in renewal theory, example involving ages of a couple      13 17
Aggregates, self-renewing      311 334 340
Alleles      133
Alphabets      129
Andersen      cf. Sparre Andersen E.
Andre, D.      72 369
Animal populations recaptures      45
Animal populations trapping      170 239 288 301
Aperiodic      cf. Periodic
Arc sine distributions      79
Arc sine law for first visits      93
Arc sine law for last visits      79
Arc sine law for maxima      93
Arc sine law for sojourn times      82
Arc sine law for sojourn times, Counterpart      94
Arrangements      cf. Ballot problem Occupancy
Average of distribution      Expectation
Averages, moving      422 426
Averaging, repeated      333 425
b(k; n, p)      148
Bachelier, L.      354
Backward equations      358 468 474 482
Bacteria counts      163
Bailey, N.T.J.      45
Ballot problem      69 73
Balls in cells      cf. Occupancy problems
Banachs match box problem      166 170 238
Barriers, classification of      343 376
Bartky, W.      363
Barton, D.E. and Mallows, C.L.      69
Bates, G.E. and Neyman, J.      285
Bayes rule      124
Bernoulli trials definition      146
Bernoulli trials interpretation in number theory      209
Bernoulli trials with variable probabilities      218 230 282
Bernoulli trials, infinite sequences of      196ff.
Bernoulli trials, multiple      168 171 238
Bernoulli trials, recurrent events connected with      313ff. 339 Betting First Random Returns Success etc.)
Bernoulli Laplace model of diffusion      378 397
Bernoulli Laplace model of diffusion generalized      424
Bernoulli, D.      251 378
Bernoulli, J.      146 251
Bernstein, S.      126
Bertrand, J.      69
beta function      173
Betting      256 344ff. 367
Betting in games with infinite expectation      246 251ff. 322
Betting on runs      196 210 327
betting systems      198 346
Betting three players taking turns      18 24 118 141 424 Ruin
Bias in dice      149
Billiards      284
Binomial coefficients      34 50ff.
Binomial coefficients, identities for      63ff. 96 97 120
Binomial distribution      147ff.
Binomial distribution as conditional distr. in Poisson process      237
Binomial distribution central term      150 180 184
Binomial distribution combined with Poisson      171 287 301
Binomial distribution expectation      223
Binomial distribution expectation, absolute      241
Binomial distribution generating function      268
Binomial distribution in occupancy problems      35 109
Binomial distribution tail estimates      151152 173 193ff.
Binomial distribution variance      228 230
Binomial distribution, as limit in Ehrenfest model      397
Binomial distribution, convolution of      173 268
Binomial distribution, for hypergeometric distr.      59 172
Binomial distribution, integrals for      118 368 370
Binomial distribution, normal approximation to      179ff.
Binomial distribution, Poisson approximation to      153ff. 171172 190
Binomial distribution, Poisson approximation to numerical examples      109 154
Binomial distribution, the negative      cf. Negative binomial
Binomial formula      51
Birth process      448ff. 478ff.
Birth process general      476
Birth process, backward equations for      468
Birth process, divergent      451ff. 476
Birth-and-death process      354ff.
Birth-and-death process in servicing problems      460 478ff.
Birth-and-death process, backward equations for      469
Birth-and-death process, inhomogeneous      472
Birthdays as occupancy problem      10 47 102
Birthdays duplications      33 105
Birthdays duplications table      487
Birthdays expected numbers      224
Birthdays, Poisson distribution for      106 155
Birthdays, Poisson distribution for, combinatorial problems involving      56 58 60 169 239
Bivariate generating functions      279 340
Bivariate negative binomial      285
Bivariate Poisson      172 279
Blackwell, D., Dewel, P. and Freedman, D.      78
Blood counts      163
Blood tests      239
Boltzmann Maxwell statistics      5 21 39ff. 59
Boltzmann Maxwell statistics as limit for Fermi Dirac statistics      58 (cf. Occupancy problems)
Bomb hits (on London)      160
Bonferronis inequalities      110 142
Books produced at random      202
Booles inequality      23
Borel Cantelli Lemmas      200ff.
Borel, E.      204 210
Bose Einstein statistics      5 20 40 61 113
Bose Einstein statistics negative binomial limit      62
Bottema, O. and Van Veen, S.C.      284.
Boundaries for Markov processes      414ff. 477
Branching processes      293ff. 373
Branching processes with two types      301.
Breakage of dishes      56
Breeding      144 380 424 441
Brelot, M.      419
Bridge ace distribution      11 57
Bridge definition      8
Bridge waiting times      57
Bridge waiting times, problems and examples      27 35 37 47 56 100 112 140 169 Poker Shuffling)
Brockmeyer, E., Halstroem, H.E. and Jensen, A.      460
Brother-sister mating      143 380 441
Brownian motion      cf. Diffusion
busy hour      293
Busy period in queuing      299 300 315
Cantelli, Borel Cantelli lemmas      200
Cantelli, F.P.      204
Cantor, G.      18 336
Car accidents      158 292
Cardano, G.      158
cards      cf. Bridge Matching Poker Shuffling
Cartesian product      129
Cascade process      cf. Branching process
Catcheside, D.J.      55 287
Catcheside, D.J., Lea, D.E. and Thoday, J.M.      112 161
Causes, probability of      124
Cell genetics, a problem in      379 400
Centenarians      156
Central force, diffusion under      378
Central limit theorem      244 254 261
Central limit theorem applications to combinatorial analysis      256
Central limit theorem to random walks      357
Central limit theorem to recurrent events      320 (cf. DeMoivre Laplace limit theorem Normal
Chain letters      56
Chain reaction      cf. Branching process
Chains, length of random      240
Chandrasekhar, S.      425
Changes of sign in random walks      84ff. 97
Changing stakes      346
Channels      cf. Servers Trunking
Chapman Kolmogorov equation for Markov chains      383 421
Chapman Kolmogorov equation for non-Markovian processes      423
Chapman Kolmogorov equation for stochastic processes      445 470ff. 482
Chapman, D.G.      45
Characteristic equation      365
Characteristic roots = eigenvalues      429
Chebyshev inequality      233 242
Chebyshev, P.L.      233
Chess      111
Chromosomes      133
Chromosomes, breaks and interchanges of      55 112
Chromosomes, Poisson distribution for      161 171 287
Chung, K.L.      82 242 312 409 413
Clarke, R.D.      160
Classification multiple      27
Closed sets in Markov chains      384ff.
Cochran, W.G.      43
Coin tossing as random walk      71 343
Coin tossing experiments      21 82 86
Coin tossing ties in multiple      316 338 Bernoulli Changes First Leads Random Returns Success etc.)
Coin tossing, simulation of      238
Coincidences = matches      100 107
Coincidences multiple      112
Collectors problem      11 61 111
Collectors problem waiting times      48 225 239 284
Colorblindness as sex-linked character      139
Colorblindness, Poisson distribution for      169
Combinatorial product      129
Combinatorial runs      cf. Runs combinatorial
Competition problem      188
Complementary event      15
Composite Markov process (shuffling)      422
composition      cf. Convolution
Compound Poisson distribution      288ff. 474
Conditional distribution      217ff. 237
Conditional expectation      223
Conditional probability      114ff. (cf. Transition probabilities)
Confidence level      189
Connection to a wrong number      161
Contagion      43 120 480
Contagion, spurious      121
Continuity equation      358
Continuity theorem      280
Convolutions      266ff.
Convolutions, special cases      173
Coordinates and coordinate spaces      130
Cornell professor      55
Correlation coefficient      236
Cosmic rays      11 289 451
Counters      cf. Geiger counter Queuing Trunking
Coupon collecting      cf. Collectors problem
Covariance      229ff. 236
Cox, D.R.      226
Cramer, H.      160
Crossing of the axis (in random walks)      84ff. 96
Cumulative distribution function      179
Cycles (in permutations)      257 270
Cyclical random walk      377 434
Cylindrical sets      130
Dahlberg, G.      140
Damage      cf. Accidents Irradiation
Darwin, C.      70
de Mires paradox      56
Death process      478
Decimals, distribution of e and $\pi$      32 61
Decimals, distribution of law of the iterated logarithm      208 (cf. Random digits)
Decomposition of Markov chains      390
Defective items, Poisson distribution for      155
Defective items, Poisson distribution for elementary problems      55 141
Defective random variables      273 309
Delayed recurrent events      316ff.
Delayed recurrent events in renewal theory      332 334
DeMoivre Laplace limit theorem      182ff.
DeMoivre Laplace limit theorem application to diffusion      357 (cf. Central limit theorem Normal
Demoivre, A.      179 264 285
Density fluctuations      425 (cf. Bernoulli Laplace model Ehrenfest
Density function      179
Dependent      cf. Independent
Derivatives partial, number of      39
Derman, C.      413
Determinants (number of terms containing diagonal elements)      111
Dewel, P.      78
Diagonal method      336
Dice ace runs      210 324
Dice ace runs as occupancy problem      11
Dice de Meres paradox      56
Dice equalization of ones, twos, ...      339
Dice Newton Pepys problem      55
Dice Weldons data      148
Difference equations      344ff.
Difference equations method of images      369
Difference equations method of particular solutions      344 350 365
Difference equations passage to limit      354ff. 370
Difference equations several dimensions      362
Difference equations several dimensions for Polya distribution      142 480
Difference equations several dimensions in occupancy problems      59 284
Difference of events      16
Diffusion      354ff. 370
Diffusion with central force      378 (cf. Bernoulli Laplace model Ehrenfest
Dirac Fermi statistics      5 41
Dirac Fermi statistics for misprints      42 57
Discrete sample space      17ff.
Dishes, test involving breakage of      56
Dispersion = variance      228
Distinguishable      cf. Indistinguishable
Distribution conditional      217ff. 237
Distribution function      179 213
Distribution function, empirical      71
Distribution joint      213
Distribution marginal      215
Doblin, W.      413
Domb, C.      301
Dominant gene      133
Domino      54
Doob, J.L.      199 419 477
Dorfman, R.      239
Doubly stochastic matrices      399
Drift      342
Drift to boundary      417
Duality      91
Dubbins, L.E. and Savage, L.J.      346
Duration of games in sequential sampling      368 (cf. Absorption probabilities Extinction First Waiting
Duration of games in the classical ruin problem      348ff.
e, distribution of decimals      32 61
Ecology      289
Efficiency, tests of      70 148 149
Eggenberger, F.      119
Ehrenfest model      121 377
Ehrenfest model density      425
Ehrenfest model reversibility      415
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