\begin{theindex}

  \item $\pi$, estimation of, 43--46
  \item $n!$, 80

  \indexspace

  \item absorbing Markov chain, 416
  \item absorbing state, 416
  \item AbsorbingChain (program), 421
  \item absorption probabilities, 420
  \item Ace, Mr., 241
  \item Ali, 178
  \item alleles, 348
  \item AllPermutations (program), 84
  \item ANDERSON, C. L., 157
  \item annuity, 246
    \subitem life, 247
    \subitem terminal, 247
  \item arc sine laws, 493
  \item area, estimation of, 42
  \item Areabargraph (program), 46
  \item asymptotically equal, 81

  \indexspace

  \item Baba, 178
  \item babies, 14, 250
  \item Banach's Matchbox, 255
  \item BAR-HILLEL, M., 176
  \item BARNES, B., 175
  \item BARNHART, R., 11
  \item BAYER, D., 120
  \item Bayes (program), 147
  \item Bayes probability, 136
  \item Bayes' formula, 146
  \item BAYES, T., 149
  \item beard, 153
  \item bell-shaped, 47
  \item Benford distribution, 195
  \item BENKOSKI, S., 40
  \item Bernoulli trials process, 96
  \item BERNOULLI, D., 227
  \item BERNOULLI, J., 113, 149, 310--312
  \item Bertrand's paradox, 47--50
  \item BERTRAND, J., 49, 181
  \item BertrandsParadox (program), 49
  \item beta density, 168
  \item BIENAYM\'E, I., 310, 377
  \item BIGGS, N. L., 85
  \item binary expansion, 69
  \item binomial coefficient, 93
  \item binomial distribution, 99, 184
    \subitem approximating a, 329
  \item Binomial Theorem, 103
  \item BinomialPlot (program), 99
  \item BinomialProbabilities (program), 98
  \item Birthday (program), 78
  \item birthday problem, 77
  \item blackjack, 247, 253
  \item blood test, 254
  \item Bose-Einstein statistics, 107
  \item Box paradox, 181
  \item BOX, G. E. P., 213
  \item boxcars, 27
  \item BRAMS, S., 179, 182
  \item Branch (program), 381
  \item branching process, 376
    \subitem customer, 393
  \item BranchingSimulation (program), 386
  \item bridge, 181, 182, 199, 203, 287
  \item BROWN, B. H., 38
  \item BROWN, E., 425
  \item Buffon's needle, 44--46, 51--53
  \item BUFFON, G. L., 9, 44, 50--51
  \item BuffonsNeedle (program), 45
  \item bus paradox, 164

  \indexspace

  \item calendar, 38
  \item cancer, 147
  \item canonical form of an absorbing\\ Markov chain, 416
  \item car, 137
  \item CARDANO, G., 30--31, 110, 249
  \item cars on a highway, 66
  \item CASANOVA, G., 11
  \item Cauchy density, 218, 400
  \item cells, 347
  \item Central Limit Theorem, 325
    \subitem for Bernoulli Trials, 330
    \subitem for Binomial Distributions, 328
    \subitem for continuous independent trials process, 357
    \subitem for discrete independent random variables, 345
    \subitem for discrete independent trials\\ process, 343
    \subitem for Markov Chains, 464
    \subitem proof of, 397
  \item chain letter, 388
  \item characteristic function, 397
  \item Chebyshev Inequality, 305, 316
  \item CHEBYSHEV, P. L., 313
  \item chi-squared density, 216, 296
  \item Chicago World's Fair, 52
  \item chord, random, 47, 54
  \item chromosomes, 348
  \item CHU, S.-C., 110
  \item CHUNG, K. L., 153
  \item Circle of Gold, 388
  \item Clinton, Bill, 196
  \item clover-leaf interchange, 39
  \item CLTBernoulliGlobal, 332
  \item CLTBernoulliLocal (program), 329
  \item CLTBernoulliPlot (program), 327
  \item CLTGeneral (program), 345
  \item CLTIndTrialsLocal (program), 342
  \item CLTIndTrialsPlot (program), 341
  \item COATES, R. M., 305
  \item CoinTosses (program), 3
  \item Collins, People v., 153, 202
  \item color-blindness, 424
  \item conditional density, 162
  \item conditional distribution, 134
  \item conditional expectation, 239
  \item conditional probability, 133
  \item CONDORCET, Le Marquis de, 12
  \item confidence interval, 334, 360
  \item conjunction fallacy, 38
  \item continuum, 41
  \item convolution, 286, 291
    \subitem of binomial distributions, 289
    \subitem of Cauchy densities, 294
    \subitem of exponential densities, 292, 300
    \subitem of geometric distributions, 289
    \subitem of normal densities, 294
    \subitem of standard normal densities, 299
    \subitem of uniform densities, 292, 299
  \item CONWAY, J., 432
  \item CRAMER, G., 227
  \item craps, 235, 240, 468
  \item Craps (program), 235
  \item CROSSEN, C., 161
  \item CROWELL, R., 468
  \item cumulative distribution function, 61
    \subitem joint, 165
  \item customer branching process, 393
  \item cut, 120

  \indexspace

  \item Dartmouth, 27
  \item darts, 56, 57, 59, 60, 64, 71, 163, 164
  \item Darts (program), 58
  \item DAVID, F. N., 86, 337, 489
  \item DAVID, F.\ N., 32
  \item de M\'ER\'E, CHEVALIER, 4, 31, 37
  \item de MOIVRE, A., 37, 88, 148, 336, 489
  \item de MONTMORT, P. R., 85
  \item degrees of freedom, 217
  \item DeMere1 (program), 4
  \item DeMere2 (program), 4
  \item density function, 56, 59
    \subitem beta, 168
    \subitem Cauchy, 218, 400
    \subitem chi-squared, 216, 296
    \subitem conditional, 162
    \subitem exponential, 53, 66, 163, 205
    \subitem gamma, 207
    \subitem joint, 165
    \subitem log normal, 224
    \subitem Maxwell, 215
    \subitem normal, 212
    \subitem Rayleigh, 215, 295
    \subitem t-, 360
    \subitem uniform, 60, 205
  \item derangement, 85
  \item DIACONIS, P., 120, 251
  \item Die (program), 225
  \item DieTest (program), 297
  \item distribution function, 1, 19
    \subitem  properties of, 22
    \subitem Benford, 195
    \subitem binomial, 99, 184
    \subitem geometric, 184
    \subitem hypergeometric, 193
    \subitem joint, 142
    \subitem marginal, 143
    \subitem negative binomial, 186
    \subitem Poisson, 187
    \subitem uniform, 183
  \item DNA, 348
  \item DOEBLIN, W., 449
  \item DOYLE, P. G., 87, 452, 470
  \item Drunkard's Walk example, 416, 419--421, 423, 427, 443
  \item Dry Gulch, 280

  \indexspace

  \item EDWARDS, A. W. F., 108
  \item Egypt, 30
  \item Ehrenfest model, 410, 433, 441, 460, 461
  \item EHRENFEST, P., 410
  \item EHRENFEST, T, 410
  \item EhrenfestUrn (program), 462
  \item EISENBERG, B., 160
  \item elevator, 89, 116
  \item Emile's restaurant, 75
  \item ENGLE, A., 445
  \item envelopes, 179, 180
  \item EPSTEIN, R., 287
  \item equalization, 472
  \item equalizations
    \subitem expected number of, 479
  \item ergodic Markov chain, 433
  \item ESP, 250, 251
  \item EUCLID, 85
  \item Euler's formula, 202
  \item Eulerian number, 127
  \item event, 18
  \item events
    \subitem attraction of, 160
    \subitem independent, 139, 164
    \subitem repulsion of, 160
  \item existence of God, 245
  \item expected value, 226, 268
  \item exponential density, 53, 66, 163, 205
  \item extinction, problem of, 378

  \indexspace

  \item factorial, 80
  \item fair game, 241
  \item FALK, R., 161, 176
  \item fall, 131
  \item fallacy, 38
  \item FELLER, W., 11, 106, 107, 191, 201, 218, 254, 344
  \item FERMAT, P., 4, 32--35, 112--113, 156
  \item Fermi-Dirac statistics, 107
  \item figurate numbers, 108
  \item financial records
    \subitem suspicious, 196
  \item finite additivity property, 23
  \item FINN, J., 178
  \item First Fundamental Mystery of Probability, 232
  \item first maximum of a random walk, 496
  \item first return to the origin, 473
  \item Fisher's Exact Test, 193
  \item FISHER, R. A., 252
  \item fixed column vector, 435
  \item fixed points, 82
  \item fixed row vector, 435
  \item FixedPoints (program), 82
  \item FixedVector (program), 437
  \item flying bombs, 191, 201
  \item Fourier transform, 397
  \item FRECHET, M., 466
  \item frequency concept of probability, 70
  \item frustration solitaire, 86
  \item Fundamental Limit Theorem for Regular Markov Chains, 448
  \item fundamental matrix, 419
    \subitem for a regular Markov chain, 457
    \subitem for an ergodic Markov chain, 458

  \indexspace

  \item GALAMBOS, J., 303
  \item GALILEO, G., 13
  \item Gallup Poll, 14, 335
  \item Galton board, 99, 351
  \item GALTON, F., 282, 345, 350, 376
  \item GaltonBoard (program), 99
  \item Gambler's Ruin, 426, 486, 487
  \item gambling systems, 241
  \item gamma density, 207
  \item GARDNER, M., 181
  \item gas diffusion
    \subitem Ehrenfest model of, 410, 433, 441, 460, 461
  \item GELLER, S., 176
  \item GeneralSimulation (program), 9
  \item generating function
    \subitem for continuous density, 393
    \subitem moment, 366, 394
    \subitem ordinary, 369
  \item genes, 348, 411
  \item genetics, 345
  \item genotypes, 348
  \item geometric distribution, 184
  \item geometric series, 29
  \item GHOSH, B. K., 160
  \item goat, 137
  \item GONSHOR, H., 425
  \item GOSSET, W. S., 360
  \item grade point average, 343
  \item GRAHAM, R., 251
  \item GRANBERG, D., 161
  \item GRAUNT, J., 246
  \item Greece, 30
  \item GRIDGEMAN, N. T., 51, 181
  \item GRINSTEAD, C. M., 87
  \item GUDDER, S., 160

  \indexspace

  \item HACKING, I., 30, 148
  \item HAMMING, R. W., 284
  \item HANES data, 345
  \item Hangtown, 280
  \item Hanover Inn, 65
  \item hard drive, Warp 9, 66
  \item Hardy-Weinberg Law, 349
  \item harmonic function, 428
  \item Harvard, 27
  \item hat check problem, 82, 85, 105
  \item heights
    \subitem distribution of, 345
  \item helium, 107
  \item HEYDE, C., 377
  \item HILL, T., 196
  \item Holmes, Sherlock, 91
  \item HorseRace (program), 6
  \item hospital, 14, 250
  \item HOWARD, R. A., 406
  \item HTSimulation (program), 6
  \item HUDDE, J., 148
  \item HUIZINGA, F., 388
  \item HUYGENS, C., 147, 243--245
  \item hypergeometric distribution, 193
  \item hypotheses, 145
  \item hypothesis testing, 101

  \indexspace

  \item Inclusion-Exclusion Principle, 104
  \item independence of events, 139, 164
    \subitem mutual, 141
  \item independence of random variables
    \subitem mutual, 143, 165
  \item independence of random\\ variables, 143, 165
  \item independent trials process, 144, 168
  \item interarrival time, average, 208
  \item interleaving, 120
  \item irreducible Markov chain, 433
  \item Isle Royale, 202

  \indexspace

  \item JAYNES, E. T., 49
  \item JOHNSONBOUGH, R., 153
  \item joint cumulative distribution\\ function, 165
  \item joint density function, 165
  \item joint distribution function, 142
  \item joint random variable, 142

  \indexspace

  \item KAHNEMAN, D., 38
  \item Kemeny's constant, 469, 470
  \item KEMENY, J. G., 200, 406, 466
  \item KENDALL, D. G., 377
  \item KEYFITZ, N., 382
  \item KILGOUR, D. M., 179, 182
  \item KINGSTON, J. G., 157
  \item KONOLD, C., 161
  \item KOZELKA, R. M., 344

  \indexspace

  \item Labouchere betting system, 12, 13
  \item LABOUCHERE, H. du P., 12
  \item LAMPERTI, J., 267, 324
  \item LAPLACE, P. S., 51, 53, 350
  \item last return to the origin, 482
  \item Law (program), 310
  \item Law of Averages, 70
  \item Law of Large Numbers, 307, 316
    \subitem for Ergodic Markov Chains, 439
    \subitem Strong, 70
  \item LawContinuous (program), 318
  \item lead change, 482
  \item LEONARD, B., 256
  \item LEONTIEF, W. W., 426
  \item LEVASSEUR, K., 485
  \item library problem, 82
  \item life table, 39
  \item light bulb, 66, 72, 172
  \item Linda problem, 38
  \item LINDEBERG, J. W., 344
  \item LIPSON, A., 161
  \item Little's law for queues, 276
  \item Lockhorn, Mr.\ and Mrs., 65
  \item log normal density, 224
  \item lottery
    \subitem Powerball, 204
  \item LUCAS, E., 119
  \item LUSINCHI, D., 12

  \indexspace

  \item MAISTROV, L., 150, 310
  \item MANN, B., 120
  \item margin of error, 335
  \item marginal distribution function, 143
  \item Markov chain, 405
    \subitem absorbing, 416
    \subitem ergodic, 433
    \subitem irreducible, 433
    \subitem regular, 433
  \item Markov Chains
    \subitem Central Limit Theorem for, 464
    \subitem Fundamental Limit Theorem for Regular, 448
  \item MARKOV, A. A., 464
  \item martingale, 241, 242, 428
    \subitem origin of word, 11
  \item martingale betting system, 11, 14, 248
  \item matrix
    \subitem fundamental, 419
  \item MatrixPowers (program), 407
  \item maximum likelihood\\ estimate, 198, 202
  \item Maximum Likelihood\\ Principle, 91, 117
  \item Maxwell density, 215
  \item maze, 440, 453
  \item McCRACKEN, D., 10
  \item mean, 226
  \item mean first passage matrix, 455
  \item mean first passage time, 453
  \item mean recurrence matrix, 455
  \item mean recurrence time, 454
  \item memoryless property, 68, 164, 206
  \item milk, 252
  \item modular arithmetic, 10
  \item moment generating function, 366, 394
  \item moment problem, 368, 397
  \item moments, 365, 393
  \item Monopoly, 469
  \item MonteCarlo (program), 42
  \item Monty Hall problem, 136, 161
  \item moose, 202
  \item mortality table, 246
  \item mule kicks, 201
  \item MULLER, M. E., 213
  \item multiple-gene hypothesis, 348
  \item mustache, 153
  \item mutually independent events, 141
  \item mutually independent random\\ variables, 143

  \indexspace

  \item negative binomial distribution, 186
  \item New York Times, 340
  \item New York Yankees, 118, 253
  \item New-Age Solitaire, 130
  \item NEWCOMB, S., 196
  \item NFoldConvolution (program), 287
  \item NIGRINI, M., 196
  \item normal density, 47, 212
  \item NormalArea (program), 322
  \item nursery rhyme, 84

  \indexspace

  \item odds, 27
  \item ordering, random, 127
  \item ordinary generating function, 369
  \item ORE, O., 30, 31
  \item outcome, 18
  \item Oz, Land of, 406, 439

  \indexspace

  \item P\'OLYA, G., 15, 17, 475
  \item Pascal's triangle, 94, 103, 108
  \item PASCAL, B., 4, 32--35, 107, 112--113, 156, 242, 245
  \item paternity suit, 222
  \item PEARSON, K., 9, 351
  \item PENNEY, W., 432
  \item People v. Collins, 153, 202
  \item PERLMAN, M. D., 45
  \item permutation, 79
    \subitem fixed points of, 82
  \item Philadelphia 76ers, 15
  \item photons, 106
  \item Pickwick, Mr., 153
  \item Pilsdorff Beer Company, 280
  \item PITTEL, B., 256
  \item point count, 287
  \item Poisson approximation to the\\ binomial distribution, 189
  \item Poisson distribution, 187
    \subitem variance of, 263
  \item poker, 95
  \item polls, 333
  \item Polya urn model, 152, 174
  \item ponytail, 153
  \item posterior probabilities, 145
  \item Powerball lottery, 204
  \item PowerCurve (program), 102
  \item Presidential election, 335
  \item PRICE, C., 86
  \item prior probabilities, 145
  \item probability
    \subitem Bayes, 136
    \subitem conditional, 133
    \subitem frequency concept of, 2
    \subitem of an event, 19
    \subitem transition, 406
    \subitem vector, 407
  \item problem of points, 32, 112, 147, 156
  \item process, random, 128
  \item PROPP, J., 256
  \item PROSSER, R., 200
  \item protons, 106

  \indexspace

  \item quadratic equation, roots of, 73
  \item quantum mechanics, 107
  \item QUETELET, A., 350
  \item Queue (program), 208
  \item queues, 186, 208, 275
  \item quincunx, 351

  \indexspace

  \item R\'ENYI, A., 167
  \item RABELAIS, F., 12
  \item racquetball, 157
  \item radioactive isotope, 66, 71
  \item RAND Corporation, 10
  \item random integer, 39
  \item random number generator, 2
  \item random ordering, 127
  \item random process, 128
  \item random variable, 1, 18
    \subitem continuous, 58
    \subitem discrete, 18
    \subitem functions of a, 210
    \subitem joint, 142
  \item random variables
    \subitem independence of, 143
    \subitem mutual independence of, 143
  \item random walk, 471
    \subitem in $n$ dimensions, 17
  \item RandomNumbers (program), 3
  \item RandomPermutation (program), 82
  \item rank event, 160
  \item raquetball, 13
  \item rat, 440, 453
  \item Rayleigh density, 215, 295
  \item records, 83, 234
  \item Records (program), 84
  \item regression on the mean, 282
  \item regression to the mean, 345, 352
  \item regular Markov chain, 433
  \item reliability of a system, 154
  \item restricted choice, principle of, 182
  \item return to the origin, 472
    \subitem first, 473
    \subitem last, 482
    \subitem probability of eventual, 475
  \item reversibility, 463
  \item reversion, 352
  \item riffle shuffle, 120
  \item RIORDAN, J., 86
  \item rising sequence, 120
  \item rnd, 42
  \item ROBERTS, F., 426
  \item Rome, 30
  \item ROSS, S., 270, 276
  \item roulette, 13, 237, 432
  \item run, 229

  \indexspace

  \item SAGAN, H., 237
  \item sample, 333
  \item sample mean, 265
  \item sample space, 18
    \subitem continuous, 58
    \subitem countably infinite, 28
    \subitem infinite, 28
  \item sample standard deviation, 265
  \item sample variance, 265
  \item SAWYER, S., 412
  \item SCHULTZ, H., 255
  \item SENETA, E., 377, 444
  \item service time, average, 208
  \item SHANNON, C. E., 465
  \item SHOLANDER, M., 39
  \item shuffling, 120
  \item SHULTZ, H., 256
  \item SimulateChain (program), 439
  \item simulating a random variable, 211
  \item snakeeyes, 27
  \item SNELL, J. L., 87, 175, 406, 466
  \item snowfall in Hanover, 83
  \item spike graph, 6
  \item Spikegraph (program), 6
  \item spinner, 41, 55, 59, 162
  \item spread, 266
  \item St. Ives, 84
  \item St. Petersburg Paradox, 227
  \item standard deviation, 257
  \item standard normal random\\ variable, 213
  \item standardized random variable, 264
  \item standardized sum, 326
  \item state
    \subitem absorbing, 416
    \subitem of a Markov chain, 405
    \subitem transient, 416
  \item statistics
    \subitem applications of the Central Limit Theorem to, 333
  \item stepping stones, 412
  \item SteppingStone (program), 413
  \item stick of unit length, 73
  \item STIFEL, M., 110
  \item STIGLER, S., 350
  \item Stirling's formula, 81
  \item STIRLING, J., 88
  \item StirlingApproximations\\ (program), 81
  \item stock prices, 241
  \item StockSystem (program), 241
  \item Strong Law of Large\\ Numbers, 70, 314
  \item suit event, 160
  \item SUTHERLAND, E., 182

  \indexspace

  \item t-density, 360
  \item TARTAGLIA, N., 110
  \item tax returns, 196
  \item tea, 252
  \item telephone books, 256
  \item tennis, 157, 424
  \item tetrahedral numbers, 108
  \item THACKERAY, W. M., 14
  \item THOMPSON, G. L., 406
  \item THORP, E., 247, 253
  \item time to absorption, 419
  \item TIPPETT, L. H. C., 10
  \item traits, independence of, 216
  \item transient state, 416
  \item transition matrix, 406
  \item transition probability, 406
  \item tree diagram, 24, 76
    \subitem infinite binary, 69
  \item Treize, 85
  \item triangle
    \subitem acute, 73
  \item triangular numbers, 108
  \item trout, 198
  \item true-false exam, 267
  \item Tunbridge, 154
  \item TVERSKY, A., 14, 38
  \item Two aces problem, 181
  \item two-armed bandit, 170
  \item TwoArm (program), 171
  \item type 1 error, 101
  \item type 2 error, 101
  \item typesetter, 189

  \indexspace

  \item ULAM, S., 11
  \item unbiased estimator, 266
  \item uniform density, 205
  \item uniform density function, 60
  \item uniform distribution, 25, 183
  \item uniform random variables
    \subitem sum of two continuous, 63
  \item unshuffle, 122
  \item USPENSKY, J. B., 299
  \item utility function, 227

  \indexspace

  \item VANDERBEI, R., 175
  \item variance, 257, 271
    \subitem calculation of, 258
  \item variation distance, 128
  \item VariationList (program), 128
  \item volleyball, 158
  \item von BORTKIEWICZ, L., 201
  \item von MISES, R., 87
  \item von NEUMANN, J., 10, 11
  \item vos SAVANT, M., 40, 86, 136, 176, 181

  \indexspace

  \item Wall Street Journal, 161
  \item watches, counterfeit, 91
  \item WATSON, H. W., 377
  \item WEAVER, W., 465
  \item Weierstrass Approximation Theorem, 315
  \item WELDON, W. F. R., 9
  \item Wheaties, 118, 253
  \item WHITAKER, C., 136
  \item WHITEHEAD, J. H. C., 181
  \item WICHURA, M. J., 45
  \item WILF, H. S., 91, 474
  \item WOLF, R., 9
  \item WOLFORD, G., 159
  \item Woodstock, 154

  \indexspace

  \item Yang, 130
  \item Yin, 130

  \indexspace

  \item ZAGIER, D., 485
  \item Zorg, planet of, 90

\end{theindex}