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| Hamming R.W. — Art of Probability for Scientists and Engineers |
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| Предметный указатель |
A random game 205
Abelard 5
Animal population 138
Approximation of a unimodal distribution 311
Astronomy 3
Bacon, F. 5
Banach — Tarski paradox 191
Bayesian vi 297
Bernoulli distribution 56—57
Bernoulli evaluation 126
Bernoulli of coin toss 127
Bernoulli symmetric payoff 127
Bernoulli trials 145
Bertrand's paradox 200
Biased coin 70 104
Binomial approximation 313 319
Binomial coefficients 48
Binomial distribution 55 82
Binomial mean and variance 80
Binomial middle coefficients 52
Binomial recurrence relation 48—49
Binomial sums 51 315 317
Birth and death systems 237
Birthday problem 27
Birthday problem, robustness 131
Birthday problem, simulation 135
Birthday problem, variant of 134
Boltzmann 254—255
Bose — Einstein statistics 62
Bounds on sums 35
Bridge hands 51
Bridge hands, void 53
Broken stick 194
Buffon needle 195
Canonical partitions 60
Card collecting 151
Cauchy distribution 290
Cauchy functional equation 257
Cauchy sequences 190
Characteristic equation 162 168 174
Chebyshev inequality 84 86
Coding theory 2
Coin, expected value 68
Coin, n heads in a row 52
Coin, three heads in a row 165
Coin, two heads in a row 160
Coincidences 30
Combinations 48
Combining information 264
Complement probability 27
Complex probability 302
Computable numbers 7 190
Comvolution 81
Conditional probability 18 268
Conservation of probability 160 166—167
Constructive mathematics 7
Continuous sample spaces 189
Convergence to the reciprocal distribution 222
Countably infinitive sample spaces 141
Craps 156
de Mere problem 90
Dead times 230
Descending factorials 30 44
di Finetti vi 296
Dice, expected value 65
Dice, sum of three 60 68
Dice, sum of two 66
Dice, variance 75
Dice, variance of sum 76
Die (dice) 10
Difference equations 119
Disraeli vi
Distance from river 192
Distance to random point 211
Distribution of numbers 214
Eddington 295
Edwards, A.W.F. 282
Einstein 255
Elementary problems 98
Elementary problems, table of 101
Enthalpy 252
Entropy, binary trials 267
Entropy, independent random variables 263
Entropy, infinite 269
Entropy, loss due to combining events 264
Entropy, properties of 262
Entropy, to first failure 268
Entropy, uniform distribution 261
enumerate 97 99 108
Event A precedes B 156
Expected value of products 67 69
Expected value of sums 68
Expected value, linear operator 69
Experiment on products distribution 243
Exponential approximation 58
Exponential bound 40
Exponential generating function 83
Fair games 103
Fair games, critique of 125 128
Falling factorial 30 44
Feller vi 41 279 288 293
Fermi — Dirac statistics 62
Feynmann 302
Fibonacci numbers 164
Finite additivity 288
First occurence 145
Five methods of solution 97 102
Floppy discs 59
FOURIER 302
Frequency approach 6
Fuzzy probability 299
Galileo 60—61 255 328
Gambler's ruin 119
Game of dice 108
Gaussian distribution 284
Gaver, Don ix
Generating function 50 78
Generating function, convolution of 81
Generating function, mean from 79
Generating function, variance from 79
Geometric probability distribution 146
Gibbs 255
Gibbs inequality 263 271
Gibbs, Good, I.J. 297
Gibbs, Gudder 3
H theorem 254
Hershel 209
Historical approach 97 99 112
Identical items 45—46
Inclusion-Exclusion Principle 136
Independence 12
Infinite entropy 269
information 256
Information theory 2
Information, no information 27
Information, representation of 91
Information, state of knowledge 31
Insurance 129
Interchangeable 9
Intuitionists 190
Invariance of the geometric distribution 152
Items in bins 53
Jayne's example 272 275
Kac, Mark vi 254 288
Khinchin, A.I. 253
Knife edge trials 237
Kolmogorov 287—288
kronecker 190
Kullback 256
kurtosis 77
| Lagrange multipliers 272
Least squares 284
Lebesgue integration 287
Legal system 4
Lewis Carroll 203
Limit theorems 307
Linear difference equations 185
LIST 8
Logic and probability 294
Logical probability 247
Lotteries 105
MacLennan, Bruce ix
Mantissas 214
Marginal distributions 271
Matching pennies 103
Mathematical probability 245 287
Maximum entropy 253 266
Maximum entropy distributions 265
Maximum entropy principle 270
Maximum likelihood 282
Maximum likelihood, binary choice 283
Maximum likelihood, least squares 284
Maximum likelihood, scale free 285
Maxwell — Boltzmann distribution 62
Mean and variance of unit interval 198
Mean does not exist 289
Mechanical probability 236
Misprints 137
Mixtures 230
Models in general 4
Modular reduction 241 250
Monte Carlo 333
Monte Carlo binomial choice 148
Monte Carlo coin test 89
Monte Carlo six faces of a die 151 174
Multinomial coefficients 46
N biased coins 116
Natural variables 250
Newton 296
Noise 2
Noncountable 190
Normal distribution 208
Normal distribution to binomial distribution 319
Normal distribution, approximations by 317—318
Normal distribution, Hershel's derivation 209
Normal distribution, standard form 310
Normal distribution, table of 311
Normal distribution, two random samples from 212
Number of boys in a family 154
Obtuse random triangles 203
Occam's razor 5
Odds 6
Pairs of socks 121
Paradoxes 5 189
Paradoxes, Banach — Tarski 191
Paradoxes, Bertrand's 200
Paradoxes, Castle Point 181
Paradoxes, Saint Petersburg 180
Paradoxes, Skolem — Lohenheim 190
Paradoxes, Urn with white and black balls 182
Pascal's triangle 50
Pedagogy viii 1
Peirce 41
permutations 43 115
Pinkham, Roger viii
Poincare 239
Poisson distribution 228
Poisson distribution in time 231—232
Popper, Karl 5
Primas, Hans v
Principle of indifference 247
Probability in science 300
Probability, measure of 9
Problem de recontre 123
Problem of points 113
Problem of points with bias 113
Product distribution 216
Product of numbers 216
Product space 12—13
Propensity 301
Quality control 281
quantum mechanics 2—3 301
Queuing theory 233
Quotient distribution 220
Raffles 105—106
Rand Tables 20
Random choice of angle 193
Random chord 200
Random distribution of chips 117
Random events in time 227
Random number generator 246
Random number generator for exponential distribution 335
Random number generator for Normal distribution 335
Random number generator for reciprocal distribution 336
Random point 189 205
Random times 226 323
Random triangles 203
Random triangles in a circle 329
Random variables 64 98 101 123
Random variables, method of 121
Randomness 20
Rational generating functions 177
Real number system 189 287
Reciprocal distribution 214 245
Reciprocal distribution, convergence to 222
Reciprocal distribution, persistence of 218
Reciprocal distribution, probability of a shift 219
Reciprocal distribution, test of 215
RECURSIVE 97 100 115
Riemann integral 191
Robustness vii 240 280
Robustness birthday problem 130
Robustness elevator problem 131
Robustness mean 74
Robustness variance 75
Roulette wheel 240
Runs of heads 116
Sample space 8
Sampling with replacement 43
Sampling without replacement 43
Selection of N items 124
Shannon, Claude 255 257
Shannon, Claude, entropy 256
Shewness 77
Shifting, probability of 219
Simulation vii 135 327
Simulation direct 330
Simulation thought 333
Single event model of probability 7
Sinusoidal motion 226
Six faces of a die 149 174
Skolem — Lohenhein paradox 190
State diagrams 159
Statistical approach 289
Statistical dynamics 254
Statistics 6 22 26 88
Stirling's approximation 39 100
Stirling's formula 39 52
Subjective probability 297
Sum of powers of the integers 70
Sum of three dice 111
Symmetry 9
The four liars 295
Thermodynamics 253
Three heads in a row 165 179
Total sample space 97—98 103
Transition equations 161
Trial 7
Tribus, Myron 255
TV program prize 31
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