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Blom G., Holst L., Sandell D. — Problems and Snapshots from the World of Probability |
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Предметный указатель |
-heads-in-advance game 205
Absorbing barrier of random walk 117 119
Absorption 6 7
Addition formula 18
Amount of overlap 175 177 208
An Essay Toward Solving a Problem in the Doctrine of Chances 57
Ape 176
Aperiodic Markov chain 158
Ars Conjectandi 41 44
Ascending factorials 68
Ascents in permutations 69
Asymptotic distribution of Markov chain 159
Ballot problem 128
Banach, Stefan 9
Banach’s match box problem 9
Bayes, Thomas 57
Bayes’s theorem 56
Bemoulli - Laplace model 164
Bernoulli random variable 20
Bernoulli, Daniel 50
Bernoulli, James 38 41 44
Bernoulli, John 36
Bernoulli, Nicholas 47
Binomial coefficients 120
Binomial distribution 21 25 44 46 97
Binomial moment 27
Birth control 204
Birth of probability 34
Birthdays 79 92 103 190
Blackjack 112
Boole’s inequality 19
Bridge 15
Buffon 50
Card file 108
Card shuffling 165
Cardano, Gerolamo 33 36 39 80
Central moment 24
Chen, L. 92
Chessboard 148
Chessboard, king on 216
Chessboard, random walk on 216
Chevalier de Mr 34
Classical occupancy problem 51 55 101
Classical random walk 6 117
Closed 115
Closed stopping region 115
Closed stopping region of random walk 123
COBWEB 121
Coin-tossing 4 7 9 11 22 49
Coin-tossing, modified 222
Coincidences 79 105
Combinations of events 17 31
Combinatorial probability 34
Combinatorial runs 62
Complete graph 149
Compound 185
Compound Poisson distribution 185
Conditional probability 13
Condorcet 50 176
Connected graph 146
Contagion 135
Coupon collecting 85 87 191
Cover time 146
Cover time, extended 146
Cover time, inequality for 155
Cover time, partial 146
Cycles in permutations 65
de Finetti’s theorem 16 136
De Mensura Sortis 45 51
De Ratiociniis in Ludo Aleae 37 46
deck of cards 80 90 165
Descending factorial moment 24
Descending factorials 56 68
Dice throwing 39 51
Different faces 54
Diffusion of molecules 140
Dinner party 59 88
Disaster, game with 217
Division problem 36
Doob, J. L. 199 201
Doubly stochastic transition matrix of Markov chain 163
Drawings with replacement 133 186
Drawings without replacement 46 83 94 192 194
D’Alembert 50
Ehrenfest’s game 142
Ehrenfest’s urn model 140 162
Election 156 160
Embedding procedures 186
Equilibrium distribution of Markov chain 159
Ergodic Markov chain 158
Essay d’Analyse sur les Jeux de Hazard 45
Euler numbers 78
Euler, Leonhard 50
Eulerian numbers 70 72
Exceedance 72
Exchangeability 15 16 199
Exchangeable random variables 199
Expectation 23
Expected value 23
Extended cover time 146
Extended partial cover time 146
Factorial generating function 28
Factorials, ascending 68
Factorials, descending 56 68
Factorials, falling 68
Factorials, rising 68
Falling factorials 68
False conjecture 152
Fermat, Pierre de 34 36 38 82
Fibonacci numbers 48 222
Fibonacci, Leonardo 222
Finetti, Bruno de 16
Finite Markov chain 157
First-to- game 195 214
Fixed point 50 98
Food package 85 86 87 191
Full house 81
Galilei, Galileo 39
gambling 201 203
Game -heads-in-advance 205
Game Ehrenfest’s 142
Game first-to- 195 214
Game for pirates 178
Game Penney’s 179
Game with disaster 217
Generalized asymptotic distribution of Markov chain 160
Generalized star 122 154
Generating functions 24 40
Goat 3
Graph 146
Graph, complete 149
Graph, connected 146
Graph, linear finite 149
Homesickness 170
Hume, D. 59
Huygens, Christiaan 37 46
Huygens’s fifth problem 38
Huygens’s fourth problem 46
Huygens’s second problem 37
Hypergeometric distribution 45
Hypergeometric distribution, -variate 46
Illiterate 1
Inclusion-exclusion formula 18
Indicator random variable 20
Inverse probability 58
Irreducible Markov chain 157
Irreducible periodic chain 160
Irresolute spider 121
Jeu du Treize 50
Joker 81
| Kallenberg, O. 199 200
King on chessboard 148 216
Kolmogorov’s criterion 170
Laplace, Pierre Simon de 40 50 57 58 173 174
Law of succession 58
Leading numbers 175
Liber Abaci 222
Liber de Ludo Aleae 33 39
Line representation of random walk 117
Linear finite graph 149
Lollipop graph 155
Lottery 14 201
Lotto 94
Mnage problem 59 88 99
Mr, Chevalier de 34 36
Markov chain 156
Markov chain, aperiodic 158
Markov chain, asymptotic distribution 159
Markov chain, equilibrium distribution 159
Markov chain, ergodic 158
Markov chain, finite 157
Markov chain, generalized asymptotic distribution 160
Markov chain, irreducible 157
Markov chain, Kolmogorov’s criterion 170
Markov chain, periodic 157
Markov chain, recurrence times 159
Markov chain, reversible 169
Markov chain, stationary distributions 158
Markov chain, transition times 167
Markov chain, with doubly stochastic transition matrix 163
Markov chain, with homesickness 170
Markov, A.A. 156
Married couples 88 99
Martian 80 194
Martingale 201
Match box problem 9
Matching problem 50
Mean 23
Missing faces 52
MISSISSIPPI problem 64
Modified coin-tossing 222
Moivre, Abraham de 17 38 39 45 47 50 51 96 173 174
Montmort, Pierre Rmond de 39 45 47 50 51 82
Multinomial distribution 45 101 103
Negative binomial distribution 82
Negative hypergeometric distribution 83 194
Newcomb, Simon 70
Oblique stopping line of random walk 138
Occupancy 51 55 86 101
open 115
Open stopping region 115
Optional stopping theorem 202
Order statistics 192
oscillations 73 76
Overlaps 175 177
Plya - Ehrenfest model 142
Plya, George 135
Plya’s urn model 135 136 137
Palindrome 224
Partial cover time 146
Pascal, Blaise 34 36 38 45 82
Patterns 4 173 207
Penney’s game 179
Periodic Markov chain 157
Permutation matrix 172
Petersburg Paradox 49
Pill problem 143
Pirates, game for 178
Points when throwing several dice 39
Poisson approximation 92 104
Poisson distribution 46 101
Poisson process 186
Poisson, Simon Denis 47 96
Poisson-binomial distribution 21 66 96 111
Polygon 150
Price fluctuations 72
Price, R. 59
Prior distribution 17
Prior probabilities 57
Probability generating function 24
Probability of at least events 17 32
Probability of exactly events 17 31
Probability state vector of Markov chain 157
Problem of points 36
Pyramid representation of random walk 115
Quadrant representation of random walk 115
Quality control 134
Rabbi Ben Ezra 33
Random division 106
Random numbers 19 53 105
Random permutation 50 62 65 71 98
Random permutation of 1’s and (-1)’s 210
Random variables, exchangeable 199
Random walk 6 115 211
Random walk, absorbing barrier 117 119
Random walk, closed stopping region 123
Random walk, cover times of 146
Random walk, in pyramid 138
Random walk, line representation 117
Random walk, oblique stopping line 138
Random walk, on chessboard 216
Random walk, Plya’s 137
Random walk, pyramid representation 115
Random walk, quadrant representation 115
Random walk, range 130
Random walk, reflecting barriers 117 161
Random walk, stopped 115
Random walk, symmetric 6
Random walk, unrestricted 115
Random walk, vertical stopping line 139
Randomly filled urn 133
Range of random walk 130
Recherches sur la probabilite des jugements 47
Records 108 110
Recurrence times of Markov chain 159
Reflecting barriers of random walk 117 161
Reflection principle 125 128
Rencontre 50 90 91 98
Rendezvous problem 219
Repetition of colours 189
Reversible Markov chain 169
Rising factorials 68
Rising of the sun 58
Roulette 217
Ruin problem 7 38 202
runs 173
Runs, combinatorial 62
Savant, Marilyn vos 3
Sequential analysis 42
Shoes 8 164
Similar pair 92
Similar triplet 93 103
Simpson 173
Socks in the laundry 193
Solitaire 70
Spacings 192
Spider 121
Star 122 153
Star, generalized 122 154
Starting vector of Markov chain 157
Stationary distributions of Markov chains 158
Stein, C. 92
Stirling numbers of the first kind 66 67 110 111
Stirling numbers of the second kind 54
STIRLING, JAMES 54
Stopped random walk 115
Stopping probabilities 177
Stopping region 115
Stopping rule 117
Stopping time 200 202
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