Blom G., Holst L., Sandell D. — Problems and Snapshots from the World of Probability :: Электронная библиотека попечительского совета мехмата МГУ

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Blom G., Holst L., Sandell D. — Problems and Snapshots from the World of Probability

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Название: Problems and Snapshots from the World of Probability

Авторы: Blom G., Holst L., Sandell D.

Аннотация:

This book comprises a collection of 125 problems and snapshots from discrete probability. The problems are selected on the basis of their historical interest whereas the snapshots provide quick overviews of topics in probability such as Markov chains, Poisson processes, random walks, patterns in random sequences, cover times, and embedding procedures. This book will appeal to all those who enjoy problems with probabilistic flavor. The authors presuppose a basic exposure to discrete mathematics and elementary probability. Students will find this a stimulating companion to their courses in probability. More advanced researchers will appreciate the original style of the problems, some of which may even inspire new areas for research.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1994

Количество страниц: 240

Добавлена в каталог: 11.04.2010

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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 M $\acute{e}$ r $\acute{e}$       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
M $\acute{e}$ nage problem      59 88 99
M $\acute{e}$ r $\acute{e}$ , 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 R $\acute{e}$ mond 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
P $\acute{o}$ lya - Ehrenfest model      142
P $\acute{o}$ lya, George      135
P $\acute{o}$ lya’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, Sim $\acute{e}$ on 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, P $\acute{o}$ lya’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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