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Gordon H. — Discrete Probability
Gordon H. — Discrete Probability

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Название: Discrete Probability

Автор: Gordon H.

Аннотация:

DISCRETE PROBABILITY is a textbook, at a post-calculus level, for a first course in probability. Since continuous probability is not treated, discrete probability can be covered in greater depth. The result is a book of special interest to students majoring in computer science as well as those majoring in mathematics. Since calculus is used only occasionally, students who have forgotten calculus can nevertheless easily understand the book. The slow, gentle style and clear exposition will appeal to students. Basic concepts such as counting, independence, conditional probability, randon variables, approximation of probabilities, generating functions, random walks and Markov chains are presented with good explanation and many worked exercises. An important feature of the book is the abundance of problems, which students may use to master the material. The 1,196 numerical answers to the 405 exercises, many with multiple parts, are included at the end of the book. Throughout the book, various comments on the history of the study of probability are inserted. Biographical information about some of the famous contributors to probability such as Fermat, Pascal, the Bernoullis, DeMoivre, Bayes, Laplace, Poisson, Markov, and many others, is presented. This volume will appeal to a wide range of readers and should be useful in the undergraduate programs at many colleges and universities.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 284

Добавлена в каталог: 12.09.2007

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$A\bigcap B$      6
$A\bigcup B$      6
$h_{ij}$      212
$p_{ij}$      212
$p_{ij}(n)$      236
$R_{1}$      213
$v_{ij}$      223
$w_{0}, w_{1}, w_{2},...$      188 206
$w_{0}, w_{1},...$      198
$\omega$      4
Absorbing      215
Average value      78
backslash      6
Bar over letter      6
Bayes's formula      62
Bayes, Thomas      62 64 65
Berkeley, George      65
Bernoulli distribution      101—102 170
Bernoulli family      184
Bernoulli trials      47 48
Bernoulli's Law of Large Numbers      115 138 149 212
Bernoulli's theorem      115 119 120 149
Bernoulli, Daniel      117
Bernoulli, Jakob      48 115—117 119 149 150 195
Bernoulli, Johann      116 117 137 194 195
Bernoulli, Nikolaus      117 195
Bienayme, Irene — Jules      112
Binomial coefficients      28
Binomial distribution      49 101 102 131 170 181
Binomial theorem      28
Bonaparte, Napoleon      67
Catalan numbers      (see $w_{0}</a></span> <span class=subjpages><a href=w_{1}$"/>)
Central limit theorems      149
Characteristic function      128
Chebyshev inequality      112—115 120 121 136 162
Chebyshev, Pafnuty Lvovich      112 119 120 211
Conditional expectation      123
Conditional probability      56
Consecutive successes      228 229
Cotes, Roger      149
D'Alembert, Jean      67
DeMoivre's theorem      149 150
DeMoivre, Abraham      57 116 138 144 149—151 156 160 166 202
DeMorgan, Augustus      7
Derangements      174
Descartes, Rene      13 14
Discrete      5
distribution      101
Doe, John      43
Duration of play      199—207
E(X | A)      123
E(X)      78 95
Elementary      7
Even and odd      (see Parity)
Event      4
Expectation      79
Expected value      78 95
Fair game      81
Fermat, Pierre de      11—14 56 78 184
Fixed probability vector      238
Gamblers' Ruin      194
Generating function      165—181
Geometric distribution      101 102 167 181
Gorky, Maxim      211
Hailey, Edmund      150 151
Hsien, Chia      30
Huygens, Christiaan      11 14 78 79 194
Hypergeo me trie distribution      132
Independent      42 44 91
Indicator      128
Insurance      120
l'Hospital's rule      137
l'Hospital, G.F.A. de      137
Lagrange, Joseph — Louis      138
Laplace, Pierre Simon      40 65 66 138 149 166
Law of Large Numbers      115 119—122 138
Law of small numbers      (see Poisson distribution)
Leibniz, Gottfried      11 117 151
Maclaurin series      166
Maclaurin, Colin      165
Markov chains      209—249
Markov property      210
Markov, Andrey Andreyevich      211
Mean value      78
Mode of binomial distribution      49—51
Mode of Pascal distribution      50
Mode of Poisson distribution      136—142
Montmort, Pierre Remond, de      116 149 150 174 183—185 194
Mortality table      150
Most probable value      (see Mode)
Multinomial coefficients      28
Multinomial theorem      28
Mutually exclusive      7 9
Negative binomial distribution      (see Pascal distribution)
Newton, Isaac      2 51 145 150 151 184
Normal approximation      149
Normal distribution      149
Odd and even      (see Parity)
P(A | B)      56
P(A)      7
Parity      40 51 180 181
Partition      61
Pascal distribution      50 101 102 170 181
Pascal's triangle      30
Pascal, Blaise      11 12 14 30 56 78 184
Pascal, Etienne      13
Pepys, Samuel      2 51
Poisson approximation      138
Poisson distribution      140 168 178 181
Poisson, Simeon Denis      138
Pope, Alexander      151
Probability vector      238
Random variable      76
Random walks      183—207
Recurrent      214
Rencontre      174
Richelieu, Cardinal      13
Riemann, Bernhard      160
Roberval, Gilles Personne de      11—14
Runs of successes      (see Successes Consecutive)
Sample space      4
Shakespeare, William      142
Standard deviation      85
Stirling's formula      144
STIRLING, JAMES      144 145 156
Transient      214
Transition matrix      212
Transition probabilities      212
Var(x)      34
Variance      84 96
With replacement      19
Without replacement      19
Xian, Jia      30
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