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Grimmett G., Welsh D. — Probability: An Introduction
Grimmett G., Welsh D. — Probability: An Introduction

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Название: Probability: An Introduction

Авторы: Grimmett G., Welsh D.

Аннотация:

This new undergraduate text offers a concise introduction to probability and random processes. Exercises and problems range from simple to difficult, and the overall treatment, though elementary, includes rigorous mathematical arguments. Chapters contain core material for a beginning course in probability, a treatment of joint distributions leading to accounts of moment-generating functions, the law of large numbers and the central limit theorem, and basic random processes.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1986

Количество страниц: 211

Добавлена в каталог: 30.03.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abel's lemma      50 158 159
Absolute convergence      29 67
Absolutely continuous distribution      60
Absorbing state      183
Arrival rate      169
Banach's matchbox problem      35
Bayes formula      14
Bernoulli distribution      24 27 43 53 136
Bernoulli distribution, probability generating function      48
Bilateral exponential distribution      63 88
Bilateral exponential distribution, characteristic function      123
Bilateral exponential distribution, moments      70
Binomial distribution      25 27 43 53 54 136
Binomial distribution, characteristic function      120
Binomial distribution, Moments      32
Binomial distribution, probability generating function      48
Binomial—Poisson limit theorem      27 139
Birth process      177
Birth rate      178 182
Birth-death process      182 187
Birth-death process, embedded random walk      184
Birth-death process, extinction      184 192
Birth-death-immigration process      192
Bivariate discrete distribution      36
Bivariate normal distribution      93 111
Bivariate normal distribution, joint moment generating function      122
Bivariate normal distribution, standard      93
Boole's inequality      18
Branching process      143 144
Branching process, critical      147
Branching process, extinction      147 149
Cantor distribution      102
Cantor set      102
Cardinality      7
Cauchy distribution      64 97 98 123 136
Cauchy distribution, Characteristic function      116
Cauchy distribution, Moments      69 105
Cauchy — Schwarz inequality      109 137
Central limit theorem      130 136
Changes of variables      185
Characteristic function      112 115 135
Characteristic function, inversion formula      119
Characteristic function, uniqueness theorem      119
Chebyshev's inequality      127 129 137
Chi-squared distribution      64 67 85 100
Chi-squared distribution, characteristic function      139
Chi-squared distribution, moment generating function      121
Chi-squared distribution, moments      106
Complement      4
Conditional, density function      89
Conditional, distribution function      89
Conditional, expectation      32 92
Conditional, probability      11
Continuity of probability measures      15
Continuity theorem      130 135
Continuous random variable      60
Convergence in distribution      132
Convergence in mean square      124 133
Convergence in probability      126 133
Convolution      42 84
Correlation      109
Countable set      6
Coupon-collecting problem      35 44 54 123
Covariance      108
Death rate      182
Decreasing sequence of events      16
Density function      60
Density function, joint      78
Dependent, events      13
Dependent, random variables      38 76
Difference equations      195
Difference equations, auxiliary equation      195
Difference equations, complementary solution      197
Difference equations, particular solution      197
Difference of sets      5
Discrete random variable      22
Distribution function      56
Distribution function, joint      75
Distribution, Bernoulli      24
Distribution, bilateral exponential      63
Distribution, binomial      25
Distribution, bivariate normal      93
Distribution, Cantor      102
Distribution, Cauchy      64
Distribution, chi-squared      64
Distribution, double exponential      63
Distribution, exponential      59
Distribution, extreme value      63
Distribution, F      99
Distribution, gamma      64
Distribution, geometric      25
Distribution, log-normal      70
Distribution, negative binomial      25
Distribution, normal      64
Distribution, Poisson      25
Distribution, t      99
Distribution, uniform      59
Double exponential distribution      63 88
Double exponential distribution, characteristic function      123
Double exponential distribution, moments      70
Duellists      54 98
Eddington's controversy      21
Elementary event      3
Embedded random walk      184
Equilibrium distribution      189
Event      4
Event, space      4
Expectation      29 37 67 90 102
Expected value      29 67
Experiment      3
Exponential distribution      59 60 63 65 90 96 98 121 174
Exponential distribution, characteristic function      116
Exponential distribution, moment generating function      112
Exponential distribution, Moments      69 104
Exponential generating function      45
Extreme value distribution      63
Extreme value distribution, moment generating function      191
F distribution      99
Fair      10 16
Finite additivity      21
Fourier, inverse theorem      119
Fourier, transform      119
Fubini's theorem      78
Gambler's ruin problem      159 184
Gamma distribution      64 65 84 99 121 190
Gamma distribution, characteristic function      120
Gamma distribution, moment generating function      115
Gamma distribution, Moments      106
Gamma function      64
Geiger counter      169
Generating function      45
Generation      144
Geometric distribution      25 34 43
Geometric distribution, Moments      31 50
Geometric distribution, probability generating function      47
Humbugs      35
Image      22 23
Immigration-death process      193
Increasing sequence of events      15
Independent events      13
Independent random variables      38 41 76 81 91
Indicator function      24 42
Integer-valued random variables      46
Inverse Formula      119
Jacobian      86
Joint, density function      78
Joint, distribution function      75 76
Joint, mass function      36
Joint, moment generating function      122
Jointly continuous random variables      78
Lack-of-memory property      34 96 175 186
Laplace, inverse theorem      114
Laplace, transform      114
Law of Averages      124
Law of large numbers, mean square      125
Law of Large Numbers, strong      128
Law of large numbers, weak      128 135
Log-normal distribution      70 106
Marginal, density function      80
Marginal, distribution function      76
Marginal, mass function      36
Markov's inequality      137
Mass function      23
Maximum      43 97
Mean value      29 49 67
Median      58 138
Minimum      43 97
Moment generating function      111
Moment generating function, joint      122
Moment generating function, uniqueness theorem      114
Moment problem      105
Moments      49 104 117
Multivariate distribution      36 75
Negative binomial distribution      25
Negative binomial distribution, Moments      51
Negative binomial distribution, probability generating function      48
NOMAD      143
Normal distribution      63 67 85 87 98 99 114 131
Normal distribution, bivariate      93 111 122
Normal distribution, characteristic function      117
Normal distribution, moment generating function      112 115
Normal distribution, Moments      69
Normal number      19
Occupancy problem      10 44
Order statistics      138
Outcome      3
Outcome, equiprobable      9
Pairwise independent, events      13
Pairwise independent, random variables      41
Partition      14
Partition, theorem      14 33
Poisson distribution      25 27 42 44 53 54 70 98
Poisson distribution, characteristic function      120
Poisson distribution, moment generating function      115
Poisson distribution, Moments      32 51
Poisson distribution, probability generating function      48
Poisson process      143 169
Poisson process, arrival times      170 174
Poisson process, compound      191
Poisson process, doubly stochastic      191
Poisson process, excess life      191
Poisson process, inhomogeneous      191
Poisson process, inter-arrival times      174
Power set      4
Probability, density function      60
Probability, distribution function      56
Probability, generating function      46 111
Probability, generating function, uniqueness theorem      47
Probability, mass function      23
Probability, measure      6
Probability, measure, countably additive      21
Probability, measure, finitely additive      21
Probability, space      3 7
Pseudo-random number      71
Pure birth process      179
QUEUE      185
Queue, baulking      194
Queue, equilibrium distribution      189
Queue, steady-state distribution      189
Queue, traffic intensity      189
Queue, waiting time      190 193 194
Rabbits      52
Random graph      44
Random integer      9
Random process      143
Random process, continuous time      168
Random process, discrete time      168
Random sum formula      51
Random variable      22 56
Random variable, function of      65
Random vector      75
Random walk      143 153 189
Random walk, absorbing barriers      160
Random walk, asymmetric      153
Random walk, recurrence      156
Random walk, retaining barriers      165
Random walk, simple      153
Random walk, symmetric      153 159
Random walk, three dimensional      166
Random walk, transience      156
Random walk, transition probabilities      154
Random walk, two dimensional      155 165 166
Recurrence      156 166
Recurrent event      167
Sample median      138
Sample space      3
Sample space, discrete      9
Service time      185
Simple queue      185
Singular distribution      104
Standard deviation      108
Standardized random variable      129
Steady-state distribution      189 192 193
Stirling's formula      155
Stochastic process      143
Sums of random variables      42 83 113 118 125 129
Sums of random variables, probability generating function      51
Symmetric difference      5
Symmetric distribution      123
t distribution      99
Theorem of total probability      14
Traffic intensity      189
Transience      156 166
Transient event      167
Trial      3
Unbiased      16
Uncorrelated random variables      110
Uniform distribution      59 63 71 80 136 139
Uniform distribution, Characteristic function      120
Uniform distribution, Moments      68 106
Uniform distribution, probability generating function      49
Variance      31 49 68
Venn diagram      8
Weierstrass's approximation theorem      139
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