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