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Ross S. Ч A First Course in Probability
Ross S. Ч A First Course in Probability



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Ќазвание: A First Course in Probability

јвтор: Ross S.

јннотаци€:

This market leader is written as an elementary introduction to the mathematical theory of probability for readers in mathematics, engineering, and the sciences who possess the prerequisite knowledge of elementary calculus. A major thrust of the Fifth Edition has been to make the book more accessible to today's readers. The exercise sets have been revised to include more simple, "mechanical" problems and new section of Self-test Problems, with fully worked out solutions, conclude each chapter. In addition many new applications have been added to demonstrate the importance of probability in real situations. A software diskette, packaged with each copy of the book, provides an easy to use tool to derive probabilities for binomial, Poisson, and normal random variables. It also illustrates and explores the central limit theorem, works with the strong law of large numbers, and more.


язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

»здание: Fifth edition

√од издани€: 1998

 оличество страниц: 514

ƒобавлена в каталог: 30.03.2008

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Antithetic variables      465Ч466
Associative laws for events      27
Axioms of probability      30Ч31
Axioms of surprise      437
Ballot problem      121
Banach match problem      165Ч166
Basic principle of counting      2
Basic principle of counting, generalized      3
BayesТ formula      79
Bernoulli random variable      144
Bernoulli trials      120
Bernoulli, Daniel      315
Bernoulli, Jacob      see УJames BernoulliФ
Bernoulli, James      93 398
Bernoulli, Nicholas      398
BertrandТs paradox      203Ч204
Beta distribution      226 240 285
Binary symmetric channel      445
Binomial coefficients      8
Binomial random variable      144Ч145 150 172 185; 335Ч336 426
Binomial random variable, approximation to hypergeometric      168Ч169
Binomial random variable, computing its distribution function      152
Binomial random variable, randomly chosen success probability      346Ч347 363
Binomial random variable, simulation of      463Ч464
Binomial random variable, sums of independent      271 360Ч361
Binomial theorem      8
Birthday problem      40Ч41 157Ч158
Bivariate normal distribution      303Ч304 354 389Ч390
BonferroniТs inequality      63 393
BooleТs inequality      66 312
Borel      411
Box Ч Muller      460
Branching process      390Ч391
Bridge      40
BuffonТs needle probem      255Ч236 300
Cauchy distribution      225 305
Cauchy distribution, standard      243
Cauchy Ч Schwarz inequality      387Ч388
Central limit theorem      204Ч205 399
Central limit theorem, for independent random variables      406
Channel capacity      449Ч450
Chapman Ч Kolmogorov equations      433
ChebyshevТs inequality      396
ChebyshevТs inequality, one-sided version      412Ч414
Chernoff bounds      415Ч417
Chi-squared distribution      267Ч268 361Ч362 367Ч368
Chi-squared distribution, relation to gamma distribution      267 284 301
Chi-squared distribution, simulation of      462
Coding theory      441Ч446
Combinations      6
Combinatorial analysis      2
Commulative laws for events      27
Complementary events      27 53
Complete graph      95
Conditional covariance formula      387
Conditional distribution      272 273
Conditional expectation      335 336 337
Conditional expectation, use in prediction      350Ч354
Conditional expectation, use in simulation      466
Conditional probability      67Ч68
Conditional probability distribution function      272 274
Conditional probability mass function      272 292
Conditional probability, as a long run relative frequency      72
Conditional probability, as a probability function      96Ч98
Conditional probability, density function      273Ч274 275 292
Conditional variance      348
Conditional variance formula      348
Conditionally independent events      102
Continuity property of probability      48Ч49 87
Continuous random variables      192
Control variates      468
Convex function      417
Convolution      265
Correlation      332Ч333
Correlation coefficient      see УCorrelationФ
Coupon collecting problems      129Ч131 315Ч316 386
Covariance      326Ч327 388
Craps      58
Cumulative distribution function      131 171
Cumulative distribution function, properties of      132Ч133
DeMere      89
DeMoivre      204 212 214Ч215 401
DeMoivre Ч Laplace limit theorem      212
DeMorganТs laws      28Ч29
Dependent events      84
Dependent random variables      253
Deviations      328
Discrete random variables      134 171
Discrete uniform random variable      241Ч242
Distribution function      see УCumulative distribution functionФ
Distributive laws for events      27
Dominant gene      112
Double exponential distribution      see УLaplacian distributionФ
Ehrenfest urn model      432 436
entropy      439
Entropy, relation to coding theory      441
Ergodic Markov chain      434Ч435
Erlang distribution      224
Event      26
Exchangeable random variables      288Ч291 292
Expectation      136Ч137 171 185 309 368Ч370 384Ч385 388
Expectation, as a center of gravity      138Ч139
Expectation, of a beta random variable      227
Expectation, of a binomial random variable      149Ч150 313
Expectation, of a continuous random variable      195Ч196
Expectation, of a function of a random variable      139Ч140 310
Expectation, of a gamma random variable      224
Expectation, of a geometric random variable      163
Expectation, of a hypergeometric random variable      169Ч170 313Ч314
Expectation, of a negative binomial random variable      166 313
Expectation, of a nonnegative random variable      197
Expectation, of a normal random variable      206
Expectation, of a Poisson random variable      156
Expectation, of a sum of a random number of random variable      339Ч340
Expectation, of a uniform random variable      201
Expectation, of an exponential random variable      216
Expectation, of number of matches      314Ч315
Expectation, of sums of random variables      310Ч325
Expectation, tables of      359 360
Expected value      see УExpectationФ
Exponential random variable      215 239 430
Exponential random variable, relation to, half-life, simulation of      456
Exponential random variable, sums of      267 286Ч288
Failure rate      see УHazard rateФ
Fermat      89Ч90 93
FermatТs combinatorial identity      21
First moment      see УMeanФ
Frequency interpretation of probability      30
Galton      407
GamblerТs ruin problem      90Ч93 120
Game theory      177
Gamma function      222Ч223 227 239
Gamma random variable      222 239 266Ч267 284Ч285 302Ч303
Gamma random variable, relation to chi-squared distribution      224 267 301
Gamma random variable, relation to exponential random variables      267
Gamma random variable, relation to Poisson process      223Ч224
Gamma random variable, simulation of      456
Gauss      214 215
Genetics      112 114 117
Geometric random variable      162 163 187 191
Geometric random variable, simulation of      463
Geometrical probability      203
Half-life      261Ч263
Hamiltonian permuation      323Ч324
Hazard rate      220Ч221 301
Huygens      89 93
Hypergeometric random variable      167 172 336
Hypergeometric random variable, relation to binomial      168Ч169 170
Importance sampling      471Ч472
Independent events      83Ч86
Independent increments      428
Independent random variables      252Ч253 257Ч258 259 263Ч264 292 301
information      439
Inheritance, theory of      147
Intersection of events      26 27 53
Inverse transform method of simulation      455
JensenТs Inequality      418
Joint cumulative probability distribution function      244 251 291
Joint moment generating function      364
Joint probability density function      247Ч248 251Ч252 291
Jointly continuous random variables      247 251 291
k-of-n system      113
Keno      183Ч184
Khintchine      398
Kolmogorov      411
Laplace      204 212 401 407
Laplace distribution      219
LaplaceТs rule of succession      102Ч103 122 123
Law of Large Numbers      395
Legendre theorem      240
Liapounoff      401
Limit of events      48
Linear prediction      353Ч354 389 390
Lognormal distribution      240 392
Marginal distribution      245 246
Markov chains      431Ч436
MarkovТs inequality      395
Matching problem      44Ч45 63 100Ч101
Maximum likelihood estimates      168
Mean of a random variable      142
Median of a random variable      238Ч239
Memoryless random variable      217 218
Mendel      147
Midrange      304
Mode of a random variable      239
Moment generating function      355 358Ч359 392
Moment generating function, of a binomial random variable      356
Moment generating function, of a normal random variable      357Ч358
Moment generating function, of a Poisson rjandom variable      356Ч357
Moment generating function, of a sum of a random number of random variables      362Ч263
Moment generating function, of an exponential random variable      357
Moment generating function, tables for      359 360
Multinomial coefficients      11Ч12
Multinomial distribution      252 334Ч335
Multinomial theorem      12
Multiplication rule of probability      71
Multivariate normal distribution      365Ч366 392
Mutually exclusive events      27 53
Negative binomial random variable      164Ч165 172
Negative binomial random variable, relation to binomial      187
Negative binomial random variable, relation to geometric      165 301
Noiseless coding theorem      443
Noisy coding theorem      446
Normal random variable      204 282Ч284 364
Normal random variable, approximation to binomial      212
Normal random variable, characterization of      256Ч257
Normal random variable, joint distribution of sample mean and sample variance      366Ч368
Normal random variable, moments of      391
Normal random variable, simulation of      458Ч462
Normal random variable, sums of independent      268Ч269 292 361
Normal random variable, table for      208
Null set      54
Odds ratio      77Ч78
Order statistics      276Ч277 278 290Ч291 292
Paradox problem      50Ч52
Parallel system      87
PARETO      171
Partition      62
Pascal      89Ч90
Pascal random variable      see УNegative binomial random variableФ
Pearson, Karl      214 215
Permutation      3Ч5
Personal probability      52Ч53
poisson      154
Poisson process      159Ч161 428Ч431
Poisson random variable      154 172 186 187 253Ч255 273 302Ч303 330 365 393 404 425
Poisson random variable, as an approximation      154Ч155 156Ч158 418Ч420
Poisson random variable, computing its distribution function      161Ч162
Poisson random variable, simulation of      464
Poisson random variable, sums of independent      270Ч271 292 361
Poker      39
Poker dice      57
PolyaТs urn model      289Ч290
Prize problem      344Ч346
Probabilistic method      95Ч96
Probability density function      192
Probability density function, relation to cumulative distribution function      195
Probability mass function      134 171
Probability mass function, relation to cumulative distribution function      135
Problem of the points      80Ч90 165
Quadratic prediction      389
Quicksort algorithm      320Ч322
Random number      393 453
Random permuation      453Ч454 469
Random subset      259Ч261 454Ч455
Random variable      126 171
Random walk      318Ч320 433Ч434
Range of a random sample      279Ч280
Rayleigh density function      221 283
Record values      386
Rejection method of simulation      456Ч458
Relative frequency definition of probability      30
Riemann hypothesis      174
Riemann zeta function      171
Round robin tournament      122
runs      46Ч48 64 99Ч100 317Ч318
Sample mean      311Ч312 328 333Ч334
Sample mean, joint distribution of sample mean and sample variance      366Ч368
Sample median      278Ч279 304
Sample space      25 53
Sample variance      328Ч329
Sampling from a finite population      330Ч332
Sampling with replacement      58
Sequential drug test      93
Shannon      446
Signal processing      352Ч353
Signal to noise ratio      424
Simulation      453
St. Petersburg paradox      178
Standard deviation      144 172 424
Standard normal random variable      207 238
Standard normal random variable, distribution function      207
Standard normal random variable, distribution function, inequalities for      211
Stationary increments      428
Stieltjes integral      368Ч369
StirlingТs approximation      151
Stochastically larger      385
Strong Law of Large Numbers      407Ч408
Strong law of large numbers, proof of      408Ч410
Subjective probability      see УPersonal probabilityФ
Sum of ranks      377Ч378
Surprise      436Ч438
Trials      86
Triangular distribution      266
Uncertainty      439 440
Uncorrelated random variables      333
Uniform random variable      200Ч201 240 343Ч344 373 381
Union of events      26 27 53
Unit normal random variable      see УStandard normal random variableФ
Variance      142Ч143 171 200 238
Variance, as a moment of inertia      144
Variance, of a binomial random variable      149Ч150 329
Variance, of a gamma random variable      224
Variance, of a geometric random variable      164 342Ч343
Variance, of a hypergeometric random variable      169Ч170 332
Variance, of a negative binomial random variable      166
Variance, of a normal random variable      206
Variance, of a Poisson random variable      156
Variance, of a sum of a random number of random variables      349
Variance, of a uniform random variable      202
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