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The Resource A first course in probability, Sheldon Ross

A first course in probability, Sheldon Ross

Label
A first course in probability
Title
A first course in probability
Statement of responsibility
Sheldon Ross
Creator
Subject
Language
eng
Summary
  • P. 15
  • P. 52
  • P. 103
  • P. 169
  • P. 225
  • P. 288
  • P. 377
  • P. 426
  • P. 451
Cataloging source
DLC
http://library.link/vocab/creatorName
Ross, Sheldon M
Index
index present
Language note
English
Literary form
non fiction
http://library.link/vocab/subjectName
Probabilities
Label
A first course in probability, Sheldon Ross
Instantiates
Publication
Note
"Pearson International edition" -- cover
Bibliography note
Includes index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Preface
  • 1.
  • Combinatorial Analysis.
  • p. 1
  • 1.1.
  • Introduction.
  • p. 1
  • 1.2.
  • Basic Principle of Counting.
  • p. 2
  • 1.3.
  • Permutations.
  • p. 3
  • 1.4.
  • Combinations.
  • p. 6
  • 1.5.
  • Multinomial Coefficients.
  • p. 10
  • 1.6.
  • Number of Integer Solutions of Equations*.
  • p. 12
  • Summary.
  • p. 15
  • Problems.
  • p. 16
  • Theoretical Exercises.
  • p. 19
  • Self-Test Problems and Exercises.
  • p. 22
  • 2.
  • Axioms of Probability.
  • p. 24
  • 2.1.
  • Introduction.
  • p. 24
  • 2.2.
  • Sample Space and Events.
  • p. 24
  • 2.3.
  • Axioms of Probability.
  • p. 29
  • 2.4.
  • Some Simple Propositions.
  • p. 31
  • 2.5.
  • Sample Spaces Having Equally Likely Outcomes.
  • p. 37
  • 2.6.
  • Probability as a Continuous Set Function*.
  • p. 49
  • 2.7.
  • Probability as a Measure of Belief.
  • p. 53
  • Summary.
  • p. 54
  • Problems.
  • p. 55
  • Theoretical Exercises.
  • p. 61
  • Self-Test Problems and Exercises.
  • p. 63
  • 3.
  • Conditional Probability and Independence.
  • p. 66
  • 3.1.
  • Introduction.
  • p. 66
  • 3.2.
  • Conditional Probabilities.
  • p. 66
  • 3.3.
  • Bayes' Formula.
  • p. 72
  • 3.4.
  • Independent Events.
  • p. 87
  • 3.5.
  • P(.[vertical bar]F) Is a Probability.
  • p. 101
  • Summary.
  • p. 110
  • Problems.
  • p. 111
  • Theoretical Exercises.
  • p. 124
  • Self-Test Problems and Exercises.
  • p. 128
  • 4.
  • Random Variables.
  • p. 132
  • 4.1.
  • Random Variables.
  • p. 132
  • 4.2.
  • Discrete Random Variables.
  • p. 138
  • 4.3.
  • Expected Value.
  • p. 140
  • 4.4.
  • Expectation of a Function of a Random Variable.
  • p. 144
  • 4.5.
  • Variance.
  • p. 148
  • 4.6.
  • Bernoulli and Binomial Random Variables.
  • p. 150
  • 4.6.1.
  • Properties of Binomial Random Variables.
  • p. 155
  • 4.6.2.
  • Computing the Binomial Distribution Function.
  • p. 158
  • 4.7.
  • Poisson Random Variable.
  • p. 160
  • 4.7.1.
  • Computing the Poisson Distribution Function.
  • p. 173
  • 4.8.
  • Other Discrete Probability Distributions.
  • p. 173
  • 4.8.1.
  • Geometric Random Variable.
  • p. 173
  • 4.8.2.
  • Negative Binomial Random Variable.
  • p. 175
  • 4.8.3.
  • Hypergeometric Random Variable.
  • p. 178
  • 4.8.4.
  • Zeta (or Zipf) Distribution.
  • p. 182
  • 4.9.
  • Properties of the Cumulative Distribution Function.
  • p. 183
  • Summary.
  • p. 185
  • Problems.
  • p. 187
  • Theoretical Exercises.
  • p. 197
  • Self-Test Problems and Exercises.
  • p. 201
  • 5.
  • Continuous Random Variables.
  • p. 205
  • 5.1.
  • Introduction.
  • p. 205
  • 5.2.
  • Expectation and Variance of Continuous Random Variables.
  • p. 209
  • 5.3.
  • Uniform Random Variable.
  • p. 214
  • 5.4.
  • Normal Random Variables.
  • p. 218
  • 5.4.1.
  • Normal Approximation to the Binomial Distribution.
  • p. 225
  • 5.5.
  • Exponential Random Variables.
  • p. 230
  • 5.5.1.
  • Hazard Rate Functions.
  • p. 234
  • 5.6.
  • Other Continuous Distributions.
  • p. 237
  • 5.6.1.
  • Gamma Distribution.
  • p. 237
  • 5.6.2.
  • Weibull Distribution.
  • p. 239
  • 5.6.3.
  • Cauchy Distribution.
  • p. 239
  • 5.6.4.
  • Beta Distribution.
  • p. 240
  • 5.7.
  • Distribution of a Function of a Random Variable.
  • p. 242
  • Summary.
  • p. 244
  • Problems.
  • p. 247
  • Theoretical Exercises.
  • p. 251
  • Self-Test Problems and Exercises.
  • p. 254
  • 6.
  • Jointly Distributed Random Variables.
  • p. 258
  • 6.1.
  • Joint Distribution Functions.
  • p. 258
  • 6.2.
  • Independent Random Variables.
  • p. 267
  • 6.3.
  • Sums of Independent Random Variables.
  • p. 280
  • 6.4.
  • Conditional Distributions: Discrete Case.
  • p. 288
  • 6.5.
  • Conditional Distributions: Continuous Case.
  • p. 291
  • 6.6.
  • Order Statistics.
  • p. 296
  • 6.7.
  • Joint Probability Distribution of Functions of Random Variables.
  • p. 300
  • 6.8.
  • Exchangeable Random Variables.
  • p. 308
  • Summary.
  • p. 311
  • Problems.
  • p. 313
  • Theoretical Exercises.
  • p. 319
  • Self-Test Problems and Exercises.
  • p. 323
  • 7.
  • Properties of Expectation.
  • p. 327
  • 7.1.
  • Introduction.
  • p. 327
  • 7.2.
  • Expectation of Sums of Random Variables.
  • p. 328
  • 7.2.1.
  • Obtaining Bounds from Expectations via the Probabilistic Method.
  • p. 342
  • 7.2.2.
  • Maximum-Minimums Identity.
  • p. 344
  • 7.3.
  • Moments of the Number of Events that Occur.
  • p. 347
  • 7.4.
  • Covariance, Variance of Sums, and Correlations.
  • p. 355
  • 7.5.
  • Conditional Expectation.
  • p. 365
  • 7.5.1.
  • Definitions.
  • p. 365
  • 7.5.2.
  • Computing Expectations by Conditioning.
  • p. 367
  • 7.5.3.
  • Computing Probabilities by Conditioning.
  • p. 376
  • 7.5.4.
  • Conditional Variance.
  • p. 380
  • 7.6.
  • Conditional Expectation and Prediction.
  • p. 382
  • 7.7.
  • Moment Generating Functions.
  • p. 387
  • 7.7.1.
  • Joint Moment Generating Functions.
  • p. 397
  • 7.8.
  • Additional Properties of Normal Random Variables.
  • p. 399
  • 7.8.1.
  • Multivariate Normal Distribution.
  • p. 399
  • 7.8.2.
  • Joint Distribution of the Sample Mean and Sample Variance.
  • p. 402
  • 7.9.
  • General Definition of Expectation.
  • p. 404
  • Summary.
  • p. 405
  • Problems.
  • p. 408
  • Theoretical Exercises.
  • p. 418
  • Self-Test Problems and Exercises.
  • p. 426
  • 8.
  • Limit Theorems.
  • p. 430
  • 8.1.
  • Introduction.
  • p. 430
  • 8.2.
  • Chebyshev's Inequality and the Weak Law of Large Numbers.
  • p. 430
  • 8.3.
  • Central Limit Theorem.
  • p. 434
  • 8.4.
  • Strong Law of Large Numbers.
  • p. 443
  • 8.5.
  • Other Inequalities.
  • p. 445
  • 8.6.
  • Bounding The Error Probability.
  • p. 454
  • Summary.
  • p. 456
  • Problems.
  • p. 457
  • Theoretical Exercises.
  • p. 459
  • Self-Test Problems and Exercises.
  • p. 461
  • 9.
  • Additional Topics in Probability.
  • p. 463
  • 9.1.
  • Poisson Process.
  • p. 463
  • 9.2.
  • Markov Chains.
  • p. 466
  • 9.3.
  • Surprise, Uncertainty, and Entropy.
  • p. 472
  • 9.4.
  • Coding Theory and Entropy.
  • p. 476
  • Summary.
  • p. 483
  • .
  • Theoretical Exercises.
  • p. 484
  • .
  • Self-Test Problems and Exercises.
  • p. 485
  • 10.
  • Simulation.
  • p. 487
  • 10.1.
  • Introduction.
  • p. 487
  • 10.2.
  • General Techniques for Simulating Continuous Random Variables.
  • p. 490
  • 10.2.1.
  • Inverse Transformation Method.
  • p. 490
  • 10.2.2.
  • Rejection Method.
  • p. 491
  • 10.3.
  • Simulating from Discrete Distributions.
  • p. 497
  • 10.4.
  • Variance Reduction Techniques.
  • p. 499
  • 10.4.1.
  • Use of Antithetic Variables.
  • p. 500
  • 10.4.2.
  • Variance Reduction by Conditioning.
  • p. 501
  • 10.4.3.
  • Control Variates.
  • p. 503
  • Summary.
  • p. 503
  • .
  • Problems.
  • p. 504
  • .
  • Self-Test Problems and Exercises.
  • p. 506
  • .
  • Appendices
  • A.
  • Answers to Selected Problems.
  • p. 508
  • B.
  • Solutions to Self-Test Problems and Exercises.
  • p. 511
  • .
  • Index.
  • p. 561
Control code
ocm59401216
Dimensions
25 cm.
Edition
7th ed.
Extent
x, 565 p.
Isbn
9780132018173
Lccn
2005047691
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
ill.
Label
A first course in probability, Sheldon Ross
Publication
Note
"Pearson International edition" -- cover
Bibliography note
Includes index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Preface
  • 1.
  • Combinatorial Analysis.
  • p. 1
  • 1.1.
  • Introduction.
  • p. 1
  • 1.2.
  • Basic Principle of Counting.
  • p. 2
  • 1.3.
  • Permutations.
  • p. 3
  • 1.4.
  • Combinations.
  • p. 6
  • 1.5.
  • Multinomial Coefficients.
  • p. 10
  • 1.6.
  • Number of Integer Solutions of Equations*.
  • p. 12
  • Summary.
  • p. 15
  • Problems.
  • p. 16
  • Theoretical Exercises.
  • p. 19
  • Self-Test Problems and Exercises.
  • p. 22
  • 2.
  • Axioms of Probability.
  • p. 24
  • 2.1.
  • Introduction.
  • p. 24
  • 2.2.
  • Sample Space and Events.
  • p. 24
  • 2.3.
  • Axioms of Probability.
  • p. 29
  • 2.4.
  • Some Simple Propositions.
  • p. 31
  • 2.5.
  • Sample Spaces Having Equally Likely Outcomes.
  • p. 37
  • 2.6.
  • Probability as a Continuous Set Function*.
  • p. 49
  • 2.7.
  • Probability as a Measure of Belief.
  • p. 53
  • Summary.
  • p. 54
  • Problems.
  • p. 55
  • Theoretical Exercises.
  • p. 61
  • Self-Test Problems and Exercises.
  • p. 63
  • 3.
  • Conditional Probability and Independence.
  • p. 66
  • 3.1.
  • Introduction.
  • p. 66
  • 3.2.
  • Conditional Probabilities.
  • p. 66
  • 3.3.
  • Bayes' Formula.
  • p. 72
  • 3.4.
  • Independent Events.
  • p. 87
  • 3.5.
  • P(.[vertical bar]F) Is a Probability.
  • p. 101
  • Summary.
  • p. 110
  • Problems.
  • p. 111
  • Theoretical Exercises.
  • p. 124
  • Self-Test Problems and Exercises.
  • p. 128
  • 4.
  • Random Variables.
  • p. 132
  • 4.1.
  • Random Variables.
  • p. 132
  • 4.2.
  • Discrete Random Variables.
  • p. 138
  • 4.3.
  • Expected Value.
  • p. 140
  • 4.4.
  • Expectation of a Function of a Random Variable.
  • p. 144
  • 4.5.
  • Variance.
  • p. 148
  • 4.6.
  • Bernoulli and Binomial Random Variables.
  • p. 150
  • 4.6.1.
  • Properties of Binomial Random Variables.
  • p. 155
  • 4.6.2.
  • Computing the Binomial Distribution Function.
  • p. 158
  • 4.7.
  • Poisson Random Variable.
  • p. 160
  • 4.7.1.
  • Computing the Poisson Distribution Function.
  • p. 173
  • 4.8.
  • Other Discrete Probability Distributions.
  • p. 173
  • 4.8.1.
  • Geometric Random Variable.
  • p. 173
  • 4.8.2.
  • Negative Binomial Random Variable.
  • p. 175
  • 4.8.3.
  • Hypergeometric Random Variable.
  • p. 178
  • 4.8.4.
  • Zeta (or Zipf) Distribution.
  • p. 182
  • 4.9.
  • Properties of the Cumulative Distribution Function.
  • p. 183
  • Summary.
  • p. 185
  • Problems.
  • p. 187
  • Theoretical Exercises.
  • p. 197
  • Self-Test Problems and Exercises.
  • p. 201
  • 5.
  • Continuous Random Variables.
  • p. 205
  • 5.1.
  • Introduction.
  • p. 205
  • 5.2.
  • Expectation and Variance of Continuous Random Variables.
  • p. 209
  • 5.3.
  • Uniform Random Variable.
  • p. 214
  • 5.4.
  • Normal Random Variables.
  • p. 218
  • 5.4.1.
  • Normal Approximation to the Binomial Distribution.
  • p. 225
  • 5.5.
  • Exponential Random Variables.
  • p. 230
  • 5.5.1.
  • Hazard Rate Functions.
  • p. 234
  • 5.6.
  • Other Continuous Distributions.
  • p. 237
  • 5.6.1.
  • Gamma Distribution.
  • p. 237
  • 5.6.2.
  • Weibull Distribution.
  • p. 239
  • 5.6.3.
  • Cauchy Distribution.
  • p. 239
  • 5.6.4.
  • Beta Distribution.
  • p. 240
  • 5.7.
  • Distribution of a Function of a Random Variable.
  • p. 242
  • Summary.
  • p. 244
  • Problems.
  • p. 247
  • Theoretical Exercises.
  • p. 251
  • Self-Test Problems and Exercises.
  • p. 254
  • 6.
  • Jointly Distributed Random Variables.
  • p. 258
  • 6.1.
  • Joint Distribution Functions.
  • p. 258
  • 6.2.
  • Independent Random Variables.
  • p. 267
  • 6.3.
  • Sums of Independent Random Variables.
  • p. 280
  • 6.4.
  • Conditional Distributions: Discrete Case.
  • p. 288
  • 6.5.
  • Conditional Distributions: Continuous Case.
  • p. 291
  • 6.6.
  • Order Statistics.
  • p. 296
  • 6.7.
  • Joint Probability Distribution of Functions of Random Variables.
  • p. 300
  • 6.8.
  • Exchangeable Random Variables.
  • p. 308
  • Summary.
  • p. 311
  • Problems.
  • p. 313
  • Theoretical Exercises.
  • p. 319
  • Self-Test Problems and Exercises.
  • p. 323
  • 7.
  • Properties of Expectation.
  • p. 327
  • 7.1.
  • Introduction.
  • p. 327
  • 7.2.
  • Expectation of Sums of Random Variables.
  • p. 328
  • 7.2.1.
  • Obtaining Bounds from Expectations via the Probabilistic Method.
  • p. 342
  • 7.2.2.
  • Maximum-Minimums Identity.
  • p. 344
  • 7.3.
  • Moments of the Number of Events that Occur.
  • p. 347
  • 7.4.
  • Covariance, Variance of Sums, and Correlations.
  • p. 355
  • 7.5.
  • Conditional Expectation.
  • p. 365
  • 7.5.1.
  • Definitions.
  • p. 365
  • 7.5.2.
  • Computing Expectations by Conditioning.
  • p. 367
  • 7.5.3.
  • Computing Probabilities by Conditioning.
  • p. 376
  • 7.5.4.
  • Conditional Variance.
  • p. 380
  • 7.6.
  • Conditional Expectation and Prediction.
  • p. 382
  • 7.7.
  • Moment Generating Functions.
  • p. 387
  • 7.7.1.
  • Joint Moment Generating Functions.
  • p. 397
  • 7.8.
  • Additional Properties of Normal Random Variables.
  • p. 399
  • 7.8.1.
  • Multivariate Normal Distribution.
  • p. 399
  • 7.8.2.
  • Joint Distribution of the Sample Mean and Sample Variance.
  • p. 402
  • 7.9.
  • General Definition of Expectation.
  • p. 404
  • Summary.
  • p. 405
  • Problems.
  • p. 408
  • Theoretical Exercises.
  • p. 418
  • Self-Test Problems and Exercises.
  • p. 426
  • 8.
  • Limit Theorems.
  • p. 430
  • 8.1.
  • Introduction.
  • p. 430
  • 8.2.
  • Chebyshev's Inequality and the Weak Law of Large Numbers.
  • p. 430
  • 8.3.
  • Central Limit Theorem.
  • p. 434
  • 8.4.
  • Strong Law of Large Numbers.
  • p. 443
  • 8.5.
  • Other Inequalities.
  • p. 445
  • 8.6.
  • Bounding The Error Probability.
  • p. 454
  • Summary.
  • p. 456
  • Problems.
  • p. 457
  • Theoretical Exercises.
  • p. 459
  • Self-Test Problems and Exercises.
  • p. 461
  • 9.
  • Additional Topics in Probability.
  • p. 463
  • 9.1.
  • Poisson Process.
  • p. 463
  • 9.2.
  • Markov Chains.
  • p. 466
  • 9.3.
  • Surprise, Uncertainty, and Entropy.
  • p. 472
  • 9.4.
  • Coding Theory and Entropy.
  • p. 476
  • Summary.
  • p. 483
  • .
  • Theoretical Exercises.
  • p. 484
  • .
  • Self-Test Problems and Exercises.
  • p. 485
  • 10.
  • Simulation.
  • p. 487
  • 10.1.
  • Introduction.
  • p. 487
  • 10.2.
  • General Techniques for Simulating Continuous Random Variables.
  • p. 490
  • 10.2.1.
  • Inverse Transformation Method.
  • p. 490
  • 10.2.2.
  • Rejection Method.
  • p. 491
  • 10.3.
  • Simulating from Discrete Distributions.
  • p. 497
  • 10.4.
  • Variance Reduction Techniques.
  • p. 499
  • 10.4.1.
  • Use of Antithetic Variables.
  • p. 500
  • 10.4.2.
  • Variance Reduction by Conditioning.
  • p. 501
  • 10.4.3.
  • Control Variates.
  • p. 503
  • Summary.
  • p. 503
  • .
  • Problems.
  • p. 504
  • .
  • Self-Test Problems and Exercises.
  • p. 506
  • .
  • Appendices
  • A.
  • Answers to Selected Problems.
  • p. 508
  • B.
  • Solutions to Self-Test Problems and Exercises.
  • p. 511
  • .
  • Index.
  • p. 561
Control code
ocm59401216
Dimensions
25 cm.
Edition
7th ed.
Extent
x, 565 p.
Isbn
9780132018173
Lccn
2005047691
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
ill.

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