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図書

図書
Sheldon Ross
出版情報: New York : Macmillan , London : Collier Macmillan, c1976  x, 305 p. ; 24 cm
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目次情報: 続きを見る
Preface
Combinatorial Analysis / 1:
Introduction / 1.1:
The Basic Principle of Counting / 1.2:
Permutations / 1.3:
Combinations / 1.4:
Multinomial Coefficients / 1.5:
The Number of Integer Solutions of Equations / 1.6:
Summary
Problems
Theoretical Exercises
Self-Test Problems and Exercises
Axioms of Probability / 2:
Sample Space and Events / 2.1:
Some Simple Propositions / 2.3:
Sample Spaces Having Equally Likely Outcomes / 2.5:
Probability As a Continuous Set Function / 2.6:
Probability As a Measure of Belief / 2.7:
Conditional Probability and Independence / 3:
Conditional Probabilities / 3.1:
Bayes' Formula / 3.3:
Independent Events / 3.4:
P(-[middle dot]F) is a Probability / 3.5:
Random Variables / 4:
Discrete Random Variables / 4.1:
Expected Value / 4.3:
Expectatio of a Function of a Random Variable / 4.4:
Variance / 4.5:
The Bernoulli and Binomial Random Variables / 4.6:
Properties of Binomial Random Variables / 4.6.1:
Computing the Binomial Distribution Function / 4.6.2:
The Poisson Random Variable / 4.7:
Computing the Poisson Distribution Function / 4.7.1:
Other Discrete Probability Distribution / 4.8:
The Geometric Random Variable / 4.8.1:
The Negative Binomial Random Variable / 4.8.2:
The Hypergeometric Random Variable / 4.8.3:
The Zeta (or Zipf) distribution / 4.8.4:
Properties of the Cumulative Distribution Function / 4.9:
Continuous Random Variables / 5:
Expectation and Variance of Continuous Random Variables / 5.1:
The Uniform Random Variable / 5.3:
Normal Random Variables / 5.4:
The Normal Approximation to the Binomial Distribution / 5.4.1:
Exponential Random Variables / 5.5:
Hazard Rate Functions / 5.5.1:
Other Continuous Distributions / 5.6:
The Gamma Distribution / 5.6.1:
The Weibull Distribution / 5.6.2:
The Cauchy Distribution / 5.6.3:
The Beta Distribution / 5.6.4:
The Distribution of a Function of a Random Variable / 5.7:
Jointly Distributed Random Variables / 6:
Joint Distribution Functions / 6.1:
Independent Random Variables / 6.2:
Sums of Independent Random Variables / 6.3:
Conditional Distributions: Discrete Case / 6.4:
Conditional Distributions: Continuous Case / 6.5:
Order Statistics / 6.6:
Joint Probability Distribution of Functions of Random Variables / 6.7:
Exchangeable Random Variables / 6.8:
Self-Test Problem and Exercises
Properties of Expectation / 7:
Expectation of Sums of Random Variables / 7.1:
Obtaining Bounds from Expectations via the Probabilistic Method / 7.2.1:
The Maximum-Minimums Identity / 7.2.2:
Covariance, Variance of Sums, and Correlations / 7.3:
Conditional Expectation / 7.4:
Definitions / 7.4.1:
Computing Expectations by Conditioning / 7.4.2:
Computing Probabilities by Conditioning / 7.4.3:
Conditional Variance / 7.4.4:
Conditional Expectation and Prediction / 7.5:
Moment Generating Functions / 7.6:
Joint Moment Generating Functions / 7.6.1:
Additional Properties of Normal Random Variables / 7.7:
The Multivariate Normal Distribution / 7.7.1:
The Joint Distribution of the Sample Mean and Sample Variance / 7.7.2:
General Definition of Expectation / 7.8:
Limit Theorems / 8:
Chebyshev's Inequality and the Weak Law of Large Numbers / 8.1:
The Central Limit Theorem / 8.3:
The Strong Law of Large Numbers / 8.4:
Other Inequalities / 8.5:
Bounding the Error Probability When Approximating a Sum of Independent Bernoulli Random Variables by a Poisson / 8.6:
Additional Topics in Probability / 9:
The Poisson Process / 9.1:
Markov Chains / 9.2:
Surprise, Uncertainty, and Entropy / 9.3:
Coding Theory and Entropy / 9.4:
Theoretical Exercises and Problems
References
Simulation / 10:
General Techniques for Simulating Continuous Random Variables / 10.1:
The Inverse Transformation Method / 10.2.1:
The Rejection Method / 10.2.2:
Simulating from Discrete Distributions / 10.3:
Variance Reduction Techniques / 10.4:
Use of Antithetic Variables / 10.4.1:
Variance Reduction by Conditioning / 10.4.2:
Control Variates / 10.4.3:
Answers to Selected Problems / Appendix A:
Solutions to Self-Test Problems and Exercises / Appendix B:
Index
Preface
Combinatorial Analysis / 1:
Introduction / 1.1:
2.

図書

図書
Sheldon M. Ross
出版情報: Amsterdam : Academic Press, c2014  xv, 767 p. ; 24 cm
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3.

図書

図書
Sheldon M. Ross
出版情報: Amsterdam ; San Diego, Calif. ; Tokyo : Academic Press, c2007  xviii, 782 p. ; 24 cm
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目次情報: 続きを見る
Preface
Introduction to Probability Theory / 1:
Random Variables / 2:
Conditional Probability and Conditional Expectation / 3:
Markov Chains / 4:
The Exponential Distribution and the Poisson Process / 5:
Continuous-Time Markov Chains / 6:
Renewal Theory and Its Applications / 7:
Queueing Theory / 8:
Reliability Theory / 9:
Brownian Motion and Stationary Processes / 10:
Simulation / 11:
Appendix: Solutions to Starred Exercises
Index
Preface
Introduction to Probability Theory / 1:
Random Variables / 2:
4.

図書

図書
by Sheldon M. Ross
出版情報: New York : Academic Press, 1972  xiii, 272 p. ; 23 cm
シリーズ名: Probability and mathematical statistics : a series of monographs and textbooks ; v. 10
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目次情報: 続きを見る
Preface
Introduction to Probability Theory / 1:
Random Variables / 2:
Conditional Probability and Conditional Expectation / 3:
Markov Chains / 4:
The Exponential Distribution and the Poisson Process / 5:
Continuous-Time Markov Chains / 6:
Renewal Theory and Its Applications / 7:
Queueing Theory / 8:
Reliability Theory / 9:
Brownian Motion and Stationary Processes / 10:
Simulation / 11:
Appendix: Solutions to Starred Exercises
Index
Preface
Introduction to Probability Theory / 1:
Random Variables / 2:
5.

図書

図書
[by] Sheldon M. Ross
出版情報: San Francisco [Calif.] : Holden-Day, c1970  198 p. ; 24 cm
シリーズ名: Holden-Day series in management science
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6.

図書

図書
Sheldon M. Ross
出版情報: Boston ; Tokyo : Academic Press, c1989  xiv, 544 p. ; 24 cm
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