 1.

Sheldon Ross
 出版情報: New York : Macmillan , London : Collier Macmillan, c1976  x, 305 p. ; 24 cm 所蔵情報: loading…

 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：
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Sheldon M. Ross
 出版情報: Amsterdam : Academic Press, c2014  xv, 767 p. ; 24 cm 所蔵情報: loading…
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Sheldon M. Ross
 出版情報: Amsterdam ; San Diego, Calif. ; Tokyo : Academic Press, c2007  xviii, 782 p. ; 24 cm 所蔵情報: loading…

 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：
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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 所蔵情報: loading…

 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：
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[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 所蔵情報: loading…
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Sheldon M. Ross
 出版情報: Boston ; Tokyo : Academic Press, c1989  xiv, 544 p. ; 24 cm 所蔵情報: loading… 文献複写・貸借依頼