Introduction to Probability and Its Applications
著者
書誌事項
Introduction to Probability and Its Applications
Duxbury Press, c1995
2nd ed.
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注記
Includes bibliographical references (p. [355]-356) and index
内容説明・目次
内容説明
In this calculus-based text, theory is developed to a practical degree around models used in real-world applications. Proofs of theorems and "tricky" probability calculations are minimized. Computing and simulation are introduced to make more difficult problems accessible (although the material does not depend on the computer for continuity).
目次
1. PROBABILITY AND THE WORLD AROUND US
Why Study Probability / Deterministic and Probabilistic Models / Applications of Probability / A Brief Historical Note / A Look Ahead
2. PROBABILITY
Understanding Randomness: An Intuitive Notion of Probability / A Brief Review of Set Notation / Definition of Probability / Counting Rules Useful in Probability / Conditional Probability and Independence / Rules of Probability / Odds, Odds Ratios, and Relative Risk / Activities for Students: Simulation / Summary / Supplementary Exercises
3. DISCRETE PROBABILITY DISTRIBUTIONS
Random Variables and Their Probability Distributions / Expected Values of Random Variables / The Bernoulli Distributions / The Binomial Distribution / The Geometric Distribution / The Negative Binomial Distribution / The Poisson Distribution / The Hypergeometric Distribution / The Moment-generating Functions / The Probability-generating Function / Markov Chains / Activities for Students: Simulation / Summary / Supplementary Exercises
4. CONTINUOUS PROBABILITY DISTRIBUTIONS
Continuous Random Variables and Their Probability Distributions / Expected Values of Continuous Random Variables / The Uniform Distribution / The Exponential Distribution / The Gamma Distribution / The Normal Distribution / The Beta Distribution / The Weibull Distribution / Reliability / Moment-generating Functions for Continuous Random Variables / Expectations of Discontinuous Functions and Mixed Probability Distributions / Activities for Students: Simulation / Summary / Supplementary Exercises
5. MULTIVARIATE PROBABILITY DISTRIBUTIONS
Bivariate and Marginal Probability Distributions / Conditional Probability Distributions / Independent Random Variables / Expected Values of Functions of Random Variables / The Multinomial Distribution / More on the Moment-generating Function / Conditional Expectations / Compounding and its Applications / Summary / Supplementary Exercises
6. FUNCTIONS OF RANDOM VARIABLES
Introduction / Method of Distribution Functions / Method of Transformations / Method of Conditioning / Method of Moment-generating Functions / Order Statistics / Probability-generating Functions: Applications to Random Sums of Random Variables / Summary / Supplementary Exercises
7. SOME APPROXIMATIONS TO PROBABILITY DISTRIBUTIONS: LIMIT THEOREMS
Introduction / Convergence in Probability / Convergence in Distribution / The Central Limit Theorem / Combination of Convergence in Probability and Convergence in Distribution / Summary / Supplementary Exercises
8. EXTENDED APPLICATIONS OF PROBABILITY
The Poisson Process / Birth and Death Processes: Biological Applications / Queues: Engineering Applications / Arrival Times for the Poisson Process / Infinite Server Queue / Renewal Theory: Reliability Applications / Summary / Exercises / APPENDIX TABLES / NOTES ON COMPUTER SIMULATIONS / REFERENCES / ANSWERS TO SELECTED EXERCISES / INDEX
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