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  • (ebook) A First Course in Probability, eBook, Global Edition
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(ebook) A First Course in Probability, eBook, Global Edition 요약정보 및 구매

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저자 : Sheldon Ross

상품 선택옵션 0 개, 추가옵션 0 개

위시리스트0
판매가격 48,000원
출판사 Pearson
발행일2020
ISBN 9781292269238
언어 ENG
포인트 0점
배송비결제 주문시 결제

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  • (ebook) A First Course in Probability, eBook, Global Edition
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    This title is a Pearson Global Edition. The Editorial team at Pearson has worked closely with educators around the world to include content which is especially relevant to students outside the United States.


    For upper-level to graduate courses in Probability or Probability and Statistics, for majors in mathematics, statistics, engineering, and the sciences.


     


    Explores both the mathematics and the many potential applications of probability theory


     


    A First Course in Probability offers an elementary introduction to the theory of probability for students in mathematics, statistics, engineering, and the sciences. Through clear and intuitive explanations, it attempts to present not only the mathematics of probability theory, but also the many diverse possible applications of this subject through numerous examples. The 10th Edition includes many new and updated problems, exercises, and text material chosen both for inherent interest and for use in building student intuition about probability.

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    1. COMBINATORIAL ANALYSIS 


    1.1 Introduction 


    1.2 The Basic Principle of Counting 


    1.3 Permutations 


    1.4 Combinations 


    1.5 Multinomial Coefficients 


    1.6 The Number of Integer Solutions of Equations 


    Summary


    Problems


    Theoretical Exercises


    Self-Test Problems and Exercises


    2. AXIOMS OF PROBABILITY


    2.1 Introduction


    2.2 Sample Space and Events


    2.3 Axioms of Probability


    2.4 Some Simple Propositions


    2.5 Sample Spaces Having Equally Likely Outcomes


    2.6 Probability as a Continuous Set Function


    2.7 Probability as a Measure of Belief


    Summary


    Problems


    Theoretical Exercises


    Self-Test Problems and Exercises


    3. CONDITIONAL PROBABILITY AND INDEPENDENCE


    3.1 Introduction


    3.2 Conditional Probabilities


    3.3 Bayes’s Formula


    3.4 Independent Events


    3.5 P(·|F) Is a Probability


    Summary


    Problems


    Theoretical Exercises


    Self-Test Problems and Exercises


    4. RANDOM VARIABLES


    4.1 Random Variables


    4.2 Discrete Random Variables


    4.3 Expected Value


    4.4 Expectation of a Function of a Random Variable


    4.5 Variance


    4.6 The Bernoulli and Binomial Random Variables


    4.7 The Poisson Random Variable


    4.8 Other Discrete Probability Distributions


    4.9 Expected Value of Sums of Random Variables


    4.10 Properties of the Cumulative Distribution Function


    Summary


    Problems


    Theoretical Exercises


    Self-Test Problems and Exercises


    5. CONTINUOUS RANDOM VARIABLES


    5.1 Introduction


    5.2 Expectation and Variance of Continuous Random Variables


    5.3 The Uniform Random Variable


    5.4 Normal Random Variables


    5.5 Exponential Random Variables


    5.6 Other Continuous Distributions


    5.7 The Distribution of a Function of a Random Variable


    Summary


    Problems


    Theoretical Exercises


    Self-Test Problems and Exercises


    6. JOINTLY DISTRIBUTED RANDOM VARIABLES


    6.1 Joint Distribution Functions


    6.2 Independent Random Variables


    6.3 Sums of Independent Random Variables


    6.4 Conditional Distributions: Discrete Case


    6.5 Conditional Distributions: Continuous Case


    6.6 Order Statistics


    6.7 Joint Probability Distribution of Functions of Random Variables


    6.8 Exchangeable Random Variables


    Summary


    Problems


    Theoretical Exercises


    Self-Test Problems and Exercises


    7. PROPERTIES OF EXPECTATION


    7.1 Introduction


    7.2 Expectation of Sums of Random Variables


    7.3 Moments of the Number of Events that Occur


    7.4 Covariance, Variance of Sums, and Correlations


    7.5 Conditional Expectation


    7.6 Conditional Expectation and Prediction


    7.7 Moment Generating Functions


    7.8 Additional Properties of Normal Random Variables


    7.9 General Definition of Expectation


    Summary


    Problems


    Theoretical Exercises


    Self-Test Problems and Exercises


    8. LIMIT THEOREMS 394


    8.1 Introduction


    8.2 Chebyshev’s Inequality and the Weak Law of Large Numbers


    8.3 The Central Limit Theorem


    8.4 The Strong Law of Large Numbers


    8.5 Other Inequalities and a Poisson Limit Result


    8.6 Bounding the Error Probability When Approximating a Sum of Independent Bernoulli Random Variables by a Poisson Random Variable


    8.7 The Lorenz Curve


    Summary


    Problems


    Theoretical Exercises


    Self-Test Problems and Exercises


    9. ADDITIONAL TOPICS IN PROBABILITY


    9.1 The Poisson Process


    9.2 Markov Chains


    9.3 Surprise, Uncertainty, and Entropy


    9.4 Coding Theory and Entropy


    Summary


    Problems and Theoretical Exercises


    Self-Test Problems and Exercises


    10. SIMULATION


    10.1 Introduction


    10.2 General Techniques for Simulating Continuous Random Variables


    10.3 Simulating from Discrete Distributions


    10.4 Variance Reduction Techniques


    Summary


    Problems


    Self-Test Problems and Exercises


    Answers to Selected Problems


    Solutions to Self-Test Problems and Exercises


    Index

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