Probability
著者
書誌事項
Probability
（Springer texts in statistics）
Springer-Verlag, c1993
- : us
- : gw
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注記
Includes index
内容説明・目次
- 巻冊次
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: us ISBN 9780387979748
内容説明
This is a text for a one-quarter or one-semester course in probability, aimed at students who have done a year of calculus. The book is organised so a student can learn the fundamental ideas of probability from the first three chapters without reliance on calculus. Later chapters develop these ideas further using calculus tools. The book contains more than the usual number of examples worked out in detail.
The most valuable thing for students to learn from a course like this is how to pick up a probability problem in a new setting and relate it to the standard body of theory. The more they see this happen in class, and the more they do it themselves in exercises, the better. The style of the text is deliberately informal. My experience is that students learn more from intuitive explanations, diagrams, and examples than they do from theorems and proofs. So the emphasis is on problem solving rather than theory.
目次
1 Introduction.- 1.1 Equally Likely Outcomes.- 1.2 Interpretations.- 1.3 Distributions.- 1.4 Conditional Probability and Independence.- 1.5 Bayes' Rule.- 1.6 Sequences of Events.- Summary.- Review Exercises.- 2 Repeated Trials and Sampling.- 2.1 The Binomial Distribution.- 2.2 Normal Approximation: Method.- 2.3 Normal Approximation: Derivation (Optional).- 2.4 Poisson Approximation.- 2.5 Random Sampling.- Summary.- Review Exercises.- 3 Random Variables.- 3.1 Introduction.- 3.2 Expectation.- 3.3 Standard Deviation and Normal Approximation.- 3.4 Discrete Distributions.- 3.5 The Poisson Distribution.- 3.6 Symmetry (Optional).- Summary.- Review Exercises.- 4 Continuous Distributions.- 4.1 Probability Densities.- 4.2 Exponential and Gamma Distributions.- 4.3 Hazard Rates (Optional).- 4.4 Change of Variable.- 4.5 Cumulative Distribution Functions.- 4.6 Order Statistics (Optional).- Summary.- Review Exercises.- 5 Continuous Joint Distributions.- 5.1 Uniform Distributions.- 5.2 Densities.- 5.3 Independent Normal Variables.- 5.4 Operations (Optional).- Summary.- Review Exercises.- 6 Dependence.- 6.1 Conditional Distributions: Discrete Case.- 6.2 Conditional Expectation: Discrete Case.- 6.3 Conditioning: Density Case.- 6.4 Covariance and Correlation.- 6.5 Bivariate Normal.- Summary.- Review Exercises.- Distribution Summaries.- Discrete.- Continuous.- Beta.- Binomial.- Exponential.- Gamma.- Geometric and Negative Binomial.- Hypergeometrie.- Normal.- Poisson.- Uniform.- Examinations.- Solutions to Examinations.- Appendices.- 1 Counting.- 2 Sums.- 3 Calculus.- 4 Exponents and Logarithms.- 5 Normal Table.- Brief Solutions to Odd-Numbered Exercises.
- 巻冊次
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: gw ISBN 9783540979746
内容説明
This textbook provides an elementary introduction to the theory of probability which will be suitable for undergraduates. Its style is deliberately informal and places its emphasis on presenting examples together with intuitive explanations, diagrams and discussion. Prerequisites are minimal in that the first four chapters may be read without reliance on calculus whilst later chapters use only some basic tools from calculus. The first chapter covers the basic definitions of outcomes, discrete distributions, and the laws of additive and multiplicative probabilities. Chapters 2 and 3 cover further material on discrete distributions, countable additivity, random variables, and introduces the binomial and other basic discrete distributions. Chapters 4 and 5 introduce continuous distributions whilst the text concludes with discussion of conditional probabilities and expectations.
目次
Introduction.- Repeated Trials and Sampling.- Random Variables.- Continuous Distributions.- Continuous Joint Distributions.- Dependence.- Distribution Summaries.- Examinations.- Appendices.- Brief Solutions to Odd-Numbered Exercises.- Index.
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