Probability and statistics
著者
書誌事項
Probability and statistics
Addison-Wesley, c2002
3rd ed
- : international ed
大学図書館所蔵 全42件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Includes bibliographical references (p. 801-806) and index
内容説明・目次
内容説明
Probability & Statistics was written for a one or two semester probability and statistics course offered primarily at four-year institutions and taken mostly by sophomore and junior level students, majoring in mathematics or statistics. Calculus is a prerequisite, and a familiarity with the concepts and elementary properties of vectors and matrices is a plus. The revision of this well-respected text presents a balanced approach of the classical and Bayesian methods and now includes a new chapter on simulation (including Markov chain Monte Carlo and the Bootstrap), expanded coverage of residual analysis in linear models, and more examples using real data.
目次
1. Introduction to Probability.
The History of Probability.
Interpretations of Probability.
Experiments and Events.
Set Theory.
The Definition of Probability.
Finite Sample Spaces.
Counting Methods.
Combinatorial Methods.
Multinomial Coefficients.
The Probability of a Union of Events.
Statistical Swindles.
Supplementary Exercises.
2. Conditional Probability.
The Definition of Conditional Probability.
Independent Events.
Bayes' Theorem.
Markov Chains.
The Gambler's Ruin Problem.
Supplementary Exercises.
3. Random Variables and Distribution.
Random Variables and Discrete Distributions.
Continuous Distributions.
The Distribution Function.
Bivariate Distributions.
Marginal Distributions.
Conditional Distributions.
Multivariate Distributions.
Functions of a Random Variable.
Functions of Two or More Random Variables.
Supplementary Exercises.
4. Expectation.
The Expectation of a Random Variable.
Properties of Expectations.
Variance.
Moments.
The Mean and The Median.
Covariance and Correlation.
Conditional Expectation.
The Sample Mean.
Utility.
Supplementary Exercises.
5. Special Distributions.
Introduction.
The Bernoulli and Binomial Distributions.
The Hypergeometric Distribution.
The Poisson Distribution.
The Negative Binomial Distribution.
The Normal Distribution.
The Central Limit Theorem.
The Correction for Continuity.
The Gamma Distribution.
The Beta Distribution.
The Multinomial Distribution.
The Bivariate Normal Distribution.
Supplementary Exercises.
6. Estimation.
Statistical Inference.
Prior and Posterior Distributions.
Conjugate Prior Distributions.
Bayes Estimators.
Maximum Likelihood Estimators.
Properties of Maximum Likelihood Estimators.
Sufficient Statistics.
Jointly Sufficient Statistics.
Improving an Estimator.
Supplementary Exercises.
7. Sampling Distributions of Estimators.
The Sampling Distribution of a Statistic.
The Chi-Square Distribution.
Joint Distribution of the Sample Mean and Sample Variance.
The t Distribution.
Confidence Intervals.
Bayesian Analysis of Samples from a Normal Distribution.
Unbiased Estimators.
Fisher Information.
Supplementary Exercises.
8. Testing Hypotheses.
Problems of Testing Hypotheses.
Testing Simple Hypotheses.
Uniformly Most Powerful Tests.
Two-Sided Alternatives.
The t Test.
Comparing the Means of Two Normal Distributions.
The F Distribution.
Bayes Test Procedures.
Foundational Issues.
Supplementary Exercises.
9. Categorical Data and Nonparametric Methods.
Tests of Goodness-of-Fit.
Goodness-of-Fit for Composite Hypotheses.
Contingency Tables.
Tests of Homogeneit.
Simpson's Paradox.
Kolmogorov-Smirnov Test.
Robust Estimation.
Sign and Rank Tests.
Supplementary Exercises.
10. Linear Statistical Models.
The Method of Least Squares.
Regression.
Statistical Inference in Simple Linear Regression.
Bayesian Inference in Simple Linear Regression.
The General Linear Model and Multiple Regression.
Analysis of Variance.
The Two-Way Layout.
The Two-Way Layout with Replications.
Supplementary Exercises.
11. Simulation.
Why is Simulation Useful?
Simulating Specific Distributions.
Importance Sampling.
Markov Chain Monte Carlo.
The Bootstrap.
Supplementary Exercises.
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