Probability & statistics with R for engineers and scientists / Michael Akritas, The Pennsylvania State University
- Author
- Akritas, Michael G.
- Additional Titles
- Probability and statistics with R for engineers and scientists
- Published
- Boston : Pearson, [2016]
- Edition
- First edition.
- Physical Description
- xi, 513 pages : illustrations ; 27 cm
- Contents
- Machine generated contents note: 1.1.Why Statistics? -- 1.2.Populations and Samples -- Exercises -- 1.3.Some Sampling Concepts -- 1.3.1.Representative Samples -- 1.3.2.Simple Random Sampling and Stratified Sampling -- 1.3.3.Sampling With and Without Replacement -- 1.3.4.Non-representative Sampling -- Exercises -- 1.4.Random Variables and Statistical Populations -- Exercises -- 1.5.Basic Graphics for Data Visualization -- 1.5.1.Histograms and Stem and Leaf Plots -- 1.5.2.Scatterplots -- 1.5.3.Pie Charts and Bar Graphs -- Exercises -- 1.6.Proportions, Averages, and Variances -- 1.6.1.Population Proportion and Sample Proportion -- 1.6.2.Population Average and Sample Average -- 1.6.3.Population Variance and Sample Variance -- Exercises -- 1.7.Medians, Percentiles, and Boxplots -- Exercises -- 1.8.Comparative Studies -- 1.8.1.Basic Concepts and Comparative Graphics -- 1.8.2.Lurking Variables and Simpson's Paradox -- 1.8.3.Causation: Experiments and Observational Studies -- 1.8.4.Factorial Experiments: Main Effects and Interactions -- Exercises -- 1.9.The Role of Probability -- 1.10.Approaches to Statistical Inference -- 2.1.Overview -- 2.2.Sample Spaces, Events, and Set Operations -- Exercises -- 2.3.Experiments with Equally Likely Outcomes -- 2.3.1.Definition and Interpretation of Probability -- 2.3.2.Counting Techniques -- 2.3.3.Probability Mass Functions and Simulations -- Exercises -- 2.4.Axioms and Properties of Probabilities -- Exercises -- 2.5.Conditional Probability -- 2.5.1.The Multiplication Rule and Tree Diagrams -- 2.5.2.Law of Total Probability and Bayes' Theorem -- Exercises -- 2.6.Independent Events -- 2.6.1.Applications to System Reliability -- Exercises -- 3.1.Introduction -- 3.2.Describing a Probability Distribution -- 3.2.1.Random Variables, Revisited -- 3.2.2.The Cumulative Distribution Function -- 3.2.3.The Density Function of a Continuous Distribution -- Exercises -- 3.3.Parameters of Probability Distributions -- 3.3.1.Expected Value -- 3.3.2.Variance and Standard Deviation -- 3.3.3.Population Percentiles -- Exercises -- 3.4.Models for Discrete Random Variables -- 3.4.1.The Bernoulli and Binomial Distributions -- 3.4.2.The Hypergeometric Distribution -- 3.4.3.The Geometric and Negative Binomial Distributions -- 3.4.4.The Poisson Distribution -- Exercises -- 3.5.Models for Continuous Random Variables -- 3.5.1.The Exponential Distribution -- 3.5.2.The Normal Distribution -- Exercises -- 4.1.Introduction -- 4.2.Describing Joint Probability Distributions -- 4.2.1.The Joint and Marginal PMF -- 4.2.2.The Joint and Marginal PDF -- Exercises -- 4.3.Conditional Distributions -- 4.3.1.Conditional Probability Mass Functions -- 4.3.2.Conditional Probability Density Functions -- 4.3.3.The Regression Function -- 4.3.4.Independence -- Exercises -- 4.4.Mean Value of Functions of Random Variables -- 4.4.1.The Basic Result -- 4.4.2.Expected Value of Sums -- 4.4.3.The Covariance and the Variance of Sums -- Exercises -- 4.5.Quantifying Dependence -- 4.5.1.Positive and Negative Dependence -- 4.5.2.Pearson's (or Linear) Correlation Coefficient -- Exercises -- 4.6.Models for Joint Distributions -- 4.6.1.Hierarchical Models -- 4.6.2.Regression Models -- 4.6.3.The Bivariate Normal Distribution -- 4.6.4.The Multinomial Distribution -- Exercises -- 5.1.Introduction -- 5.2.The LLN and the Consistency of Averages -- Exercises -- 5.3.Convolutions -- 5.3.1.What They Are and How They Are Used -- 5.3.2.The Distribution of X in the Normal Case -- Exercises -- 5.4.The Central Limit Theorem -- 5.4.1.The DeMoivre-Laplace Theorem -- Exercises -- 6.1.Introduction -- 6.2.Some Estimation Concepts -- 6.2.1.Unbiased Estimation -- 6.2.2.Model-Free vs Model-Based Estimation -- Exercises -- 6.3.Methods for Fitting Models to Data -- 6.3.1.The Method of Moments -- 6.3.2.The Method of Maximum Likelihood -- 6.3.3.The Method of Least Squares -- Exercises -- 6.4.Comparing Estimators: The MSE Criterion -- Exercises -- 7.1.Introduction to Confidence Intervals -- 7.1.1.Construction of Confidence Intervals -- 7.1.2.Z Confidence Intervals -- 7.1.3.The T Distribution and T Confidence Intervals -- 7.1.4.Outline of the Chapter -- 7.2.Cl Semantics: The Meaning of "Confidence" -- 7.3.Types of Confidence Intervals -- 7.3.1.T Cls for the Mean -- 7.3.2.Z Cls for Proportions -- 7.3.3.T Cls for the Regression Parameters -- 7.3.4.The Sign CI for the Median -- 7.3.5.x2 Cls for the Normal Variance and Standard Deviation -- Exercises -- 7.4.The Issue of Precision -- Exercises -- 7.5.Prediction Intervals -- 7.5.1.Basic Concepts -- 7.5.2.Prediction of a Normal Random Variable -- 7.5.3.Prediction in Normal Simple Linear Regression -- Exercises -- 8.1.Introduction -- 8.2.Setting Up a Test Procedure -- 8.2.1.The Null and Alternative Hypotheses -- 8.2.2.Test Statistics and Rejection Rules -- 8.2.3.Z Tests and T Tests -- 8.2.4.P-Values -- Exercises -- 8.3.Types of Tests -- 8.3.1.T Tests for the Mean -- 8.3.2.Z Tests for Proportions -- 8.3.3.T Tests about the Regression Parameters -- 8.3.4.The ANOVA F Test in Regression -- 8.3.5.The Sign Test for the Median -- 8.3.6.x2 Tests for a Normal Variance -- Exercises -- 8.4.Precision in Hypothesis Testing -- 8.4.1.Type I and Type II Errors -- 8.4.2.Power and Sample Size Calculations -- Exercises -- 9.1.Introduction -- 9.2.Two-Sample Tests and CIs for Means -- 9.2.1.Some Basic Results -- 9.2.2.Confidence Intervals -- 9.2.3.Hypothesis Testing -- Exercises -- 9.3.The Rank-Sum Test Procedure -- Exercises -- 9.4.Comparing Two Variances -- 9.4.1.Levene's Test -- 9.4.2.The F Test Under Normality -- Exercises -- 9.5.Paired Data -- 9.5.1.Definition and Examples of Paired Data -- 9.5.2.The Paired Data T Test -- 9.5.3.The Paired T Test for Proportions -- 9.5.4.The Wilcoxon Signed-Rank Test -- Exercises -- 10.1.Introduction -- 10.2.Types of k-Sample Tests -- 10.2.1.The ANOVA F Test for Means -- 10.2.2.The Kruskal-Wallis Test -- 10.2.3.The Chi-Square Test for Proportions -- Exercises -- 10.3.Simultaneous Cls and Multiple Comparisons -- 10.3.1.Bonferroni Multiple Comparisons and Simultaneous Cls -- 10.3.2.Tukey's Multiple Comparisons and Simultaneous Cls -- 10.3.3.Tukey's Multiple Comparisons on the Ranks -- Exercises -- 10.4.Randomized Block Designs -- 10.4.1.The Statistical Model and Hypothesis -- 10.4.2.The ANOVA F Test -- 10.4.3.Friedman's Test and F Test on the Ranks -- 10.4.4.Multiple Comparisons -- Exercises -- 11.1.Introduction -- 11.2.Two-Factor Designs -- 11.2.1.F Tests for Main Effects and Interactions -- 11.2.2.Testing the Validity of Assumptions -- 11.2.3.One Observation per Cell -- Exercises -- 11.3.Three-Factor Designs -- Exercises -- 11.4.2r Factorial Experiments -- 11.4.1.Blocking and Confounding -- 11.4.2.Fractional Factorial Designs -- Exercises -- 12.1.Introduction -- 12.2.The Multiple Linear Regression Model -- Exercises -- 12.3.Estimation, Testing, and Prediction -- 12.3.1.The Least Squares Estimators -- 12.3.2.Model Utility Test -- 12.3.3.Testing the Significance of Regression Coefficients -- 12.3.4.Confidence Intervals and Prediction -- Exercises -- 12.4.Additional Topics -- 12.4.1.Weighted Least Squares -- 12.4.2.Applications to Factorial Designs -- 12.4.3.Variable Selection -- 12.4.4.Influential Observations -- 12.4.5.Multicollinearity -- 12.4.6.Logistic Regression -- Exercises -- 13.1.Introduction and Overview -- 13.2.The X Chart -- 13.2.1.X Chart with Known Target Values -- 13.2.2.TC Chart with Estimated Target Values -- 13.2.3.The X Chart -- 13.2.4.Average Run Length and Supplemental Rules -- Exercises -- 13.3.The S and R Charts -- Exercises -- 13.4.The p and c Charts -- 13.4.1.The p Chart -- 13.4.2.The c Chart -- Exercises -- 13.5.CUSUM and EWMA Charts -- 13.5.1.The CUSUM Chart -- 13.5.2.The EWMA Chart -- Exercises -- A.Tables -- B.Answers To Selected Exercises.
- Subject(s)
- ISBN
- 9780321852991
0321852990 - Note
- Includes index.
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