Introduction to probability and statistics
Subtitle: principles and applications for engineering and the computing sciences
By: J.S. Milton, Jesse C. Arnold.
Contributors: Arnold, Jesse C.
Edition: 3rd ed.
Series: Schaum's solved problems series
Publisher: McGraw-Hill; McGraw-Hill Companies
Published: 1995
Place of publication: New York
Language: eng
Number of pages: 811
Subjects: Engineering mathematics; Computer science -- Mathematics; Probabilities; Statistics
Notes: Includes bibliographical references (p. 716-717) and index.
Table of contents: label: Preface
title: Preface
pagenum: xvi; label: Chapter 1
title: Introduction to Probability and Counting
pagenum: 1; label: 1.1
title: Interpreting Probabilities
pagenum: 3; label: 1.2
title: Sample Spaces and Events
pagenum: 5; label: 1.3
title: Permutations and Combinations
pagenum: 9; title: Counting Permutations
pagenum: 10; title: Counting Combinations
pagenum: 14; title: Permutations of Indistinguishable Objects
pagenum: 15; title: Chapter Summary
pagenum: 16; title: Exercises
pagenum: 16; title: Review Exercises
pagenum: 22; label: Chapter 2
title: Some Probability Laws
pagenum: 24; label: 2.1
title: Axioms of Probability
pagenum: 24; label: 2.2
title: Conditional Probability
pagenum: 28; label: 2.3
title: Independence and the Multiplication Rule
pagenum: 29; title: The Multiplication Rule
pagenum: 34; label: 2.4
title: Bayes' Theorem
pagenum: 35; title: Chapter Summary
pagenum: 37; title: Exercises
pagenum: 37; title: Review Exercises
pagenum: 42; label: Chapter 3
title: Discrete Distributions
pagenum: 44; label: 3.1
title: Random Variables
pagenum: 44; label: 3.2
title: Discrete Probability Densities
pagenum: 45; title: Cumulative Distribution
pagenum: 48; label: 3.3
title: Expectation and Distribution Parameters
pagenum: 50; title: Variance and Standard Deviation
pagenum: 53; label: 3.4
title: Moment Generating Function and the Geometric Distribution
pagenum: 57; title: Geometric Distribution
pagenum: 57; title: Moment Generating Function
pagenum: 60; title: Forgetfulness Property: Geometric
pagenum: 64; label: 3.5
title: Binomial Distribution
pagenum: 65; label: 3.6
title: Negative Binomial Distribution
pagenum: 69; label: 3.7
title: Hypergeometric Distribution
pagenum: 71; label: 3.8
title: Poisson Distribution
pagenum: 75; title: Poisson Approximation to the Binomial Distribution
pagenum: 77; label: 3.9
title: Simulating a Discrete Distribution
pagenum: 80; title: Chapter Summary
pagenum: 82; title: Exercises
pagenum: 83; title: Review Exercises
pagenum: 96; label: Chapter 4
title: Continuous Distributions
pagenum: 99; label: 4.1
title: Continuous Densities
pagenum: 99; title: Cumulative Distribution
pagenum: 103; title: Uniform Distribution
pagenum: 105; label: 4.2
title: Expectation and Distribution Parameters
pagenum: 105; label: 4.3
title: Gamma Distribution
pagenum: 108; title: Gamma Distribution (continued)
pagenum: 110; title: Exponential Distribution
pagenum: 111; title: Forgetfulness Property: Exponential
pagenum: 113; title: Chi-Squared Distribution
pagenum: 113; label: 4.4
title: Normal Distribution
pagenum: 114; title: Standard Normal Distribution
pagenum: 117; label: 4.5
title: Normal Probability Rule and Chebyshev's Inequality
pagenum: 120; label: 4.6
title: Normal Approximations
pagenum: 123; label: 4.7
title: Weibull Distribution and Reliability
pagenum: 125; title: Reliability
pagenum: 127; title: Reliability of Series and Parallel Systems
pagenum: 130; label: 4.8
title: Transformation of Variables
pagenum: 132; label: 4.9
title: Simulating a Continuous Distribution
pagenum: 135; title: Chapter Summary
pagenum: 136; title: Exercises
pagenum: 139; title: Review Exercises
pagenum: 153; label: Chapter 5
title: Joint Distribution
pagenum: 156; label: 5.1
title: Joint Densities and Independence
pagenum: 156; title: Marginal Distributions: Discrete
pagenum: 158; title: Joint and Marginal Distributions: Continuous
pagenum: 159; title: Independence
pagenum: 163; label: 5.2
title: Expectation and Covariance
pagenum: 164; title: Covariance
pagenum: 166; label: 5.3
title: Correlation
pagenum: 168; label: 5.4
title: Conditional Densities and Regression
pagenum: 172; title: Curves of Regression
pagenum: 174; label: 5.5
title: Transformation of Variables
pagenum: 176; title: Chapter Summary
pagenum: 180; title: Exercises
pagenum: 181; title: Review Exercises
pagenum: 188; label: Chapter 6
title: Descriptive Statistics
pagenum: 190; label: 6.1
title: Random Sampling
pagenum: 190; label: 6.2
title: Picturing the Distribution
pagenum: 193; title: Stem-and-Leaf Charts
pagenum: 194; title: Histograms and Ogives
pagenum: 195; title: Rules for Breaking Data into Categories
pagenum: 195; label: 6.3
title: Sample Statistics
pagenum: 200; title: Location Statistics
pagenum: 200; title: Measures of Variability
pagenum: 202; label: 6.4
title: Boxplots
pagenum: 204; title: Chapter Summary
pagenum: 209; title: Exercises
pagenum: 210; title: Review Exercises
pagenum: 218; title: Computing Supplement: SAS
pagenum: 220; label: I
title: Summary Statistics and Histograms
pagenum: 220; label: Chapter 7
title: Estimation
pagenum: 226; label: 7.1
title: Point Estimation
pagenum: 226; label: 7.2
title: The Method of Moments and Maximum Likelihood
pagenum: 229; title: Maximum Likelihood Estimators
pagenum: 231; label: 7.3
title: Functions of Random Variables — Distribution of X
pagenum: 234; title: Distribution of X
pagenum: 236; label: 7.4
title: Interval Estimation and the Central Limit Theorem
pagenum: 237; title: Confidence Interval on the Mean: Variance Known
pagenum: 238; title: Central Limit Theorem
pagenum: 241; title: Chapter Summary
pagenum: 242; title: Exercises
pagenum: 243; title: Review Exercises
pagenum: 253; label: Chapter 8
title: Inferences on the Mean and Variance of a Distribution
pagenum: 257; label: 8.1
title: Interval Estimation of Variability
pagenum: 258; label: 8.2
title: Estimating the Mean and the Student-t Distribution
pagenum: 261; title: The T Distribution
pagenum: 262; title: Confidence Interval on the Mean: Variance Estimated
pagenum: 265; label: 8.3
title: Hypothesis Testing
pagenum: 267; label: 8.4
title: Significance Testing
pagenum: 271; label: 8.5
title: Hypothesis and Significance Tests on the Mean
pagenum: 273; label: 8.6
title: Testing for Normality and Hypothesis Tests on the Variance
pagenum: 278; title: Testing for Normality
pagenum: 278; title: Testing Hypotheses on the Variance
pagenum: 281; label: 8.7
title: Alternative Nonparametric Methods
pagenum: 282; title: Sign Test for Median
pagenum: 283; title: Wilcoxon Signed-Rank Test
pagenum: 285; title: Chapter Summary
pagenum: 288; title: Exercises
pagenum: 289; title: Review Exercises
pagenum: 308; title: Computing Supplement
pagenum: 512; label: II
title: One Sample T Tests and Confidence Intervals
pagenum: 312; label: III
title: Testing for Normality
pagenum: 313; label: Chapter 9
title: Inference on Proportions
pagenum: 316; label: 9.1
title: Estimating Proportions
pagenum: 316; title: Confidence Interval on p
pagenum: 317; title: Sample Size for Estimating p
pagenum: 320; label: 9.2
title: Testing Hypotheses on a Proportion
pagenum: 321; label: 9.3
title: Comparing Two Proportions: Estimation
pagenum: 323; title: Confidence Interval on p1 - p2
pagenum: 324; label: 9.4
title: Comparing Two Proportions: Hypothesis Testing
pagenum: 326; title: Pooled Proportions
pagenum: 328; title: Chapter Summary
pagenum: 330; title: Exercises
pagenum: 330; title: Review Exercises
pagenum: 337; label: Chapter 10
title: Comparing Two Means and Two Variances
pagenum: 340; label: 10.1
title: Point Estimation: Independent Samples
pagenum: 340; label: 10.2
title: Comparing Variances: The F Distribution
pagenum: 342; label: 10.3
title: Comparing Means: Variances Equal (Pooled Test)
pagenum: 346; title: Confidence Interval on μ1 - μ2: Pooled
pagenum: 347; title: Pooled T Test
pagenum: 350; label: 10.4
title: Comparing Means: Variances Unequal
pagenum: 351; label: 10.5
title: Comparing Means: Paired Data
pagenum: 353; title: Paired T Test
pagenum: 354; label: 10.6
title: Alternative Nonparametric Methods
pagenum: 355; title: Wilcoxon Rank-Sum Test
pagenum: 356; title: Wilcoxon Signed-Rank Test for Paired Observations
pagenum: 358; title: Chapter Summary
pagenum: 360; title: Exercises
pagenum: 360; title: Review Exercises
pagenum: 375; title: Computing Supplement
pagenum: 379; label: IV
title: Comparing Means and Variances
pagenum: 379; label: V
title: Paired T Test
pagenum: 380; label: Chapter 11
title: Simple Linear Regression and Correlation
pagenum: 382; label: 11.1
title: Model and Parameter Estimation
pagenum: 384; title: Description of the Model
pagenum: 384; title: Least-Squares Estimation
pagenum: 386; label: 11.2
title: Properties of Least-Squares Estimators
pagenum: 391; title: Distribution of β1
pagenum: 393; title: Distribution of β0
pagenum: 395; title: Estimator of σ²
pagenum: 397; title: Summary of Theoretical Results
pagenum: 398; label: 11.3
title: Confidence Interval Estimation and Hypothesis Testing
pagenum: 399; title: Inferences about Slope
pagenum: 399; title: Inferences about Intercept
pagenum: 403; title: Inferences about Estimated Mean
pagenum: 404; title: Inferences about Single Predicted Value
pagenum: 406; label: 11.4
title: Repeated Measures and Lack of Fit
pagenum: 411; label: 11.5
title: Residual Analysis
pagenum: 414; title: Residual Plots
pagenum: 414; title: Checking for Normality: Stem-and-Leaf and Boxplots
pagenum: 418; label: 11.6
title: Correlation
pagenum: 425; title: Interval Estimation and Hypothesis Tests on ρ
pagenum: 429; title: Coefficient of Determination
pagenum: 432; title: Chapter Summary
pagenum: 434; title: Exercises
pagenum: 434; title: Review Exercises
pagenum: 445; title: Computing Supplement
pagenum: 448; label: VI
title: Scattergrams, Estimation of β0 and β1, and the Use of the Regression Line for Predictions
pagenum: 448; label: VII
title: Testing H0: β1 = 0
pagenum: 452; label: VIII
title: Confidence Intervals on β0, β1, μYx, Yx
pagenum: 452; label: IX
title: Testing for Lack of Fit
pagenum: 455; label: X
title: Residual Plots
pagenum: 456; label: XI
title: Correlation
pagenum: 460; label: Chapter 12
title: Multiple Linear Regression Models
pagenum: 462; label: 12.1
title: Least-Squares Procedures for Model Fitting
pagenum: 462; title: Polynomial Model of Degree p
pagenum: 463; title: Multiple Linear Regression Model
pagenum: 467; label: 12.2
title: A Matrix Approach to Least Squares
pagenum: 470; title: The Normal Equations
pagenum: 473; title: Solving the Normal Equations
pagenum: 475; title: Simple Linear Regression: Matrix Formulation
pagenum: 477; title: Polynomial Model: Matrix Formulation
pagenum: 479; label: 12.3
title: Properties of the Least-Squares Estimators
pagenum: 481; title: Expected Value of β̂
pagenum: 483; title: Estimation of σ² and Variance of β̂
pagenum: 483; label: 12.4
title: Interval Estimation
pagenum: 488; title: Confidence Interval on Coefficients
pagenum: 488; title: Confidence Interval on Estimated Mean
pagenum: 489; title: Prediction Interval on a Single Predicted Response
pagenum: 491; label: 12.5
title: Testing Hypotheses about Model Parameters
pagenum: 492; title: Testing a Single Predictor Variable
pagenum: 492; title: Testing for Significant Regression
pagenum: 493; title: Testing a Subset of Predictor Variables
pagenum: 495; label: 12.6
title: Use of Indicator or "Dummy" Variables
pagenum: 497; label: 12.7
title: Criteria for Variable Selection
pagenum: 501; title: Forward Selection Method
pagenum: 502; title: Backward Elimination Procedure
pagenum: 503; title: Stepwise Method
pagenum: 504; title: Maximum R² Method
pagenum: 506; title: Mallows Ck Statistic
pagenum: 506; title: PRESS Statistic
pagenum: 506; label: 12.8
title: Model Transformation and Concluding Remarks
pagenum: 512; title: Chapter Summary
pagenum: 516; title: Exercises
pagenum: 517; title: Review Exercises
pagenum: 528; title: Computing Supplement
pagenum: 530; label: XII
title: Multiple Regression
pagenum: 530; label: XIII
title: Polynomial Regression
pagenum: 531; label: Chapter 13
title: Analysis of Variance
pagenum: 535; label: 13.1
title: One-Way Classification Fixed-Effects Model
pagenum: 536; title: The Model
pagenum: 539; title: Testing H0
pagenum: 541; label: 13.2
title: Comparing Variances
pagenum: 547; label: 13.3
title: Pairwise Comparisons
pagenum: 549; title: Bonferroni T Tests
pagenum: 550; title: Duncan's Multiple Range Test
pagenum: 552; label: 13.4
title: Testing Contrasts
pagenum: 555; label: 13.5
title: Randomized Complete Block Design
pagenum: 559; title: The Model
pagenum: 561; title: Testing H0
pagenum: 565; title: Effectiveness of Blocking
pagenum: 565; title: Paired Comparisons
pagenum: 568; label: 13.6
title: Latin Squares
pagenum: 569; label: 13.7
title: Random-Effects Model
pagenum: 573; title: One-Way Classification
pagenum: 573; label: 13.8
title: Design Models in Matrix Form
pagenum: 576; label: 13.9
title: Alternative Nonparametric Methods
pagenum: 580; title: Kruskal-Wallis Test
pagenum: 580; title: Friedman Test
pagenum: 582; title: Chapter Summary
pagenum: 583; title: Exercises
pagenum: 584; title: Review Exercises
pagenum: 596; title: Computing Supplement
pagenum: 599; label: XIV
title: One-Way Classification with Multiple Comparisons
pagenum: 599; label: XV
title: Randomized Complete Blocks with Multiple Comparisons
pagenum: 601; label: Chapter 14
title: Factorial Experiments
pagenum: 604; label: 14.1
title: Two-Factor Analysis of Variance
pagenum: 606; title: Testing H0
pagenum: 608; title: Paired Comparisons
pagenum: 612; title: Sample Size
pagenum: 616; label: 14.2
title: Extension to Three Factors
pagenum: 616; label: 14.3
title: Random and Mixed Model Factorial Experiments
pagenum: 616; title: Random-Effects Model
pagenum: 617; title: Mixed-Effects Model
pagenum: 620; label: 14.4
title: 2k Factorial Experiments
pagenum: 620; title: Computational Techniques — Yates Method
pagenum: 629; label: 14.5
title: 2k Factorial Experiments in an Incomplete Block Design
pagenum: 631; label: 14.6
title: Fractional Factorial Experiments
pagenum: 634; title: Exercises
pagenum: 648; title: Review Exercises
pagenum: 648; title: Computing Supplement
pagenum: 650; label: XVI
title: Two-Way Classification with Multiple Comparisons
pagenum: 650; label: XVII
title: 2k Factorial Experiments
pagenum: 654; label: Chapter 15
title: Categorical Data
pagenum: 656; label: 15.1
title: Multinomial Distribution
pagenum: 656; label: 15.2
title: Chi-Squared Goodness of Fit Tests
pagenum: 658; label: 15.3
title: Testing for Independence
pagenum: 660; title: r × c Test for Independence
pagenum: 665; label: 15.4
title: Comparing Proportions
pagenum: 667; title: r × c Test for Homogeneity
pagenum: 670; title: Comparing Proportions with Paired Data: McNemar's Test
pagenum: 672; title: Chapter Summary
pagenum: 673; title: Exercises
pagenum: 674; title: Review Exercises
pagenum: 680; label: Chapter 16
title: Statistical Quality Control
pagenum: 683; label: 16.1
title: Properties of Control Charts
pagenum: 684; title: Monitoring Means
pagenum: 685; title: Distribution of Run Lengths
pagenum: 686; label: 16.2
title: Shewhart Control Charts for Measurements
pagenum: 689; title: X Chart (Mean)
pagenum: 690; title: R Chart (Range)
pagenum: 693; label: 16.3
title: Shewhart Control Charts for Attributes
pagenum: 696; title: P Chart (Proportion Defective)
pagenum: 697; title: C Charts (Average Number of Defects)
pagenum: 700; label: 16.4
title: Acceptance Sampling
pagenum: 702; label: 16.5
title: Two-Stage Acceptance Sampling
pagenum: 706; label: 16.6
title: Extensions in Quality Control
pagenum: 709; title: Modifications of Control Charts
pagenum: 709; title: Parameter Design Procedures
pagenum: 710; title: Exercises
pagenum: 711; label: Appendix A
title: Statistical Tables
pagenum: 719; label: Appendix B
title: Answers to Selected Problems
pagenum: 764; title: Index
pagenum: 807