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Introduction and Data Description 1 (27)
The Field of Probability and Statistics 1 (3)
Graphical Presentation of Data 4 (4)
Measurement Data: the Frequency 4 (3)
Distribution and Histogram
Count Data: the Pareto Chart 7 (1)
Numerical Description of Data 8 (10)
Measures of Central Tendency 9 (2)
Measures of Dispersion 11 (4)
Grouped Data 15 (3)
Exploratory Data Analysis 18 (3)
The Stem and Leaf Plot 18 (2)
The Box Plot 20 (1)
Summary 21 (1)
Exercises 22 (6)
An Introduction to Probability 28 (35)
Introduction 28 (1)
A Review of Sets 29 (4)
Experiments and Sample Spaces 33 (3)
Events 36 (1)
Probability Definitions and Assignment 37 (5)
Finite Sample Spaces and Enumeration 42 (5)
Tree Diagram 43 (1)
Multiplication Principle 43 (1)
Permutations 44 (1)
Combinations 45 (2)
Permutations of Like Objects 47 (1)
Conditional Probability 47 (7)
Partitions, Total Probability, and Bayes' 54 (2)
Theorem
Summary 56 (1)
Exercises 57 (6)
One-Dimension Random Variables 63 (23)
Introduction 63 (4)
The Distribution Function 67 (2)
Discrete Random Variables 69 (4)
Continuous Random Variables 73 (2)
Some Characteristics of Distributions 75 (5)
Chebyshev's Inequality 80 (2)
Summary 82 (1)
Exercises 82 (4)
Functions of One Random Variable and 86 (22)
Expectation
Introduction 86 (1)
Equivalent Events 86 (2)
Functions of a Discrete Random Variable 88 (2)
Continuous Functions of a Continuous Random 90 (3)
Variable
Expectation 93 (4)
Approximations to E(H(X)) and V(H(X)) 97 (2)
The Moment-Generating Function 99 (3)
Summary 102(1)
Exercises 103(5)
Joint Probability Distributions 108(43)
Introduction 108(1)
Joint Distributions for Two-Dimensional 109(4)
Random Variables
Marginal Distributions 113(5)
Conditional Distributions 118(5)
Conditional Expectation 123(2)
Regression of the Mean 125(2)
Independence of Random Variables 127(1)
Covariance and Correlation 128(3)
The Distribution Function for 131(2)
Two-Dimensional Random Variables
Functions of Two Random Variables 133(3)
Joint Distributions of Dimension n > 2 136(2)
Linear Combinations 138(4)
Moment Generating Functions and Linear 142(1)
Combinations
The Law of Large Numbers 142(2)
Summary 144(1)
Exercises 145(6)
Some Important Discrete Distributions 151(25)
Introduction 151(1)
Bernoulli Trials and the Bernoulli 151(3)
Distribution
The Binomial Distribution 154(5)
Mean and Variance of the Binomial 154(2)
Distribution
The Cumulative Binomial Distribution 156(1)
An Application of the Binomial 156(3)
Distribution
The Geometric Distribution 159(2)
Mean and Variance of the Geometric 159(2)
Distribution
The Pascal Distribution 161(1)
Mean and Variance of the Pascal 162(1)
Distribution
The Multinomial Distribution 162(1)
The Hypergeometric Distribution 163(2)
Mean and Variance of the Hypergeometric 164(1)
Distribution
The Poisson Distribution 165(4)
Development from a Poisson Process 165(1)
Development of the Poisson Distribution 166(1)
from the Binomial
Mean and Variance of the Poisson 167(2)
Distribution
Some Approximations 169(1)
Generation of Realizations 170(1)
Summary 170(2)
Exercises 172(4)
Some Important Continuous Distributions 176(18)
Introduction 176(1)
The Uniform Distribution 176(3)
Mean and Variance of the Uniform 177(2)
Distribution
The Exponential Distribution 179(4)
The Relationship of the Exponential 179(1)
Distribution to the Poisson Distribution
Mean and Variance of the Exponential 180(3)
Distribution
Memoryless Property of the Exponential 183(1)
Distribution
The Gamma Distribution 183(4)
The Gamma Function 183(1)
Definition of the Gamma Distribution 184(1)
Relationship Between the Gamma 184(1)
Distribution and the Exponential
Distribution
Mean and Variance of the Gamma 185(2)
Distribution
The Weibull Distribution 187(1)
Mean and Variance of the Weibull 187(1)
Distribution
Generation of Realizations 188(1)
Summary 189(2)
Exercises 191(3)
The Normal Distribution 194(34)
Introduction 194(1)
The Normal Distribution 194(8)
Properties of the Normal Distribution 195(1)
Mean and Variance of the Normal 196(1)
Distribution
The Cumulative Normal Distribution 197(1)
The Standard Normal Distribution 197(1)
Problem-Solving Procedure 198(4)
The Reproductive Property of the Normal 202(3)
Distribution
The Central Limit Theorem 205(4)
The Normal Approximation to the Binomial 209(3)
Distribution
The Lognormal Distribution 212(4)
Density Function 212(1)
Mean and Variance of the Lognormal 213(1)
Distribution
Other Moments 214(1)
Properties of the Lognormal Distribution 214(2)
The Bivariate Normal Distribution 216(5)
Generations of Normal Realizations 221(1)
Summary 222(1)
Exercises 222(6)
Random Samples and Sampling Distributions 228(16)
Random Samples 228(1)
Statistics and Sampling Distributions 229(2)
The Chi-Square Distribution 231(3)
The t Distribution 234(4)
The F Distribution 238(3)
Summary 241(1)
Exercises 241(3)
Parameter Estimation 244(44)
Point Estimation 244(11)
Properties of Estimators 245(5)
The Method of Maximum Likelihood 250(3)
The Method of Moments 253(1)
Precision of Estimation: the Standard 254(1)
Error
Confidence Interval Estimation 255(23)
Confidence Interval on the Mean, Variance 257(3)
Known
Confidence Interval on the Difference in 260(2)
Two Means, Variance Known
Confidence Interval on the Mean of a 262(3)
Normal Distribution, Variance Unknown
Confidence Interval on the Difference in 265(3)
Means of Two Normal Distributions,
Variances Unknown
Confidence Interval on 1-2 for Paired 268(1)
Observations
Confidence Interval on the Variance of a 269(2)
Normal Distribution
Confidence Interval on the Ratio of 271(2)
Variances of Two Normal Distributions
Confidence Interval on a Proportion 273(2)
Confidence Interval on the Difference in 275(1)
Two Proportions
Approximate Confidence Intervals in 276(1)
Maximum Likelihood Estimation
Simultaneous Confidence Intervals 277(1)
Summary 278(3)
Exercises 281(7)
Tests of Hypotheses 288(65)
Introduction 288(6)
Statistical Hypotheses 288(1)
Type I and Type II Errors 289(3)
One-Sided and Two-Sided Hypotheses 292(2)
Tests of Hypotheses on the Mean, Variance 294(7)
Known
Statistical Analysis 294(2)
Choice of Sample Size 296(4)
The Relationship Between Tests of 300(1)
Hypotheses and Confidence
Large Sample Test with Unknown Variance 300(1)
P-Values 300(1)
Tests of Hypotheses on the Equality of Two 301(3)
Means, Variances Known
Statistical Analysis 301(2)
Choice of Sample Size 303(1)
Tests of Hypotheses on the Mean of a Normal 304(4)
Distribution, Variance Unknown
Statistical Analysis 305(1)
Choice of Sample Size 306(2)
Tests of Hypotheses on the Means of Two 308(4)
Normal Distributions, Variances Unknown
Case 1: σ21 = σ22 308(2)
Case 2: σ21 = σ22 310(1)
Choice of Sample Size 311(1)
The Paired t-Test 312(3)
Tests of Hypotheses on the Variance 315(3)
Test Procedures for a Normal Population 315(1)
Choice of Sample Size 316(1)
A Large-Sample Test Procedure 317(1)
Tests for the Equality of Two Variances 318(3)
Test Procedure for Normal Populations 318(2)
Choice of Sample Size 320(1)
A Large-Sample Test Procedure 320(1)
Tests of Hypotheses on a Proportion 321(2)
Statistical Analysis 321(1)
Choice of Sample Size 322(1)
Tests of Hypotheses on Two Proportions 323(4)
A Large-Sample Test for H0: p1 = p2 323(1)
Choice of Sample Size 324(1)
A Small Sample Test for H0: p1 = p2 325(2)
Testing for Goodness of Fit 327(8)
The Chi-Square Goodness-of-Fit Test 327(4)
Probability Plotting 331(2)
Selecting the Form of a Distribution 333(2)
Contingency Table Tests 335(5)
Summary 340(1)
Exercises 340(13)
Design and Analysis of Single-Factor 353(37)
Experiments: the Analysis of Variance
The Completely Randomized Single-Factor 353(13)
Experiment
An Example 353(1)
The Analysis of Variance 354(7)
Estimation of the Model Parameters 361(2)
Residual Analysis and Model Checking 363(2)
An Unbalanced Design 365(1)
Tests on Individual Treatment Means 366(5)
Orthogonal Contrasts 366(3)
Duncan's Multiple Range Test 369(2)
The Random Effects Model 371(4)
The Randomized Block Design 375(7)
Design and Statistical Analysis 375(4)
Tests on Individual Treatment Means 379(1)
Residual Analysis and Model Checking 380(2)
Determining Sample Size in Single-Factor 382(3)
Experiments
Summary 385(1)
Exercises 385(5)
Design of Experiments with Several Factors 390(65)
Examples of Experiment Design Applications 390(3)
Factorial Experiments 393(4)
Two-Factor Factorial Experiments 397(12)
Statistical Analysis of the Fixed Effects 398(5)
Model
Model Adequacy Checking 403(2)
One Observation per Cell 405(1)
The Random Effects Model 405(3)
The Mixed Model 408(1)
General Factorial Experiments 409(4)
The 2k Factorial Design 413(20)
The 22 Design 414(7)
The 2k Design for k > 2 Factors 421(7)
A Single Replicate of the 2k Design 428(5)
Confounding in the 2k Design 433(5)
Fractional Replication of the 2k Design 438(9)
The One-Half Fraction of the 2k 438(6)
Smaller Fractions: the 2k-p Fractional 444(3)
Fact