ISBN-10:
144968534X
ISBN-13:
2901449685347
Pub. Date:
02/19/2013
Publisher:
Jones & Bartlett Learning

# Essentials Of Mathematical Statistics

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ISBN-13: 2901449685347 Jones & Bartlett Learning 02/19/2013 New Edition 598 7.10(w) x 9.20(h) x 1.50(d)

Concordia University

Preface xi

1 Basics of Probability 1

1.1 Introduction 2

1.2 Basic Concepts and Definitions 2

1.3 Counting Problems 13

1.4 Axioms of Probability and the Addition Rule 26

1.5 Conditional Probability and the Multiplication Rule 37

1.6 Bayes' Theorem 44

1.7 Independent Events 54

2 Discrete Random Variables 65

2.1 Introduction 66

2.2 Probability Mass Functions 67

2.3 The Hypergeometric and Binomial Distributions 78

2.4 The Poisson Distribution 92

2.5 Mean and Variance 101

2.6 Functions of a Random Variable 111

2.7 The Moment-Generating Function 117

3 Continuous Random Variables 125

3.1 Introduction 126

3.2 Definitions 128

3.3 The Uniform and Exponential Distributions 139

3.4 The Normal Distribution 150

3.5 Functions of Continuous Random Variables 161

3.6 Joint Distributions 168

3.7 Functions of Independent Random Variables 179

3.8 The Central Limit Theorem 190

3.9 The Gamma and Related Distributions 198

3.10 Approximating the Binomial Distribution 212

4 Statistics 219

4.1 What Is Statistics? 220

4.2 Summarizing Data 232

4.3 Maximum Likelihood Estimates 249

4.4 Sampling Distributions 259

4.5 Confidence Intervals for a Proportion 270

4.6 Confidence Intervals for a Mean 281

4.7 Confidence Intervals for a Variance 293

4.8 Confidence Intervals for Differences 300

4.9 Sample Size 315

4.10 Assessing Normality 324

5 Hypothesis Testing 333

5.1 Introduction 334

5.2 Testing Claims About a Proportion 342

5.3 Testing Claims About a Mean 356

5.4 Comparing Two Proportions 365

5.5 Comparing Two Variances 374

5.6 Comparing Two Means 383

5.7 Goodness-of-Fit Tests 397

5.8 Test of Independence 408

5.9 One-Way ANOVA 418

5.10 Two-Way ANOVA 431

6 Simple Regression 443

6.1 Introduction 444

6.2 Covariance and Correlation 446

6.3 Method of Least Squares 459

6.4 The Simple Linear Model 468

6.5 Sums of Squares and ANOVA 478

6.6 Nonlinear Regression 484

6.7 Multiple Regression 492

7 Nonparametric Statistics 509

7.1 Introduction 510

7.2 The Sign Test 510

7.3 The Wilcoxon Signed-Rank Test 518

7.4 The Wilcoxon Rank-Sum Test 524

7.5 The Runs Test for Randomness 532

A Proofs of Selected Theorems 541

A.1 A Proof of Theorem 3.7.5 541

A.2 A Proof of the Central Limit Theorem 542

A.3 A Proof of the Limit Theorem of De Moivre and Laplace 545

A.4 A Proof of Theorem 4.6.1 547

A.5 Confidence Intervals for the Difference of Two Means 547

A.6 Coefficients in the Linear Regression Equation 550

A.7 Wilcoxon Signed-Rank Test Distribution 551

B Software Basics 555

B.1 Minitab 555

B.2 R 555

B.3 Excel 558

B.4 TI-83/84 Calculators 560

C Tables 561

D Answers to Selected Exercises 577

Index 587

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