An accessible and engaging introduction to the study of probability and statistics Utilizing entertaining real-world examples, A Probability and Statistics Companion provides aunique, interesting, and accessible introduction to probability and statistics. This one-of-a-kind book delves into practical topics that are crucial in the analysis of sample surveys and experimentation. This handy book contains introductory explanations of the major topics in probability and statistics, including hypothesis testing and regression, while also delving into more advanced topics such as the analysis of sample surveys, analysis of experimental data, and statistical process control. The book recognizes that there are many sampling techniques that can actually improve on simple random sampling, and in addition, an introduction to the design of experiments is provided to reflect recent advances in conducting scientific experiments. This blend of coverage results in the development of a deeper understanding and solid foundation for the study of probability and statistics. Additional topical coverage includes: Probability and sample spaces Choosing the best candidate Acceptance sampling Conditional probability Random variables and discrete probability distributions Waiting time problems Continuous probability distributions Statistical inference Nonparametric methods Least squares and medians Recursions and probability Each chapter contains exercises and explorations for readers who wish to conduct independent projects or investigations. The discussion of most methods is complemented with applications to engaging, real-world scenarios such as winning speeds at the Indianapolis 500 and predicting winners of the World Series. In addition, the book enhances the visual nature of the subject with numerous multidimensional graphical representations of the presented examples. A Probability and Statistics Companion is an excellent book for introductory probability and statistics courses at the undergraduate level. It is also a valuable reference for professionals who use statistical concepts to make informed decisions in their day-to-day work.

Table of Contents:
Preface xv 1. Probability and Sample Spaces 1 Why Study Probability? 1 Probability 2 Sample Spaces 2 Some Properties of Probabilities 8 Finding Probabilities of Events 11 Conclusions 16 Explorations 16 2. Permutations and Combinations: Choosing the Best Candidate; Acceptance Sampling 18 Permutations 19 Counting Principle 19 Permutations with Some Objects Alike 20 Permuting Only Some of the Objects 21 Combinations 22 General Addition Theorem and Applications 25 Conclusions 35 Explorations 35 3. Conditional Probability 37 Introduction 37 Some Notation 40 Bayes’ Theorem 45 Conclusions 46 Explorations 46 4. Geometric Probability 48 Conclusion 56 Explorations 57 5. Random Variables and Discrete Probability Distributions—Uniform, Binomial, Hypergeometric, and Geometric Distributions 58 Introduction 58 Discrete Uniform Distribution 59 Mean and Variance of a Discrete Random Variable 60 Intervals, σ, and German Tanks 61 Sums 62 Binomial Probability Distribution 64 Mean and Variance of the Binomial Distribution 68 Sums 69 Hypergeometric Distribution 70 Other Properties of the Hypergeometric Distribution 72 Geometric Probability Distribution 72 Conclusions 73 Explorations 74 6. Seven-Game Series in Sports 75 Introduction 75 Seven-Game Series 75 Winning the First Game 78 How Long Should the Series Last? 79 Conclusions 81 Explorations 81 7. Waiting Time Problems 83 Waiting for the First Success 83 The Mythical Island 84 Waiting for the Second Success 85 Waiting for the rth Success 87 Mean of the Negative Binomial 87 Collecting Cereal Box Prizes 88 Heads Before Tails 88 Waiting for Patterns 90 Expected Waiting Time for HH 91 Expected Waiting Time for TH 93 An Unfair Game with a Fair Coin 94 Three Tosses 95 Who Pays for Lunch? 96 Expected Number of Lunches 98 Negative Hypergeometric Distribution 99 Mean and Variance of the Negative Hypergeometric 101 Negative Binomial Approximation 103 The Meaning of the Mean 104 First Occurrences 104 Waiting Time for c Special Items to Occur 104 Estimating k 105 Conclusions 106 Explorations 106 8. Continuous Probability Distributions: Sums, the Normal Distribution, and the Central Limit Theorem; Bivariate Random Variables 108 Uniform Random Variable 109 Sums 111 A Fact About Means 111 Normal Probability Distribution 113 Facts About Normal Curves 114 Bivariate Random Variables 115 Variance 119 Central Limit Theorem: Sums 121 Central Limit Theorem: Means 123 Central Limit Theorem 124 Expected Values and Bivariate Random Variables 124 Means and Variances of Means 124 A Note on the Uniform Distribution 126 Conclusions 128 Explorations 129 9. Statistical Inference I 130 Estimation 131 Confidence Intervals 131 Hypothesis Testing 133 β and the Power of a Test 137 p-Value for a Test 139 Conclusions 140 Explorations 140 10. Statistical Inference II: Continuous Probability Distributions II—Comparing Two Samples 141 The Chi-Squared Distribution 141 Statistical Inference on the Variance 144 Student t Distribution 146 Testing the Ratio of Variances: The F Distribution 148 Tests on Means from Two Samples 150 Conclusions 154 Explorations 154 11. Statistical Process Control 155 Control Charts 155 Estimating σ Using the Sample Standard Deviations 157 Estimating σ Using the Sample Ranges 159 Control Charts for Attributes 161 np Control Chart 161 p Chart 163 Some Characteristics of Control Charts 164 Some Additional Tests for Control Charts 165 Conclusions 168 Explorations 168 12. Nonparametric Methods 170 Introduction 170 The Rank Sum Test 170 Order Statistics 173 Median 174 Maximum 176 Runs 180 Some Theory of Runs 182 Conclusions 186 Explorations 187 13. Least Squares, Medians, and the Indy 500 188 Introduction 188 Least Squares 191 Principle of Least Squares 191 Influential Observations 193 The Indy 500 195 A Test for Linearity: The Analysis of Variance 197 A Caution 201 Nonlinear Models 201 The Median–Median Line 202 When Are the Lines Identical? 205 Determining the Median–Median Line 207 Analysis for Years 1911–1969 209 Conclusions 210 Explorations 210 14. Sampling 211 Simple Random Sampling 212 Stratification 214 Proportional Allocation 215 Optimal Allocation 217 Some Practical Considerations 219 Strata 221 Conclusions 221 Explorations 221 15. Design of Experiments 223 Yates Algorithm 230 Randomization and Some Notation 231 Confounding 233 Multiple Observations 234 Design Models and Multiple Regression Models 235 Testing the Effects for Significance 235 Conclusions 238 Explorations 238 16. Recursions and Probability 240 Introduction 240 Conclusions 250 Explorations 250 17. Generating Functions and the Central Limit Theorem 251 Means and Variances 253 A Normal Approximation 254 Conclusions 255 Explorations 255 Bibliography 257 Where to Learn More 257 Index 259