Statistics and probability with applications for engineers and scientists using MINITAB, R and JMP. (2020)

• Record Type: Book
• Further Information: Note: Bhisham C. Gupta, Irwin Guttman, Kalanka P. Jayalath.
• Authors: Gupta, Bhisham C, 1942-; Guttman, Irwin; Jayalath, Kalanka
• Contents: Preface xvii Acknowledgments xxi About The Companion Site xxiii 1 Introduction 1 1.1 Designed Experiment 2 1.1.1 Motivation for the Study 2 1.1.2 Investigation 3 1.1.3 Changing Criteria 3 1.1.4 A Summary of the Various Phases of the Investigation 5 1.2 A Survey 6 1.3 An Observational Study 6 1.4 A Set of Historical Data 7 1.5 A Brief Description of What is Covered in this Book 7 Part I Fundamentals of Probability and Statistics 2 Describing Data Graphically and Numerically 13 2.1 Getting Started with Statistics 14 2.1.1 What is Statistics? 14 2.1.2 Population and Sample in a Statistical Study 14 2.2 Classification of Various Types of Data 18 2.2.1 Nominal Data 18 2.2.2 Ordinal Data 19 2.2.3 Interval Data 19 2.2.4 Ratio Data 19 2.3 Frequency Distribution Tables for Qualitative and Quantitative Data 20 2.3.1 Qualitative Data 21 2.3.2 Quantitative Data 24 2.4 Graphical Description of Qualitative and Quantitative Data 30 2.4.1 Dot Plot 30 2.4.2 Pie Chart 31 2.4.3 Bar Chart 33 2.4.4 Histograms 37 2.4.5 Line Graph 44 2.4.6 Stem-and-Leaf Plot 45 2.5 Numerical Measures of Quantitative Data 50 2.5.1 Measures of Centrality 51 2.5.2 Measures of Dispersion 56 2.6 Numerical Measures of Grouped Data 67 2.6.1 Mean of a Grouped Data 67 2.6.2 Median of a Grouped Data 68 2.6.3 Mode of a Grouped Data 69 2.6.4 Variance of a Grouped Data 69 2.7 Measures of Relative Position 70 2.7.1 Percentiles 71 2.7.2 Quartiles 72 2.7.3 Interquartile Range (IQR) 72 2.7.4 Coefficient of Variation 73 2.8 Box-Whisker Plot 75 2.8.1 Construction of a Box Plot 75 2.8.2 How to Use the Box Plot 76 2.9 Measures of Association 80 2.10 Case Studies 84 2.10.1 About St. Luke’s Hospital 85 2.11 Using JMP 86 Review Practice Problems 87 3 Elements of Probability 97 3.1 Introduction 97 3.2 Random Experiments, Sample Spaces, and Events 98 3.2.1 Random Experiments and Sample Spaces 98 3.2.2 Events 99 3.3 Concepts of Probability 103 3.4 Techniques of Counting Sample Points 108 3.4.1 Tree Diagram 108 3.4.2 Permutations 110 3.4.3 Combinations 110 3.4.4 Arrangements of n Objects Involving Several Kinds of Objects 111 3.5 Conditional Probability 113 3.6 Bayes’s Theorem 116 3.7 Introducing Random Variables 120 Review Practice Problems 122 4 Discrete Random Variables and Some Important Discrete Probability Distributions 128 4.1 Graphical Descriptions of Discrete Distributions 129 4.2 Mean and Variance of a Discrete Random Variable 130 4.2.1 Expected Value of Discrete Random Variables and Their Functions 130 4.2.2 The Moment-Generating Function-Expected Value of a Special Function of X 133 4.3 The Discrete Uniform Distribution 136 4.4 The Hypergeometric Distribution 137 4.5 The Bernoulli Distribution 141 4.6 The Binomial Distribution 142 4.7 The Multinomial Distribution 146 4.8 The Poisson Distribution 147 4.8.1 Definition and Properties of the Poisson Distribution 147 4.8.2 Poisson Process 148 4.8.3 Poisson Distribution as a Limiting Form of the Binomial 148 4.9 The Negative Binomial Distribution 153 4.10 Some Derivations and Proofs (Optional) 156 4.11 A Case Study 156 4.12 Using JMP 157 Review Practice Problems 157 5 Continuous Random Variables and Some Important Continuous Probability Distributions 164 5.1 Continuous Random Variables 165 5.2 Mean and Variance of Continuous Random Variables 168 5.2.1 Expected Value of Continuous Random Variables and Their Functions 168 5.2.2 The Moment-Generating Function and Expected Value of a Special Function of X 171 5.3 Chebyshev’s Inequality 173 5.4 The Uniform Distribution 175 5.4.1 Definition and Properties 175 5.4.2 Mean and Standard Deviation of the Uniform Distribution 178 5.5 The Normal Distribution 180 5.5.1 Definition and Properties 180 5.5.2 The Standard Normal Distribution 182 5.5.3 The Moment-Generating Function of the Normal Distribution 187 5.6 Distribution of Linear Combination of Independent Normal Variables 189 5.7 Approximation of the Binomial and Poisson Distributions by the Normal Distribution 193 5.7.1 Approximation of the Binomial Distribution by the Normal Distribution 193 5.7.2 Approximation of the Poisson Distribution by the Normal Distribution 196 5.8 A Test of Normality 196 5.9 Probability Models Commonly used in Reliability Theory 201 5.9.1 The Lognormal Distribution 202 5.9.2 The Exponential Distribution 206 5.9.3 The Gamma Distribution 211 5.9.4 The Weibull Distribution 214 5.10 A Case Study 218 5.11 Using JMP 219 Review Practice Problems 220 6 Distribution of Functions Of Random Variables 228 6.1 Introduction 229 6.2 Distribution Functions of Two Random Variables 229 6.2.1 Case of Two Discrete Random Variables 229 6.2.2 Case of Two Continuous Random Variables 232 6.2.3 The Mean Value and Variance of Functions of Two Random Variables 233 6.2.4 Conditional Distributions 235 6.2.5 Correlation between Two Random Variables 238 6.2.6 Bivariate Normal Distribution 241 6.3 Extension to Several Random Variables 244 6.4 The Moment-Generating Function Revisited 245 Review Practice Problems 249 7 Sampling Distributions 253 7.1 Random Sampling 253 7.1.1 Random Sampling from an Infinite Population 254 7.1.2 Random Sampling from a Finite Population 256 7.2 The Sampling Distribution of the Sample Mean 258 7.2.1 Normal Sampled Population 258 7.2.2 Nonnormal Sampled Population 258 7.2.3 The Central Limit Theorem 259 7.3 Sampling from a Normal Population 264 7.3.1 The Chi-Square Distribution 264 7.3.2 The Student t -Distribution 271 7.3.3 Snedecor’s F -Distribution 276 7.4 Order Statistics 279 7.4.1 Distribution of the Largest Element in a Sample 280 7.4.2 Distribution of the Smallest Element in a Sample 281 7.4.3 Distribution of the Median of a Sample and of the kth Order Statistic 282 7.4.4 Other Uses of Order Statistics 284 7.5 Using JMP 286 Review Practice Problems 286 8 Estimation of Population Parameters 289 8.1 Introduction 290 8.2 Point Estimators for the Population Mean and Variance 290 8.2.1 Properties of Point Estimators 292 8.2.2 Methods of Finding Point Estimators 295 8.3 Interval Estimators for the Mean μ of a Normal Population 301 8.3.1 σ 2 Known 301 8.3.2 σ 2 Unknown 304 8.3.3 Sample Size is Large 306 8.4 Interval Estimators for The Difference of Means of Two Normal Populations 313 8.4.1 Variances are Known 313 8.4.2 Variances are Unknown 314 8.5 Interval Estimators for the Variance of a Normal Population 322 8.6 Interval Estimator for the Ratio of Variances of Two Normal Populations 327 8.7 Point and Interval Estimators for the Parameters of Binomial Populations 331 8.7.1 One Binomial Population 331&lt
• Edition: 2nd edition
• Publisher Details: Hoboken, New Jersey : John Wiley & Sons, Inc
• Publication Date: 2020
• Extent: 1 online resource
• Subjects: 519.202462; Probabilities; Engineering -- Statistical methods; Science -- Statistical methods; R (Computer program language)
• Languages: English
• ISBNs: 9781119516620
• Notes: Note: Description based on CIP data; resource not viewed.
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