Fundamentals of Probability and Statistics for Engineers

xContents9 PARAMETER ESTIMATION 2599.1 Samples and Statistics 2599.1.1 Sample Mean 2619.1.2 Sample Variance 2629.1.3 Sample Moments 2639.1.4 Order Statistics 2649.2 Quality Criteria for Estimates 2649.2.1 Unbiasedness 2659.2.2 Minimum Variance 2669.2.3 Consistency 2749.2.4 Sufficiency 2759.3 Methods of Estimation 2779.3.1 Point Estimation 2779.3.2 Interval Estimation 294References 306Further Reading and Comments 306Problems 30710 MODEL VERIFICATION 31510.1 Preliminaries 31510.1.1 Type-I and Type-II Errors 31610.2 Chi-Squared Goodness-of-Fit Test 31610.2.1 The Case of Known Parameters 31710.2.2 The Case of Estimated Parameters 32210.3 Kolmogorov–Smirnov Test 327References 330Further Reading and Comments 330Problems 33011 LINEAR MODELS AND LINEAR REGRESSION 33511.1 Simple Linear Regression 33511.1.1 Least Squares Method of Estimation 33611.1.2 Properties of Least-Square Estimators 34211.1.3 Unbiased Estimator for234511.1.4 Confidence Intervals for Regression Coefficients 34711.1.5 Significance Tests 35111.2 Multiple Linear Regression 35411.2.1 Least Squares Method of Estimation 35411.3 Other Regression Models 357Reference 359Further Reading 359Problems 359TLFeBOOK