This well-respected text is designed for the first course in probability and statistics taken by students majoring in Engineering and the Computing Sciences. The prerequisite is one year of calculus. The text offers a balanced presentation of applications and theory. The authors take care to develop the theoretical foundations for the statistical methods presented at a level that is accessible to students with only a calculus background. They explore the practical implications of the formal results to problem-solving so students gain an understanding of the logic behind the techniques as well…mehr
This well-respected text is designed for the first course in probability and statistics taken by students majoring in Engineering and the Computing Sciences. The prerequisite is one year of calculus. The text offers a balanced presentation of applications and theory. The authors take care to develop the theoretical foundations for the statistical methods presented at a level that is accessible to students with only a calculus background. They explore the practical implications of the formal results to problem-solving so students gain an understanding of the logic behind the techniques as well as practice in using them. The examples, exercises, and applications were chosen specifically for students in engineering and computer science and include opportunities for real data analysis.
J.Susan Milton is professor Emeritus of Satatics at Radford University. Dr. Milton recieved the B.S. degree from Western Carolina University, the M.A. degree from the University of North Carolina at Chapel Hill, and the Ph.D degree in Statistics from Virginia Polytechnic Institute and State university. She is a Danforth Associate and is a recipient of the Radford University Foundation Award for Excellence in Teaching. Dr. Milton is the author of Statistical Methods in the Biological and Health Sciences as well as Introduction to statistics, Probability with the Essential Analysis, and a first Course in the Theory of Linear Statistical Models.
Inhaltsangabe
1 Introduction to Probability and Counting 1.1 Interpreting Probabilities 1.2 Sample Spaces and Events 1.3 Permutations and Combinations 2 Some Probability Laws 2.1 Axioms of Probability 2.2 Conditional Probability 2.3 Independence and the Multiplication Rule 2.4 Bayes' Theorem 3 Discrete Distributions 3.1 Random Variables 3.2 Discrete Probablility Densities 3.3 Expectation and Distribution Parameters 3.4 Geometric Distribution and the Moment Generating Function 3.5 Binomial Distribution 3.6 Negative Binomial Distribution 3.7 Hypergeometric Distribution 3.8 Poisson Distribution 4 Continuous Distributions 4.1 Continuous Densities 4.2 Expectation and Distribution Parameters 4.3 Gamma Distribution 4.4 Normal Distribution 4.5 Normal Probability Rule and Chebyshev's Inequality 4.6 Normal Approximation to the Binomial Distribution 4.7 Weibull Distribution and Reliability 4.8 Transformation of Variables 4.9 Simulating a Continuous Distribution 5 Joint Distributions 5.1 Joint Densities and Independence 5.2 Expectation and Covariance 5.3 Correlation 5.4 Conditional Densities and Regression 5.5 Transformation of Variables 6 Descriptive Statistics 6.1 Random Sampling 6.2 Picturing the Distribution 6.3 Sample Statistics 6.4 Boxplots 7 Estimation 7.1 Point Estimation 7.2 The Method of Moments and Maximum Likelihood 7.3 Functions of Random Variables--Distribution of X 7.4 Interval Estimation and the Central Limit Theorem 8 Inferences on the Mean and Variance of a Distribution 8.1 Interval Estimation of Variability 8.2 Estimating the Mean and the Student-t Distribution 8.3 Hypothesis Testing 8.4 Significance Testing 8.5 Hypothesis and Significance Tests on the Mean 8.6 Hypothesis Tests 8.7 Alternative Nonparametric Methods 9 Inferences on Proportions 9.1 Estimating Proportions 9.2 Testing Hypothesis on a Proportion 9.3 Comparing Two Proportions: Estimation 9.4 Coparing Two Proportions: Hypothesis Testing 10 Comparing Two Means and Two Variances 10.1 Point Estimation 10.2 Comparing Variances: The F Distribution 10.3 Comparing Means: Variances Equal (Pooled Test) 10.4 Comparing Means: Variances Unequal 10.5 Compairing Means: Paried Data 10.6 Alternative Nonparametric Methods 10.7 A Note on Technology 11 Sample Linear Regression and Correlation 11.1 Model and Parameter Estimation 11.2 Properties of Least-Squares Estimators 11.3 Confidence Interval Estimation and Hypothesis Testing 11.4 Repeated Measurements and Lack of Fit 11.5 Residual Analysis 11.6 Correlation 12 Multiple Linear Regression Models 12.1 Least-Squares Procedures for Model Fitting 12.2 A Matrix Approach to Least Squares 12.3 Properties of the Least-Squares Estimators 12.4 Interval Estimation 12.5 Testing Hypotheses about Model Parameters 12.6 Use of Indicator or "Dummy" Variables 12.7 Criteria for Variable Selection 12.8 Model Transformation and Concluding Remarks 13 Analysis of Variance 13.1 One-Way Classification Fixed-Effects Model 13.2 Comparing Variances 13.3 Pairwise Comparison 13.4 Testing Contrasts 13.5 Randomized Complete Block Design 13.6 Latin Squares 13.7 Random-Effects Models 13.8 Design Models in Matrix Form 13.9 Alternative Nonparametric Methods 14 Factorial Experiments 14.1 Two-Factor Analysis of Variance 14.2 Extension to Three Factors 14.3 Random and Mixed Model Factorial Experiments 14.4 2^k Factorial Experiments 14.5 2^k Factorial Experiments in an Incomplete Block Design 14.6 Fractional Factorial Experiments 15 Categorical Data 15.1 Multinomial Distribution 15.2 Chi-Squared Goodness of Fit Tests 15.3 Testing for Independence 15.4 Comparing Proportions 16 Statistical Quality Control 16.1 Properties of Control Charts 16.2 Shewart Control Charts for Measurements 16.3 Shewart Control Charts for Attributes 16.4 Tolerance Limits 16.5 Acceptance Sampling 16.6 Two-Stage Acceptance Sampling 16.7 Extensions in Quality Control Appendix A Statistical Tables Appendix B Answers to Selected Problems Appendix C Selected Derivations
1 Introduction to Probability and Counting 1.1 Interpreting Probabilities 1.2 Sample Spaces and Events 1.3 Permutations and Combinations 2 Some Probability Laws 2.1 Axioms of Probability 2.2 Conditional Probability 2.3 Independence and the Multiplication Rule 2.4 Bayes' Theorem 3 Discrete Distributions 3.1 Random Variables 3.2 Discrete Probablility Densities 3.3 Expectation and Distribution Parameters 3.4 Geometric Distribution and the Moment Generating Function 3.5 Binomial Distribution 3.6 Negative Binomial Distribution 3.7 Hypergeometric Distribution 3.8 Poisson Distribution 4 Continuous Distributions 4.1 Continuous Densities 4.2 Expectation and Distribution Parameters 4.3 Gamma Distribution 4.4 Normal Distribution 4.5 Normal Probability Rule and Chebyshev's Inequality 4.6 Normal Approximation to the Binomial Distribution 4.7 Weibull Distribution and Reliability 4.8 Transformation of Variables 4.9 Simulating a Continuous Distribution 5 Joint Distributions 5.1 Joint Densities and Independence 5.2 Expectation and Covariance 5.3 Correlation 5.4 Conditional Densities and Regression 5.5 Transformation of Variables 6 Descriptive Statistics 6.1 Random Sampling 6.2 Picturing the Distribution 6.3 Sample Statistics 6.4 Boxplots 7 Estimation 7.1 Point Estimation 7.2 The Method of Moments and Maximum Likelihood 7.3 Functions of Random Variables--Distribution of X 7.4 Interval Estimation and the Central Limit Theorem 8 Inferences on the Mean and Variance of a Distribution 8.1 Interval Estimation of Variability 8.2 Estimating the Mean and the Student-t Distribution 8.3 Hypothesis Testing 8.4 Significance Testing 8.5 Hypothesis and Significance Tests on the Mean 8.6 Hypothesis Tests 8.7 Alternative Nonparametric Methods 9 Inferences on Proportions 9.1 Estimating Proportions 9.2 Testing Hypothesis on a Proportion 9.3 Comparing Two Proportions: Estimation 9.4 Coparing Two Proportions: Hypothesis Testing 10 Comparing Two Means and Two Variances 10.1 Point Estimation 10.2 Comparing Variances: The F Distribution 10.3 Comparing Means: Variances Equal (Pooled Test) 10.4 Comparing Means: Variances Unequal 10.5 Compairing Means: Paried Data 10.6 Alternative Nonparametric Methods 10.7 A Note on Technology 11 Sample Linear Regression and Correlation 11.1 Model and Parameter Estimation 11.2 Properties of Least-Squares Estimators 11.3 Confidence Interval Estimation and Hypothesis Testing 11.4 Repeated Measurements and Lack of Fit 11.5 Residual Analysis 11.6 Correlation 12 Multiple Linear Regression Models 12.1 Least-Squares Procedures for Model Fitting 12.2 A Matrix Approach to Least Squares 12.3 Properties of the Least-Squares Estimators 12.4 Interval Estimation 12.5 Testing Hypotheses about Model Parameters 12.6 Use of Indicator or "Dummy" Variables 12.7 Criteria for Variable Selection 12.8 Model Transformation and Concluding Remarks 13 Analysis of Variance 13.1 One-Way Classification Fixed-Effects Model 13.2 Comparing Variances 13.3 Pairwise Comparison 13.4 Testing Contrasts 13.5 Randomized Complete Block Design 13.6 Latin Squares 13.7 Random-Effects Models 13.8 Design Models in Matrix Form 13.9 Alternative Nonparametric Methods 14 Factorial Experiments 14.1 Two-Factor Analysis of Variance 14.2 Extension to Three Factors 14.3 Random and Mixed Model Factorial Experiments 14.4 2^k Factorial Experiments 14.5 2^k Factorial Experiments in an Incomplete Block Design 14.6 Fractional Factorial Experiments 15 Categorical Data 15.1 Multinomial Distribution 15.2 Chi-Squared Goodness of Fit Tests 15.3 Testing for Independence 15.4 Comparing Proportions 16 Statistical Quality Control 16.1 Properties of Control Charts 16.2 Shewart Control Charts for Measurements 16.3 Shewart Control Charts for Attributes 16.4 Tolerance Limits 16.5 Acceptance Sampling 16.6 Two-Stage Acceptance Sampling 16.7 Extensions in Quality Control Appendix A Statistical Tables Appendix B Answers to Selected Problems Appendix C Selected Derivations
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