Introduction To Probability Statistics

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.

List of contents

Chapter 1 - Introduction to Probability and Counting 1.1 Interpreting Probabilities 1.2 Sample Spaces and Events 1.3 Permutations and Combinations Chapter Summary Exercises Review Exercises Chapter 2 - Some Probability Laws 2.1 Axioms of Probability 2.2 Conditional Probability 2.3 Independence and the Multiplication Rule 2.4 Bayes' Theorem Chapter Summary Exercises Review Exercises Chapter 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 Chapter Summary Exercises Review Exercises Chapter 4 - Continuous Distributions 4.1 Continuous Densities 4.2 Expectation and Distribution Parameters 4.3 Gamma, Exponential, and Chi-Squared Distributions 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 Chapter Summary Exercises Review Exercises Chapter 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 Chapter Summary Exercises Review Exercises Chapter 6 - Descriptive Statistics 6.1 Random Sampling 6.2 Picturing the Distribution 6.3 Sample Statistics 6.4 Boxplots Chapter Summary Exercises Review Exercises Chapter 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 Chapter Summary Exercises Review Exercises Chapter 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 Test on the Variance 8.7 Alternative Nonparametric Methods Chapter Summary Exercises Review Exercises Chapter 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 Chapter Summary Exercises Review Exercises Chapter 10 - Comparing Two Means and Two Variances 10.1 Point Estimation: Independent Samples 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 Chapter Summary Exercises Review Exercises Chapter 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 Chapter Summary Exercises Review Exercises Chapter 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 Hypothesis about Model Parameters 12.6 Use of Indicator or "Dummy" Variables (Optional) 12.7 Criteria for Variable Selection 12.8 Model Transformation and Concluding Remarks Chapter Summary Exercises Review Exercises Chapter 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 Nonparametirc Methods Chapter Summary Exercises Review Exercises Chapter 14 - Factorial Experiments 14.1 Two-Factor Analysis of Varia

About the author

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.

Jesse C. arnold is a Professor of Statistics at Virginia Polytechnic Insitute and state University. Dr. arnold received the B.S. Degree from Southeastern state University, and the M.A and Ph. D degrees in statistics from Florida state university. He served as head of Statistics department for ten years, is a fellow of the American Statistical Association, and elected member of the International Statistics Institute. Ha has served as President of the International Biometric Society (Eastern North American Region) and Chairman of the statistical Educational Section of the American Statistical Association.

Summary

Designed for the first course in probability and statistics taken by students majoring in engineering and the computing sciences, this text offers a presentation of applications and theory. It aims to develop the theoretical foundations for the statistical methods. It explores the practical implications of the formal results to problem-solving.

Product details

• Authors: Jesse Arnold, Jesse C. Arnold, Milton, J. Susan Milton, J.Susan Milton, Milton J. Susan
• Publisher: MCGRAW-HILL Higher Education
• Languages: English
• Product format: Hardback
• Released: 01.01.2002
• EAN: 9780071198592
• ISBN: 978-0-07-119859-2
• No. of pages: 816
• Weight: 1036 g
• Series: College Ie Overruns
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics; MATHEMATICS / Probability & Statistics / General, Probability & statistics, Systems analysis & design, Probability and statistics, Systems analysis and design