Introduction to Probability and Statistics for Engineers and Scientists

by Ross

• ISBN13: 9780125980579
• ISBN10: 0125980574
• Edition: 3rd
• Format: Hardcover
• Copyright: 2004-07-06
• Publisher: Elsevier Science
• More Book Details
• Purchase Benefits

Summary

This updated classic provides a superior introduction to applied probability and statistics for engineering or science majors. Author Sheldon Ross shows how probability yields insight into statistical problems, resulting in an intuitive understanding of the statistical procedures most often used by practicing engineers and scientists. Real data sets are incorporated in a wide variety of exercises and examples, and the enclosed CD-ROM includes software that automates the required computations. The Third Edition includes new exercises, examples, and applications, updated statistical material, and more. New in this edition: * New exercises and data examples including: - The One-sided Chebyshev Inequality for Data - The Logistics Distribution and Logistic Regression - Estimation and Testing in proofreader problems - Product Form Estimates of Life Distributions - Observational Studies * Updated statistical material * New, contemporary applications Hallmark features: * Reflects Sheldon Ross's masterfully clear exposition * Contains numerous examples, exercises, and homework problems * Unique, easy-to-use software automates required computations * Applies probability theory to everyday statistical problems and situations * Careful development of probability, modeling, and statistical procedures leads to intuitive understanding * Instructor's Solutions Manual is available to adopters

Author Biography

Sheldon M. Ross has published numerous textbooks and technical articles in the areas of statistics and applied probability. He is a fellow of the Institute of Mathematical Statistics and a recipient of the Humboldt U.S. Senior Scientist award. After many distinguished years at the University of California at Berkley, Professor Ross will become the Daniel J. Epstein professor of Industrial and Systems Engineering at the University of Southern California in September 2004

Table of Contents

Preface	xiii
Introduction to Statistics	1	(8)
Introduction	1	(1)
Data Collection and Descriptive Statistics	1	(1)
Inferential Statistics and Probability Models	2	(1)
Populations and Samples	3	(1)
A Brief History of Statistics	3	(6)
Problems	7	(2)
Descriptive Statistics	9	(46)
Introduction	9	(1)
Describing Data Sets	9	(8)
Frequency Tables and Graphs	10	(1)
Relative Frequency Tables and Graphs	10	(4)
Grouped Data, Histograms, Ogives, and Stem and Leaf Plots	14	(3)
Summarizing Data Sets	17	(10)
Sample Mean, Sample Median, and Sample Mode	17	(5)
Sample Variance and Sample Standard Deviation	22	(2)
Sample Percentiles and Box Plots	24	(3)
Chebyshev's Inequality	27	(4)
Normal Data Sets	31	(2)
Paired Data Sets and the Sample Correlation Coefficient	33	(22)
Problems	41	(14)
Elements of Probability	55	(34)
Introduction	55	(1)
Sample Space and Events	56	(2)
Venn Diagrams and the Algebra of Events	58	(1)
Axioms of Probability	59	(2)
Sample Spaces Having Equally Likely Outcomes	61	(6)
Conditional Probability	67	(3)
Bayes' Formula	70	(6)
Independent Events	76	(13)
Problems	80	(9)
Random Variables and Expectation	89	(52)
Random Variables	89	(3)
Types of Random Variables	92	(3)
Jointly Distributed Random Variables	95	(12)
Independent Random Variables	101	(4)
Conditional Distributions	105	(2)
Expectation	107	(4)
Properties of the Expected Value	111	(7)
Expected Value of Sums of Random Variables	115	(3)
Variance	118	(3)
Covariance and Variance of Sums of Random Variables	121	(5)
Moment Generating Functions	126	(1)
Chebyshev's Inequality and the Weak Law of Large Numbers	127	(14)
Problems	130	(11)
Special Random Variables	141	(60)
The Bernoulli and Binomial Random Variables	141	(7)
Computing the Binomial Distribution Function	147	(1)
The Poisson Random Variable	148	(8)
Computing the Poisson Distribution Function	155	(1)
The Hypergeometric Random Variable	156	(4)
The Uniform Random Variable	160	(8)
Normal Random Variables	168	(7)
Exponential Random Variables	175	(7)
The Poisson Process	179	(3)
The Gamma Distribution	182	(3)
Distributions Arising from the Normal	185	(7)
The Chi-Square Distribution	185	(2)
The Relation Between Chi-Square and Gamma Random Variables	187	(2)
The t-Distribution	189	(2)
The F-Distribution	191	(1)
The Logistics Distribution	192	(9)
Problems	194	(7)
Distributions of Sampling Statistics	201	(28)
Introduction	201	(1)
The Sample Mean	202	(2)
The Central Limit Theorem	204	(9)
Approximate Distribution of the Sample Mean	210	(2)
How Large a Sample is Needed?	212	(1)
The Sample Variance	213	(1)
Sampling Distributions from a Normal Population	214	(3)
Distribution of the Sample Mean	215	(1)
Joint Distribution of X and S2	215	(2)
Sampling from a Finite Population	217	(12)
Problems	221	(8)
Parameter Estimation	229	(62)
Introduction	229	(1)
Maximum Likelihood Estimators	230	(10)
Estimating Life Distributions	238	(2)
Interval Estimates	240	(13)
Confidence Interval for a Normal Mean When the Variance is Unknown	246	(5)
Confidence Intervals for the Variances of a Normal Distribution	251	(2)
Estimating the Difference in Means of Two Normal Populations	253	(7)
Approximate Confidence Interval for the Mean of a Bernoulli Random Variable	260	(5)
Confidence Interval of the Mean of the Exponential Distribution	265	(1)
Evaluating a Point Estimator	266	(6)
The Bayes Estimator	272	(19)
Problems	277	(14)
Hypothesis Testing	291	(60)
Introduction	291	(1)
Significance Levels	292	(1)
Tests Concerning the Mean of a Normal Population	293	(19)
Case of Known Variance	293	(12)
Case of Unknown Variance: The t-Test	305	(7)
Testing the Equality of Means of Two Normal Populations	312	(9)
Case of Known Variances	312	(2)
Case of Unknown Variances	314	(4)
Case of Unknown and Unequal Variances	318	(1)
The Paired t-Test	319	(2)
Hypothesis Tests Concerning the Variance of a Normal Population	321	(2)
Testing for the Equality of Variances of Two Normal Populations	322	(1)
Hypothesis Tests in Bernoulli Populations	323	(7)
Testing the Equality of Parameters in Two Bernoulli Populations	327	(3)
Tests Concerning the Mean of a Poisson Distribution	330	(21)
Testing the Relationship Between Two Poisson Parameters	331	(3)
Problems	334	(17)
Regression	351	(88)
Introduction	351	(2)
Least Squares Estimators of the Regression Parameters	353	(2)
Distribution of the Estimators	355	(6)
Statistical Inferences about the Regression Parameters	361	(15)
Inferences Concerning β	362	(4)
Regression to the Mean	366	(4)
Inferences Concerning α	370	(1)
Inferences Concerning the Mean Response α + βx0	371	(2)
Prediction Interval of a Future Response	373	(2)
Summary of Distributional Results	375	(1)
The Coefficient of Determination and the Sample Correlation Coefficient	376	(2)
Analysis of Residuals: Assessing the Model	378	(3)
Transforming to Linearity	381	(3)
Weighted Least Squares	384	(7)
Polynomial Regression	391	(3)
Multiple Linear Regression	394	(16)
Predicting Future Responses	405	(5)
Logistic Regression Models for Binary Output Data	410	(29)
Problems	413	(26)
Analysis of Variance	439	(44)
Introduction	439	(1)
An Overview	440	(2)
One-Way Analysis of Variance	442	(12)
Multiple Comparisons of Sample Means	450	(2)
One-Way Analysis of Variance with Unequal Sample Sizes	452	(2)
Two-Factor Analysis of Variance: Introduction and Parameter Estimation	454	(4)
Two-Factor Analysis of Variance: Testing Hypotheses	458	(5)
Two-Way Analysis of Variance with Interaction	463	(20)
Problems	471	(12)
Goodness of Fit Tests and Categorical Data Analysis	483	(32)
Introduction	483	(1)
Goodness of Fit Tests When all Parameters are Specified	484	(9)
Determining the Critical Region by Simulation	490	(3)
Goodness of Fit Tests When Some Parameters are Unspecified	493	(2)
Tests of Independence in Contingency Tables	495	(4)
Tests of Independence in Contingency Tables Having Fixed Marginal Totals	499	(5)
The Kolmogorov--Smirnov Goodness of Fit Test for Continuous Data	504	(11)
Problems	508	(7)
Nonparametric Hypothesis Tests	515	(30)
Introduction	515	(1)
The Sign Test	515	(4)
The Signed Rank Test	519	(6)
The Two-Sample Problem	525	(8)
The Classical Approximation and Simulation	529	(4)
The Runs Test for Randomness	533	(12)
Problems	537	(8)
Quality Control	545	(36)
Introduction	545	(1)
Control Charts for Average Values: The X-Control Chart	546	(8)
Case of Unknown μ and σ	549	(5)
S-Control Charts	554	(3)
Control Charts for the Fraction Defective	557	(2)
Control Charts for Number of Defects	559	(4)
Other Control Charts for Detecting Changes in the Population Mean	563	(18)
Moving-Average Control Charts	563	(2)
Exponentially Weighted Moving-Average Control Charts	565	(6)
Cumulative Sum Control Charts	571	(2)
Problems	573	(8)
Life Testing	581	(36)
Introduction	581	(1)
Hazard Rate Functions	581	(3)
The Exponential Distribution in Life Testing	584	(14)
Simultaneous Testing --- Stopping at the rth Failure	584	(6)
Sequential Testing	590	(4)
Simultaneous Testing --- Stopping by a Fixed Time	594	(2)
The Bayesian Approach	596	(2)
A Two-Sample Problem	598	(2)
The Weibull Distribution in Life Testing	600	(17)
Parameter Estimation by Least Squares	602	(2)
Problems	604	(7)
Appendix of Tables	611	(6)
Index	617