Introduction to Probability and Statistics for Engineers and Scientists

by Ross

• ISBN13: 9780125984720
• ISBN10: 0125984723
• Edition: 2nd
• Format: Hardcover
• Copyright: 1999-10-11
• Publisher: Elsevier Science & Technology
• More Book Details
• Purchase Benefits

Summary

Suited for a first course in applied probability and statistics for engineering or science majors, this is a superior textbook. Introduction to Probability and Statistics for Engineers and Scientists, Second Edition, includes expanded coverage of quality control, and offers unique software that automates the computations required for exercises, as well as illustrating the main concepts of probability. The author emphasizes the manner in which probability yields insight into statistical problems; ultimately 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 throughout the book, and this emphasis on data motivates the probability coverage.

Author Biography

Sheldon M. Ross has published numerous textbooks and technical articles in the areas of statistics and applied probability. Professor Ross is the founding and continuing editor of the journal Probability in the Engineering and Informational Sciences, published by Cambridge University Press. He is a fellow of the Institute of Mathematical Statistics and a recipient of the Humboldt U.S. Senior Scientist award.

Table of Contents

Preface	xiii
Chapter 1 Introduction to Statistics	1	(8)
1.1 Introduction	1	(1)
1.2 Data Collection and Descriptive Statistics	1	(1)
1.3 Inferential Statistics and Probability Models	2	(1)
1.4 Populations and Samples	3	(1)
1.5 A Brief History of Statistics	3	(4)
Problems	7	(2)
Chapter 2 Descriptive Statistics	9	(50)
2.1 Introduction	9	(1)
2.2 Describing Data Sets	9	(10)
2.2.1 Frequency Tables and Graphs	10	(1)
2.2.2 Relative Frequency Tables and Graphs	10	(4)
2.2.3 Grouped Data, Histograms, Ogives, and Stem and Leaf Plots	14	(5)
2.3 Summarizing Data Sets	19	(10)
2.3.1 Sample Mean, Sample Median, and Sample Mode	19	(4)
2.3.2 Sample Variance and Sample Standard Deviation	23	(2)
2.3.3 Sample Percentiles and Box Plots	25	(4)
2.4 Chebyshev's Inequality	29	(1)
2.5 Normal Data Sets	30	(4)
2.6 Paired Data Sets and the Sample Correlation Coefficient	34	(6)
Problems	40	(19)
Chapter 3 Elements of Probability	59	(30)
3.1 Introduction	59	(1)
3.2 Sample Space and Events	60	(2)
3.3 Venn Diagrams and the Algebra of Events	62	(1)
3.4 Axioms of Probability	63	(2)
3.5 Sample Spaces Having Equally Likely Outcomes	65	(5)
3.6 Conditional Probability	70	(4)
3.7 Bayes' Formula	74	(5)
3.8 Independent Events	79	(3)
Problems	82	(7)
Chapter 4 Random Variables and Expectation	89	(48)
4.1 Random Variables	89	(2)
4.2 Types of Random Variables	91	(4)
4.3 Jointly Distributed Random Variables	95	(10)
4.3.1 Independent Random Variables	100	(3)
*4.3.2 Conditional Distributions	103	(2)
4.4 Expectation	105	(5)
4.5 Properties of the Expected Value	110	(6)
4.5.1 Expected Value of Sums of Random Variables	113	(3)
4.6 Variance	116	(3)
4.7 Covariance and Variance of Sums of Random Variables	119	(4)
4.8 Moment Generating Functions	123	(1)
4.9 Chebyshev's Inequality and the Weak Law of Large Numbers	124	(3)
Problems	127	(10)
Chapter 5 Special Random Variables	137	(54)
5.1 The Bernoulli and Binomial Random Variables	137	(7)
5.1.1 Computing the Binomial Distribution Function	142	(2)
5.2 The Poisson Random Variable	144	(6)
5.2.1 Computing the Poisson Distribution Function	150	(1)
5.3 The Hypergeometric Random Variable	150	(4)
5.4 The Uniform Random Variable	154	(6)
5.5 Normal Random Variables	160	(7)
5.6 Exponential Random Variables	167	(6)
*5.6.1 The Poisson Process	171	(2)
*5.7 The Gamma Distribution	173	(4)
5.8 Distributions Arising from the Normal	177	(7)
5.8.1 The Chi-Square Distribution	177	(1)
*5.8.1.1 The Relation between Chi-Square and Gamma Random Variables	178	(2)
5.8.2 The t-Distribution	180	(2)
5.8.3 The F-Distribution	182	(2)
Problems	184	(7)
Chapter 6 Distributions of Sampling Statistics	191	(26)
6.1 Introduction	191	(1)
6.2 The Sample Mean	192	(1)
6.3 The Central Limit Theorem	193	(10)
6.3.1 Approximate Distribution of the Sample Mean	200	(3)
6.3.2 How Large a Sample Is Needed	203	(1)
6.4 The Sample Variance	203	(1)
6.5 Sampling Distributions from a Normal Population	204	(2)
6.5.1 Distribution of the Sample Mean	204	(1)
6.5.2 Joint Distribution of X and S^(2)	204	(2)
6.6 Sampling from A Finite Population	206	(4)
Problems	210	(7)
Chapter 7 Parameter Estimation	217	(54)
7.1 Introduction	217	(1)
7.2 Maximum Likelihood Estimators	218	(5)
7.3 Interval Estimates	223	(12)
7.3.1 Confidence Interval for a Normal Mean When the Variance Is Unknown	229	(5)
7.3.2 Confidence Intervals for the Variance of a Normal Distribution	234	(1)
7.4 Estimating the Difference in Means of Two Normal Populations	235	(7)
7.5 Approximate Confidence Interval for the Mean of a Bernoulli Random Variable	242	(4)
*7.6 Confidence Interval of the Mean of the Exponential Distribution	246	(1)
*7.7 Evaluating a Point Estimator	247	(6)
*7.8 The Bays Estimator	253	(5)
Problems	258	(13)
Chapter 8 Hypothesis Testing	271	(54)
8.1 Introduction	271	(1)
8.2 Significance Levels	272	(1)
8.3 Tests Concerning the Mean of a Normal Population	273	(18)
8.3.1 Case of Known Variance	273	(6)
8.3.1.1 One-Sided Tests	279	(5)
8.3.2 Case of Unknown Variance: The t-Test	284	(7)
8.4 Testing the Equality of Means of Two Normal Populations	291	(8)
8.4.1 Case of Known Variances	291	(2)
8.4.2 Case of Unknown Variances	293	(4)
8.4.3 Case of Unknown and Unequal Variances	297	(1)
8.4.4 The Paired t-Test	297	(2)
8.5 Hypothesis Tests Concerning the Variance of a Normal Population	299	(3)
8.5.1 Testing for the Equality of Variances of Two Normal Populations	301	(1)
8.6 Hypothesis Tests in Bernoulli Populations	302	(5)
8.6.1 Testing the Equality of Parameters in Two Bernoulli Populations	305	(1)
8.6.1.1 Computations for the Fisher-Irwin Test	306	(1)
8.7 Tests Concerning the Mean of a Poisson Distribution	307	(2)
8.7.1 Testing the Relationship between Two Poisson Parameters	308	(1)
Problems	309	(16)
Chapter 9 Regression	325	(80)
9.1 Introduction	325	(2)
9.2 Least Squares Estimators of the Regression Parameters	327	(3)
9.3 Distribution of the Estimators	330	(5)
9.4 Statistical Inferences about the Regression Parameters	335	(13)
9.4.1 Inferences Concerning Beta	335	(4)
9.4.1.1 Regression to the Mean	339	(4)
9.4.2 Inferences Concerning Alpha	343	(1)
9.4.3 Inferences Concerning the Mean Response Alpha + (Beta)X	343	(2)
9.4.4 Prediction Interval of a Future Response	345	(2)
9.4.5 Summary of Distributional Results	347	(1)
9.5 The Coefficient of Determination and the Sample Correlation Coefficient	348	(2)
9.6 Analysis of Residuals: Assessing the Model	350	(2)
9.7 Transforming to Linearity	352	(4)
9.8 Weighted Least Squares	356	(6)
9.9 Polynomial Regression	362	(3)
*9.10 Multiple Linear Regression	365	(16)
9.10.1 Predicting Future Responses	376	(5)
Problems	381	(24)
Chapter 10 Analysis of Variance	405	(42)
10.1 Introduction	405	(1)
10.2 An Overview	406	(2)
10.3 One-Way Analysis of Variance	408	(9)
10.3.1 Multiple Comparisons of Sample Means	414	(2)
10.3.2 One-Way Analysis of Variance with Unequal Sample Sizes	416	(1)
10.4 Two-Factor Analysis of Variance: Introduction and Parameter Estimation	417	(4)
10.5 Two-Factor Analysis of Variance: Testing Hypotheses	421	(4)
10.6 Two-Way Analysis of Variance with Interaction	425	(9)
Problems	434	(13)
Chapter 11 Goodness of Fit Tests and Categorical Data Analysis	447	(32)
11.1 Introduction	447	(1)
11.2 Goodness of Fit Tests When All Parameters Are Specified	448	(8)
11.2.1 Determining the Critical Region by Simulation	453	(3)
11.3 Goodness of Fit Tests When Some Parameters Are Unspecified	456	(2)
11.4 Tests of Independence in Contingency Tables	458	(5)
11.5 Tests of Independence in Contingency Tables Having Fixed Marginal Totals	463	(3)
*11.6 The Kolmogorov-Smirnov Goodness of Fit Test for Continuous Data	466	(4)
Problems	470	(9)
Chapter 12 Nonparametric Hypothesis Tests	479	(28)
12.1 Introduction	479	(1)
12.2 The Sign Test	479	(4)
12.3 The Signed Rank Test	483	(5)
12.4 The Two-Sample Problem	488	(6)
12.4.1 The Classical Approximation and Simulation	492	(2)
12.5 The Runs Test for Randomness	494	(5)
Problems	499	(8)
Chapter 13 Quality Control	507	(34)
13.1 Introduction	507	(1)
13.2 Control Charts for Average Values: The X-Control Charts	508	(7)
13.2.1 Case of Unknown Mu and Sigma	511	(4)
13.3 S-Control Charts	515	(3)
13.4 Control Charts for the Fraction Defective	518	(2)
13.5 Control Charts for Number of Defects	520	(3)
13.6 Other Control Charts for Detecting Changes in the Population Mean	523	(10)
13.6.1 Moving-Average Control Charts	524	(2)
13.6.2 Exponentially Weighted Moving-Average Control Charts	526	(4)
13.6.3 Cumulative Sum Control Charts	530	(3)
Problems	533	(8)
Chapter 14* Life Testing	541	(28)
14.1 Introduction	541	(1)
14.2 Hazard Rate Functions	541	(3)
14.3 The Exponential Distribution in Life Testing	544	(13)
14.3.1 Simultaneous Testing--Stopping at the rth Failure	544	(5)
14.3.2 Sequential Testing	549	(4)
14.3.3 Simultaneous Testing--Stopping by a Fixed Time	553	(2)
14.3.4 The Bayesian Approach	555	(2)
14.4 A Two-Sample Problem	557	(1)
14.5 The Weibull Distribution in Life Testing	558	(4)
14.5.1 Parameter Estimation by Least Squares	560	(2)
Problems	562	(7)
Appendix of Tables	569	(6)
Index	575
*Denotes optional material.