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Prob Solution Manual (Probability Statistics)

Nov 04, 2014

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(Probability Statistics)

Instructor Solution ManualProbability and Statistics for Engineers and Scientists(3rd Edition)AnthonyHayter1InstructorSolutionManualThis instructor solution manual to accompany the third edition ofProbability and Statistics for Engineers and Scientists by Anthony Hayterprovides worked solutions and answers to all of the problems given in the textbook. The studentsolutionmanual providesworkedsolutionsandanswerstoonlytheodd-numberedproblemsgiven at the end of the chapter sections. In addition to the material contained in the studentsolutionmanual, thisinstructormanual thereforeprovidesworkedsolutionsandanswerstothe even-numbered problems given at the end of the chapter sections together with all of thesupplementary problems at the end of each chapter.2Contents1 ProbabilityTheory 71.1 Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.2 Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.3 Combinations of Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.4 Conditional Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161.5 Probabilities of Event Intersections . . . . . . . . . . . . . . . . . . . . . . . . . . 221.6 Posterior Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281.7 Counting Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321.9 Supplementary Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372 RandomVariables 492.1 Discrete Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492.2 Continuous Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 542.3 The Expectation of a Random Variable . . . . . . . . . . . . . . . . . . . . . . . 582.4 The Variance of a Random Variable . . . . . . . . . . . . . . . . . . . . . . . . . 622.5 Jointly Distributed Random Variables . . . . . . . . . . . . . . . . . . . . . . . . 682.6 Combinations and Functions of Random variables . . . . . . . . . . . . . . . . . . 772.8 Supplementary Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 863 DiscreteProbabilityDistributions 953.1 The Binomial Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 953.2 The Geometric and Negative Binomial Distributions . . . . . . . . . . . . . . . . 993.3 The Hypergeometric Distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . 1023.4 The Poisson Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1053.5 The Multinomial Distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1073.7 Supplementary Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1094 ContinuousProbabilityDistributions 1134.1 The Uniform Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1134.2 The Exponential Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1164.3 The Gamma Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1194.4 The Weibull Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1214.5 The Beta Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1234.7 Supplementary Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12534 CONTENTS5 TheNormalDistribution 1295.1 Probability Calculations using the Normal Distribution . . . . . . . . . . . . . . 1295.2 Linear Combinations of Normal Random Variables . . . . . . . . . . . . . . . . . 1355.3 Approximating Distributions with the Normal Distribution . . . . . . . . . . . . 1405.4 Distributions Related to the Normal Distribution. . . . . . . . . . . . . . . . . . 1445.6 Supplementary Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1486 DescriptiveStatistics 1576.1 Experimentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1576.2 Data Presentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1596.3 Sample Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1616.6 Supplementary Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1647 StatisticalEstimationandSamplingDistributions 1677.2 Properties of Point Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1677.3 Sampling Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1707.4 Constructing Parameter Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . 1767.6 Supplementary Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1778 InferencesonaPopulationMean 1838.1 Condence Intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1838.2 Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1898.5 Supplementary Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1969 ComparingTwoPopulationMeans 2059.2 Analysis of Paired Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2059.3 Analysis of Independent Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . 2099.6 Supplementary Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21810 DiscreteDataAnalysis 22510.1Inferences on a Population Proportion . . . . . . . . . . . . . . . . . . . . . . . . 22510.2Comparing Two Population Proportions . . . . . . . . . . . . . . . . . . . . . . . 23210.3Goodness of Fit Tests for One-way Contingency Tables . . . . . . . . . . . . . . . 24010.4Testing for Independence in Two-way Contingency Tables . . . . . . . . . . . . . 24610.6Supplementary Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25111 TheAnalysisofVariance 26311.1One Factor Analysis of Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . 26311.2Randomized Block Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27311.4Supplementary Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28112 SimpleLinearRegressionandCorrelation 28712.1The Simple Linear Regression Model . . . . . . . . . . . . . . . . . . . . . . . . . 28712.2Fitting the Regression Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28912.3Inferences on the Slope Parameter1 . . . . . . . . . . . . . . . . . . . . . . . . . 29212.4Inferences on the Regression Line. . . . . . . . . . . . . . . . . . . . . . . . . . . 29612.5Prediction Intervals for Future Response Values. . . . . . . . . . . . . . . . . . . 29812.6The Analysis of Variance Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30012.7Residual Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302CONTENTS 512.8Variable Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30312.9Correlation Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30512.11Supplementary Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30613 MultipleLinearRegressionandNonlinearRegression 31713.1Introduction to Multiple Linear Regression . . . . . . . . . . . . . . . . . . . . . 31713.2Examples of Multiple Linear Regression . . . . . . . . . . . . . . . . . . . . . . . 32013.3Matrix Algebra Formulation of Multiple Linear Regression . . . . . . . . . . . . . 32213.4Evaluating Model Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32713.6Supplementary Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32814 MultifactorExperimentalDesignandAnalysis 33314.1Experiments with Two Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33314.2Experiments with Three or More Factors . . . . . . . . . . . . . . . . . . . . . . 33614.3Supplementary Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34015 NonparametricStatisticalAnalysis 34315.1The Analysis of a Single Population . . . . . . . . . . . . . . . . . . . . . . . . . 34315.2Comparing Two Populations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34715.3Comparing Three or More Populations. . . . . . . . . . . . . . . . . . . . . . . . 35015.4Supplementary Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35416 QualityControlMethods 35916.2Statistical Process Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35916.3Variable Control Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36116.4Attribute Control Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36316.5Acceptance Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36416.6Supplementary Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36517 ReliabilityAnalysisandLifeTesting 36717.1System Reliability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36717.2Modeling Failure Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36917.3Life Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37217.4Supplementary Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3746 CONTENTSChapter1ProbabilityTheory1.1 Probabilities1.1.1 S= {(head, head, head), (head, head, tail), (head, tail, head), (head, tail, tail),(tail, head, head), (tail, head, tail), (tail, tail, head), (tail, tail, tail)}1.1.2 S = {0 females, 1 female, 2 females, 3 females, . . . , n females}1.1.3 S= {0,1,2,3,4}1.1.4 S= {January 1, January 2, .... , February 29, .... , December 31}1.1.5 S= {(on time, satisfactory), (on time, unsatisfactory),(late, satisfactory), (late, unsatisfactory)}1.1.6 S= {(red, shiny), (red, dull), (blue, shiny), (blue, dull)}1.1.7 (a)p1p= 1p = 0.5(b)p1p= 2p =23(c) p = 0.25p1p=131.1.8 0.13 + 0.24 + 0.07 + 0.38 +P(V ) = 1P(V ) = 0.1878 CHAPTER1. PROBABILITYTHEOR