Efnisyfirlit

• Introduction to Probability and Statistics for Engineers and Scientists
• Copyright
• Contents
• Preface
• Organization and coverage
• Preface
• Acknowledgments
• 1 Introduction to statistics
• 1.1 Introduction
• 1.2 Data collection and descriptive statistics
• 1.3 Inferential statistics and probability models
• 1.4 Populations and samples
• 1.5 A brief history of statistics
• Problems
• 2 Descriptive statistics
• 2.1 Introduction
• 2.2 Describing data sets
• 2.2.1 Frequency tables and graphs
• 2.2.2 Relative frequency tables and graphs
• 2.2.3 Grouped data, histograms, ogives, and stem and leaf plots
• 2.3 Summarizing data sets
• 2.3.1 Sample mean, sample median, and sample mode
• Germ-Free Mice
• Conventional Mice
• 2.3.2 Sample variance and sample standard deviation
• An algebraic identity
• 2.3.3 Sample percentiles and box plots
• 2.4 Chebyshev’s inequality
• Chebyshev’s inequality
• The one-sided Chebyshev inequality
• 2.5 Normal data sets
• The empirical rule
• 2.6 Paired data sets and the sample correlation coefficient
• Properties of r
• 2.7 The Lorenz curve and Gini index
• 2.8 Using R
• Problems
• 3 Elements of probability
• 3.1 Introduction
• 3.2 Sample space and events
• 3.3 Venn diagrams and the algebra of events
• 3.4 Axioms of probability
• 3.5 Sample spaces having equally likely outcomes
• Basic principle of counting
• Proof of the Basic Principle
• Notation and terminology
• 3.6 Conditional probability
• 3.7 Bayes’ formula
• 3.8 Independent events
• Problems
• 4 Random variables and expectation
• 4.1 Random variables
• 4.2 Types of random variables
• 4.3 Jointly distributed random variables
• 4.3.1 Independent random variables
• 4.3.2 Conditional distributions
• 4.4 Expectation
• Remarks
• 4.5 Properties of the expected value
• 4.5.1 Expected value of sums of random variables
• 4.6 Variance
• Remark
• Remark
• 4.7 Covariance and variance of sums of random variables
• 4.8 Moment generating functions
• 4.9 Chebyshev’s inequality and the weak law of large numbers
• Problems
• 5 Special random variables
• 5.1 The Bernoulli and binomial random variables
• 5.1.1 Using R to calculate binomial probabilities
• 5.2 The Poisson random variable
• 5.2.1 Using R to calculate Poisson probabilities
• 5.3 The hypergeometric random variable
• 5.4 The uniform random variable
• 5.5 Normal random variables
• 5.6 Exponential random variables
• 5.6.1 The Poisson process
• 5.6.2 The Pareto distribution
• 5.7 The gamma distribution
• 5.8 Distributions arising from the normal
• 5.8.1 The chi-square distribution
• 5.8.1.1 The relation between chi-square and gamma random variables
• 5.8.2 The t-distribution
• 5.8.3 The F-distribution
• 5.9 The logistics distribution
• 5.10 Distributions in R
• Problems
• 6 Distributions of sampling statistics
• 6.1 Introduction
• 6.2 The sample mean
• 6.3 The central limit theorem
• 6.3.1 Approximate distribution of the sample mean
• 6.3.2 How large a sample is needed?
• 6.4 The sample variance
• 6.5 Sampling distributions from a normal population
• 6.5.1 Distribution of the sample mean
• 6.5.2 Joint distribution of X and S2
• 6.6 Sampling from a finite population
• Remark
• Problems
• 7 Parameter estimation
• 7.1 Introduction
• 7.2 Maximum likelihood estimators
• 7.2.1 Estimating life distributions
• 7.3 Interval estimates
• Remark
• 7.3.1 Confidence interval for a normal mean when the variance is unknown
• Remarks
• 7.3.2 Prediction intervals
• 7.3.3 Confidence intervals for the variance of a normal distribution
• 7.4 Estimating the difference in means of two normal populations
• Remark
• 7.5 Approximate confidence interval for the mean of a Bernoulli random variable
• Remark
• 7.6 Confidence interval of the mean of the exponential distribution
• 7.7 Evaluating a point estimator
• 7.8 The Bayes estimator
• Remark
• Remark: On choosing a normal prior
• Problems
• 8 Hypothesis testing
• 8.1 Introduction
• 8.2 Significance levels
• 8.3 Tests concerning the mean of a normal population
• 8.3.1 Case of known variance
• Remark
• 8.3.1.1 One-sided tests
• Remark
• Remarks
• 8.3.2 Case of unknown variance: the t-test
• 8.4 Testing the equality of means of two normal populations
• 8.4.1 Case of known variances
• 8.4.2 Case of unknown variances
• 8.4.3 Case of unknown and unequal variances
• 8.4.4 The paired t-test
• 8.5 Hypothesis tests concerning the variance of a normal population
• 8.5.1 Testing for the equality of variances of two normal populations
• 8.6 Hypothesis tests in Bernoulli populations
• 8.6.1 Testing the equality of parameters in two Bernoulli populations
• 8.7 Tests concerning the mean of a Poisson distribution
• 8.7.1 Testing the relationship between two Poisson parameters
• Problems
• 9 Regression
• 9.1 Introduction
• 9.2 Least squares estimators of the regression parameters
• 9.3 Distribution of the estimators
• Remarks
• Notation
• Computational identity for SSR
• 9.4 Statistical inferences about the regression parameters
• 9.4.1 Inferences concerning β
• Hypothesis test of H0: β= 0
• Confidence interval for β
• Remark
• 9.4.1.1 Regression to the mean
• 9.4.2 Inferences concerning α
• Confidence interval estimator of α
• 9.4.3 Inferences concerning the mean response α+βx0
• Confidence interval estimator of α+βx0
• 9.4.4 Prediction interval of a future response
• Prediction interval for a response at the input level x0
• Remarks
• 9.4.5 Summary of distributional results
• 9.5 The coefficient of determination and the sample correlation coefficient
• 9.6 Analysis of residuals: assessing the model
• 9.7 Transforming to linearity
• 9.8 Weighted least squares
• Remarks
• Remarks
• 9.9 Polynomial regression
• Remark
• 9.10 Multiple linear regression
• Remark
• Remark
• 9.10.1 Predicting future responses
• Confidence interval estimate of E [ Y|x] =∑ ki=0xiβi, (x 0≡ 1)
• Prediction Interval for Y(x)
• 9.10.2 Dummy variables for categorical data
• 9.11 Logistic regression models for binary output data
• Problems
• 10 Analysis of variance
• 10.1 Introduction
• 10.2 An overview
• 10.3 One-way analysis of variance
• The sum of squares identity
• 10.3.1 Using R to do the computations
• 10.3.2 Multiple comparisons of sample means
• 10.3.3 One-way analysis of variance with unequal sample sizes
• Remark
• 10.4 Two-factor analysis of variance: introduction and parameter estimation
• 10.5 Two-factor analysis of variance: testing hypotheses
• 10.6 Two-way analysis of variance with interaction
• Problems
• 11 Goodness of fit tests and categorical data analysis
• 11.1 Introduction
• 11.2 Goodness of fit tests when all parameters are specified
• Remarks
• 11.2.1 Determining the critical region by simulation
• Remarks
• 11.3 Goodness of fit tests when some parameters are unspecified
• 11.4 Tests of independence in contingency tables
• 11.5 Tests of independence in contingency tables having fixed marginal totals
• 11.6 The Kolmogorov-Smirnov goodness of fit test for continuous data
• Problems
• 12 Nonparametric hypothesis tests
• 12.1 Introduction
• 12.2 The sign test
• 12.3 The signed rank test
• 12.4 The two-sample problem
• 12.4.1 Testing the equality of multiple probability distributions
• 12.5 The runs test for randomness
• Problems
• 13 Quality control
• 13.1 Introduction
• 13.2 Control charts for average values: the x control chart
• Remarks
• 13.2.1 Case of unknown μ and σ
• Technical remark
• Remarks
• 13.3 S-control charts
• 13.4 Control charts for the fraction defective
• Remark
• 13.5 Control charts for number of defects
• 13.6 Other control charts for detecting changes in the population mean
• 13.6.1 Moving-average control charts
• 13.6.2 Exponentially weighted moving-average control charts
• 13.6.3 Cumulative sum control charts
• Problems
• 14 Life testing
• 14.1 Introduction
• 14.2 Hazard rate functions
• Remark on terminology
• 14.3 The exponential distribution in life testing
• 14.3.1 Simultaneous testing – stopping at the rth failure
• Remark
• 14.3.2 Sequential testing
• 14.3.3 Simultaneous testing – stopping by a fixed time
• Remark
• 14.3.4 The Bayesian approach
• Remark
• 14.4 A two-sample problem
• 14.5 The Weibull distribution in life testing
• 14.5.1 Parameter estimation by least squares
• Remarks
• Problems
• 15 Simulation, bootstrap statistical methods, and permutation tests
• 15.1 Introduction
• 15.2 Random numbers
• 15.2.1 The Monte Carlo simulation approach
• 15.3 The bootstrap method
• 15.4 Permutation tests
• 15.4.1 Normal approximations in permutation tests
• 15.4.2 Two-sample permutation tests
• 15.5 Generating discrete random variables
• 15.6 Generating continuous random variables
• 15.6.1 Generating a normal random variable
• 15.7 Determining the number of simulation runs in a Monte Carlo study
• Problems
• 16 Machine learning and big data
• 16.1 Introduction
• 16.2 Late flight probabilities
• 16.3 The naive Bayes approach
• 16.3.1 A variation of naive Bayes approach
• 16.4 Distance-based estimators. The k-nearest neighbors rule
• 16.4.1 A distance-weighted method
• 16.4.2 Component-weighted distances
• 16.5 Assessing the approaches
• 16.6 When characterizing vectors are quantitative
• 16.6.1 Nearest neighbor rules
• 16.6.2 Logistics regression
• 16.7 Choosing the best probability: a bandit problem
• Remarks
• Problems
• Appendix of Tables
• Index
• Back Cover