Introduction to Probability and Statistics for Engineers and Scientists

Höfundur: Sheldon M. Ross (Útgáfa: 6)
Introduction to Probability and Statistics for Engineers and Scientists

Kaup valmöguleikar

Introduction to Probability and Statistics for Engineers and Scientists, Sixth Edition, uniquely emphasizes how probability informs statistical problems, thus helping readers develop an intuitive understanding of the statistical procedures commonly used by practicing engineers and scientists. Utilizing real data from actual studies across life science, engineering, computing and business, this useful introduction supports reader comprehension through a wide variety of exercises and examples.

End-of-chapter reviews of materials highlight key ideas, also discussing the risks associated with the practical application of each material. In the new edition, coverage includes information on Big Data and the use of R. This book is intended for upper level undergraduate and graduate students taking a probability and statistics course in engineering programs as well as those across the biological, physical and computer science departments.

It is also appropriate for scientists, engineers and other professionals seeking a reference of foundational content and application to these fields. Provides the author’s uniquely accessible and engaging approach as tailored for the needs of Engineers and Scientists Features examples that use significant real data from actual studies across life science, engineering, computing and business Includes new coverage to support the use of R Offers new chapters on big data techniques.

Nánar um bókina

Útgefandi
Elsevier S & T
ISBN
9780128177471
Print ISBN
9780128243466
Format
Page Fidelity (PDF)
Útgáfa
6
Höfundar
Sheldon M. Ross
Tungumál
English
Útgefið
2020-09-11
Prent takmörkun á líftíma
10

Kaflar

  • 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