Probability and statistics for scientists and engineers / Rao V. Dukkipati
- Author
- Dukkipati, Rao V.
- Published
- Tunbridge Wells : New Academic Science, [2011]
- Copyright Date
- ©2011
- Physical Description
- xvii, 513 pages : illustrations ; 25 cm
- Contents
- Machine generated contents note: 1.Numerical Descriptive Measures -- 1.1.Introduction -- 1.1.1.Population and Sample -- 1.1.2.Types of Variables -- 1.1.3.Organising Data -- 1.1.3.1.Qualitative Data -- 1.1.3.2.Graphical Representation of Qualitative Data -- 1.1.3.3.Graphical Representation of Quantitative Data -- 1.2.Numerical Summary Measures -- 1.2.1.Measures of Central Tendency for Ungrouped Data -- 1.2.1.1.Mean for Ungrouped Data -- 1.2.1.2.Median -- 1.2.1.3.Mode -- 1.2.1.4.Empirical Relation among Mean, Median and Mode -- 1.2.2.Measures of Dispersion for Ungrouped Data -- 1.2.2.1.Range -- 1.2.2.2.Variance and Standard Deviation -- 1.2.3.Mean, Variance and Standard Deviation for Grouped Data -- 1.2.3.1.Mean for Grouped Data -- 1.2.3.2.Variance and Standard Deviation for Grouped Data -- 1.2.4.Measures of Position -- 1.2.4.1.Quartiles and Interquartile Range -- 1.2.4.2.Percentiles -- 1.2.4.3.Skewness and Kurtosis -- 1.2.4.4.Box-and-Whisker Plot -- 1.3.Summary -- Problems -- Review Questions -- State True or False -- Answers to State True or False -- 2.Probability -- 2.1.Experiment, Outcome and Sample Space -- 2.2.Simple and Composite Events -- 2.3.Axioms of Probability -- 2.4.Finite Probability Spaces -- 2.5.Infinite Probability Spaces -- 2.6.Properties of Probability -- 2.7.Venn Diagram -- 2.8.Probability Tree or Tree Diagram -- 2.9.Approaches to Probability -- 2.9.1.Classical Probability -- 2.9.2.Relative Frequency Concept of Probability -- 2.9.3.Subjective Probability -- 2.9.4.Marginal Probability -- 2.9.5.Conditional Probability -- 2.10.Mutually Exclusive Events -- 2.11.Independent and Dependent Events -- 2.12.Complementary Events -- 2.13.Intersection of Events and Multiplication Rule -- 2.13.1.Intersection of Events -- 2.13.2.Multiplication Rule -- 2.14.Union of Events and the Addition Rule -- 2.14.1.Union of Events -- 2.14.2.Addition Rule -- 2.15.Baye's Formula -- 2.16.Additional Examples and Solutions -- 2.17.Summary -- Problems -- Review Questions -- State True or False -- Answers to State True or False -- 3.Random Variables And Probability Distributions -- 3.1.Random Variables -- 3.1.1.Discrete Random Variables -- 3.1.2.Mean and Standard Deviation of a Discrete Random Variable -- 3.1.3.Continuous Random Variables -- 3.1.4.Mean and Variance for Continuous Random Variables -- 3.1.5.Expectation -- 3.2.Permutations and Combinations -- 3.2.1.Permutations -- 3.2.2.Combinations -- 3.3.Discrete Distributions -- 3.3.1.Hypergeometric Distribution -- 3.3.2.The Binomial Probability Distribution -- 3.3.3.The Binomial Experiment -- 3.3.4.The Binomial Formula -- 3.3.4.1.Binomial Theorem -- 3.3.4.2.Cumulative Terms for Binomial Distribution -- 3.3.4.3.Mean and Standard Deviation of Binomial Distribution -- 3.3.5.Poisson Distribution -- 3.3.5.1.Derivation from Binomial Distribution -- 3.3.5.2.Mean and Standard Deviation -- 3.4.Continuous Probability Distributions -- 3.4.1.The Normal Distribution -- 3.4.1.1.Properties of the Normal Distribution -- 3.4.1.2.Mean and Variance of the Normal Distribution -- 3.4.1.3.The Cumulative Normal Distribution -- 3.4.1.4.The Standard Normal Distribution -- 3.4.1.5.Problem-Solving Procedure -- 3.5.Approximating Probability Distributions -- 3.5.1.Binomial Approximation to the Hypergeometric -- 3.5.2.Poisson Approximation to the Binomial -- 3.5.3.Normal Approximation to the Binomial -- 3.5.4.Normal Approximation to the Poisson -- 3.6.Chebyshev's Theorem -- 3.7.Empirical Rule -- 3.8.The Central Limit Theorem -- Problems -- Review Questions -- State True or False -- Answers to State True or False -- 4.Sampling Distributions -- 4.1.Properties of Sample Mean and Variance -- 4.2.Population and Sampling Distributions -- 4.2.1.Population Distribution -- 4.2.2.Sampling Distribution -- 4.3.Sampling and Nonsampling Errors -- 4.4.Mean and Standard Deviation of -- 4.5.Shape of the Sampling Distribution of x -- 4.5.1.Sampling from a Normally Distributed Population -- 4.5.2.Sampling from a Population that is not Normally Distributed -- 4.6.Applications of the Sampling Distribution of x -- 4.7.Population and Sample Proportions -- 4.8.Sampling Distribution of p -- 4.9.Mean and Standard Deviation of p -- 4.10.The Chi-square Distribution -- 4.11.The t-Distribution -- 4.12.The F-Distribution -- 4.13.Summary -- Problems -- Review Questions -- State True or False -- Answers to State True or False -- 5.Estimation -- 5.1.Point Estimation -- 5.2.Interval Estimation -- 5.3.Confidence Interval on Mean, Variance Known -- 5.4.Confidence Interval on the Mean of a Normal Distribution, Variance Unknown -- 5.5.Confidence Interval on the Variance of a Normal Distribution -- 5.6.Confidence Interval on a Population Proportion -- 5.7.Confidence Interval on the Difference in Two Means, Variance Known -- 5.8.Confidence Interval on the Difference in Means of Two Normal Distributions, Variances Unknown -- 5.9.Confidence Interval on μ1 - μ2 for Paired Observations -- 5.10.Confidence Interval on the Ratio of Variance of Two Normal Distributions -- 5.11.Confidence Interval on the Difference in Two Proportions -- 5.12.Sample Size Selection -- 5.12.1.Sample Size Selection for Estimating Population Mean -- 5.12.2.Sample Size for the Estimation of Proportion -- 5.13.Summary -- Problems -- Review Questions -- State True or False -- Answers to State True or False -- 6.Hypothesis Testing -- 6.1.Null Hypothesis and Alternative Hypothesis -- 6.2.The Critical Region -- 6.3.Types of Sampling Error (Type I and Type II Errors) -- 6.4.Level of Significance -- 6.5.Tails of a Test -- 6.6.Hypothesis Test on the Population Mean, Standard Deviation Known -- 6.7.Hypothesis Test on the Population Mean, Standard Deviation Unknown -- 6.8.Hypothesis Test for a Population Variance -- 6.9.Hypothesis Test on a Population Proportion -- 6.10.Hypothesis Test on Equality of Two Means, Variances Known -- 6.11.Hypothesis Test on the Means of Two Normal Distributions, Variances Unknown -- 6.11.1.Case 1: σ2 1 = σ2 2 = σ2 -- 6.11.2.Case 2: σ2 1 [≠] σ2 2 -- 6.12.Hypothesis Test to Compare Two Population Means (Paired t-test) -- 6.13.Hypothesis Test on the Equality of Two Variances -- 6.14.Hypothesis Test on Two Proportions -- 6.15.Summary -- Problems -- Review Questions -- State True or False -- Answers to State True or False -- 7.Curve Fitting, Regression And Correlation -- 7.1.Linear Equation -- 7.2.Curve Fitting with a Linear Equation -- 7.3.Criteria for a "Best" Fit -- 7.4.Linear Least-Squares Regression -- 7.5.Linear Regression Analysis -- 7.6.Interpretation of a and b -- 7.7.Standard Deviation of Random Errors -- 7.8.Coefficient of Determination -- 7.9.Sampling Distribution of b -- 7.10.Hypothesis Testing about B -- 7.11.Linear Correlation -- 7.12.Estimating the Mean Value of y -- 7.13.Estimating a Particular Value of y -- 7.14.Linearization of Nonlinear Relationship -- 7.15.Polynomial Regression -- 7.16.Quantification of Error of Linear Regression -- 7.17.Multiple Linear Regression -- 7.18.Weighted Least-Squares Method -- 7.19.Orthogonal Polynomials and Least Squares Approximation -- 7.20.Least-Squares Method for Continuous Data -- 7.21.Approximation using Orthogonal Polynomials -- 7.22.Gram-Schmidt Orthogonalization Process -- 7.23.Additional Example Problems and Solutions -- 7.24.Summary -- Problems -- Review Questions -- State True or False -- Answers to State True or False -- 8.Chi-Square Tests -- 8.1.Introduction -- 8.2.A Goodness-of-Fit Test -- 8.3.Contingency Table -- 8.4.A Test of Independence or Homogeneity -- 8.5.Inferences about the Population Variance -- 8.6.Estimation of the Population Variance -- 8.7.Hypothesis Tests about the Population Variance -- Problems -- Review Questions -- State True or False -- Answers to State True or False -- 9.Analysis Of Variance -- 9.1.Introduction -- 9.2.One-way Analysis of Variance -- 9.3.Test Statistic -- 9.4.One-way ANOVA Test -- Problems -- Review Questions -- State True or False -- Answers to State True or False -- APPENDICES -- Appendix-A.Values for n Factorial -- Appendix-B.Binomial Coefficients -- Appendix-C.Table of Binomial Probablities -- Appendix-D.Cumulative Poisson Distibutions -- Appendix-E.Cumulative Standard Nornal Distribution -- Appendix-F.chi-square Distribution Table -- Appendix-G.The t-Distribution Table -- Appendix-H.The F-Distribution Table -- Appendix-I.Cramer's Rule.
- Subject(s)
- ISBN
- 9781906574833 (pbk.)
1906574839 (pbk.) - Note
- AUTH: FAIRFIELD UNIVERSITY. TEXTBOOK--ADV. UNDERGRAD.
- Bibliography Note
- Includes bibliographical references.
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