Introduction to probability and statistics : principles and applications for engineering and the computing sciences / J. Susan Milton, Jesse C. Arnold

Includes index

1. Introduction to probability and counting -- Interpreting probabilities -- Sample spaces and events -- Mutually exclusive events -- Permutations and combinations -- Counting permutations -- Counting combinations -- Permutations of indistinguishable objects -- 2. Some probability laws -- Axioms of probability -- The General Addition Rule -- Conditional probability -- Independence oft he multiplication rule -- The Multiplication Rule -- Bayes' theorem -- 3. Discrete distributions -- Random variables -- Discrete probability densities -- Cumulative distribution -- Expectation and distribution parameters -- Variance and standard deviation -- Geometric distribution and the moment generating function -- Geometric distribution -- Moment generating function -- Binomial distribution -- Negative binomial distribution -- Hypergeometric distribution -- Poisson distribution -- Simulating discrete distribution -- 4. Continuous distributions -- Continuous densities -- Cumulative distribution -- Uniform distribution -- Expectation and distribution parameters -- Gamma, exponential, and chi-squared distributions -- Gamma distribution -- Exponential distribution -- Chi-squared distribution -- Normal distribution -- Standard normal distribution -- Normal probability rule and Chebyshev's inequality -- Normal approximation to the binomial distribution -- Weibull distribution and reliability -- Reliability -- Reliability of series and parallel systems -- Transformation of variables -- Simulating a continuous distribution -- 5. Joint distributions -- Joint densities and independence -- Marginal distributions : discrete -- Joint and marginal distributions : continuous -- Independence -- Expectation and covariance -- Covariance -- Correlation -- Conditional densities and regression -- Curves of regression -- Transformation of variables -- 6. Descriptive statistics -- Random sampling -- Picturing the distribution -- Stem-and-leaf diagram -- Histograms and ogives -- Cumulative distribution plots (ogives) -- Sample statistics -- Location statistics -- Measures of variability -- Boxplots -- 7. Estimation -- Point estimation -- The method of moments and maximum likelihood -- Maximum likelihood estimators -- Functions of random variables -- Distribution of X -- Interval estimation and the central limit theorem -- Confidence interval on the mean : variance known -- Central limit theorem -- 8. Inferences on the mean and variance of a distribution -- Interval estimation of variability -- The T distribution -- Confidence interval on the mean : variance estimated -- Hypothesis testing -- Significance testing -- Hypothesis and significance tests on the mean -- Hypothesis tests on the variance -- Alternative nonparametric methods -- Sign test for median -- Wilcoxon signed-rank test

9. Inferences on proportions -- Estimating proportions -- Confidence interval on p -- Sample size for estimating p -- Testing hypotheses on a proportion -- Comparing two proportions : estimation -- Comparing two proportions : hypothesis testing -- Pooled proportions -- 10. Comparing two means and two variances -- Point estimation : independent samples -- Comparing variances : the F distribution -- Comparing means : variances equal (pooled test) -- Pooled T test -- Comparing means : variances unequal -- comparing means : paired data -- Paired T test -- Alternative nonparametric methods -- Wilcoxon rank-sum test -- Wilcoxon signed-rank test for paired observations -- 11. Simple linear regression and correlation -- Model and parameter estimation -- Description of the model -- Least-squares estimation -- Properties of least-squares estimators -- Summary of theoretical results -- Confidence interval estimation and hypothesis testing -- Inferences about slope -- Inferences about intercept -- Inferences about estimated mean -- Inferences about single predicted value -- Repeated measures and lack of fit -- Residual analysis -- Residual plots -- Checking for normality : stem-and-leaf plots and boxplots -- Correlation -- Interval estimation and hypothesis tests on p -- Coefficient of determination -- 12. Multiple linear regression models -- Least-squares procedures for model fitting -- Polynomial model of degree p -- Multiple linear regression model -- Matrix approach to least squares -- Normal equations -- Solving the normal equations -- Simple linear regression : matrix formulation -- Polynomial model : matrix formulation -- Properties of the least-squares estimators -- Interval estimation -- Confidence interval on coefficients -- Confidence interval on estimated mean -- Prediction interval on a single predicted response -- Testing hypotheses about model parameters -- Testing a single predictor variable -- Testing for significant regression -- Testing a subset of predictor variables Use of indicator or "dummy" variables -- Criteria for variable selection -- Forward selection method -- Backward elimination procedure -- Stepwise method -- Maximum R2 method -- Mallows Ck statistic -- PRESS statistic -- Model transformation and concluding remarks -- 13. Analysis of variance -- One-way classification fixed-effects model -- Comparing variances -- Pairwise comparisons -- Bonferroni T tests -- Duncan's multiple range test -- Tukey's test -- Testing contrasts -- Randomized complete block design -- Effectiveness of blocking -- Paired comparisons -- Latin squares -- Random-effects model -- One-way classification -- Design models in matrix form -- Alternative nonparametric methods -- Kruskal-Wallis test -- Friedman test -- 14. Factorial experiments -- Two-factor analysis of variance -- Extension to three factors -- Random and mixed model factorial experiments -- Random-effects model -- Mixed-effects model -- 2k factorial experiments -- Computational techniques : Yates method -- 2k factorial experiments in an incomplete block design -- Fractional factorial experiments -- 15. Categorical data -- Multinomial distribution -- Chi-squared goodness of fit tests -- Testing for independence -- r X c test for independence -- Comparing proportions -- r X c test for homogeneity -- Comparing proportions with paired data : McNemar's test -- 16. Statistical quality control -- Properties of control charts -- Monitoring means -- Distribution of run lengths -- Shewhart control charts for measurements -- Mean -- Range -- Shewhart control charts for attributes -- P chart (proportion defective) -- C charts (average number of defects) -- Tolerance limits -- Two-sided tolerance limits -- Assumed normal distribution -- One-sided tolerance limits -- Nonparametric tolerance interval -- Acceptance sampling -- Two-stage acceptance sampling -- Extensions in quality control -- Modifications of control charts -- Parameter design procedures -- Statistics tables