
Schaum's Outline of Probability and Statistics, 4th Edition
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Content
- Cover Page
- Schaum's Outline of Probability and Statistics, 4th Edition
- Copyright Page
- Preface to the Third Edition
- Preface to the Second Edition
- Preface to the First Edition
- Contents
- Part I Probability
- Chapter 1 Basic Probability
- Random Experiments
- Sample Spaces
- Events
- The Concept of Probability
- The Axioms of Probability
- Some Important Theorems on Probability
- Assignment of Probabilities
- Conditional Probability
- Theorems on Conditional Probability
- Independent Events
- Bayes' Theorem or Rule
- Combinatorial Analysis
- Fundamental Principle of Counting Tree Diagrams
- Permutations
- Combinations
- Binomial Coefficients
- Stirling's Approximation to n!
- Chapter 2 Random Variables and Probability Distributions
- Random Variables
- Discrete Probability Distributions
- Distribution Functions for Random Variables
- Distribution Functions for Discrete Random Variables
- Continuous Random Variables
- Graphical Interpretations
- Joint Distributions
- Independent Random Variables
- Change of Variables
- Probability Distributions of Functions of Random Variables
- Convolutions
- Conditional Distributions
- Applications to Geometric Probability
- Chapter 3 Mathematical Expectation
- Definition of Mathematical Expectation
- Functions of Random Variables
- Some Theorems on Expectation
- The Variance and Standard Deviation
- Some Theorems on Variance
- Standardized Random Variables
- Moments
- Moment Generating Functions
- Some Theorems on Moment Generating Functions
- Characteristic Functions
- Variance for Joint Distributions. Covariance
- Correlation Coefficient
- Conditional Expectation, Variance, and Moments
- Chebyshev's Inequality
- Law of Large Numbers
- Other Measures of Central Tendency
- Percentiles
- Other Measures of Dispersion
- Skewness and Kurtosis
- Chapter 4 Special Probability Distributions
- The Binomial Distribution
- Some Properties of the Binomial Distribution
- The Law of Large Numbers for Bernoulli Trials
- The Normal Distribution
- Some Properties of the Normal Distribution
- Relation Between Binomial and Normal Distributions
- The Poisson Distribution
- Some Properties of the Poisson Distribution
- Relation Between the Binomial and Poisson Distributions
- Relation Between the Poisson and Normal Distributions
- The Central Limit Theorem
- The Multinomial Distribution
- The Hypergeometric Distribution
- The Uniform Distribution
- The Cauchy Distribution
- The Gamma Distribution
- The Beta Distribution
- The Chi-Square Distribution
- Student's t Distribution
- The F Distribution
- Relationships Among Chi-Square, t, and F Distributions
- The Bivariate Normal Distribution
- Miscellaneous Distributions
- Part II Statistics
- Chapter 5 Sampling Theory
- Population and Sample. Statistical Inference
- Sampling With and Without Replacement
- Random Samples. Random Numbers
- Population Parameters
- Sample Statistics
- Sampling Distributions
- The Sample Mean
- Sampling Distribution of Means
- Sampling Distribution of Proportions
- Sampling Distribution of Differences and Sums
- The Sample Variance
- Sampling Distribution of Variances
- Case Where Population Variance Is Unknown
- Sampling Distribution of Ratios of Variances
- Other Statistics
- Frequency Distributions
- Relative Frequency Distributions
- Computation of Mean, Variance, and Moments for Grouped Data
- Chapter 6 Estimation Theory
- Unbiased Estimates and Efficient Estimates
- Point Estimates and Interval Estimates. Reliability
- Confidence Interval Estimates of Population Parameters
- Confidence Intervals for Means
- Confidence Intervals for Proportions
- Confidence Intervals for Differences and Sums
- Confidence Intervals for the Variance of a Normal Distribution
- Confidence Intervals for Variance Ratios
- Maximum Likelihood Estimates
- Chapter 7 Tests of Hypotheses and Significance
- Statistical Decisions
- Statistical Hypotheses. Null Hypotheses
- Tests of Hypotheses and Significance
- Type I and Type II Errors
- Level of Significance
- Tests Involving the Normal Distribution
- One-Tailed and Two-Tailed Tests
- P Value
- Special Tests of Significance for Large Samples
- Special Tests of Significance for Small Samples
- Relationship Between Estimation Theory and Hypothesis Testing
- Operating Characteristic Curves. Power of a Test
- Quality Control Charts
- Fitting Theoretical Distributions to Sample Frequency Distributions
- The Chi-Square Test for Goodness of Fit
- Contingency Tables
- Yates' Correction for Continuity
- Coefficient of Contingency
- Chapter 8 Curve Fitting, Regression, and Correlation
- Curve Fitting
- Regression
- The Method of Least Squares
- The Least-Squares Line
- The Least-Squares Line in Terms of Sample Variances and Covariance
- The Least-Squares Parabola
- Multiple Regression
- Standard Error of Estimate
- The Linear Correlation Coefficient
- Generalized Correlation Coefficient
- Rank Correlation
- Probability Interpretation of Regression
- Probability Interpretation of Correlation
- Sampling Theory of Regression
- Sampling Theory of Correlation
- Correlation and Dependence
- Chapter 9 Analysis of Variance
- The Purpose of Analysis of Variance
- One-Way Classification or One-Factor Experiments
- Total Variation. Variation Within Treatments. Variation Between Treatments
- Shortcut Methods for Obtaining Variations
- Linear Mathematical Model for Analysis of Variance
- Expected Values of the Variations
- Distributions of the Variations
- The F Test for the Null Hypothesis of Equal Means
- Analysis of Variance Tables
- Modifications for Unequal Numbers of Observations
- Two-Way Classification or Two-Factor Experiments
- Notation for Two-Factor Experiments
- Variations for Two-Factor Experiments
- Analysis of Variance for Two-Factor Experiments
- Two-Factor Experiments with Replication
- Experimental Design
- Chapter 10 Nonparametric Tests
- Introduction
- The Sign Test
- The Mann-Whitney U Test
- The Kruskal-Wallis H Test
- The H Test Corrected for Ties
- The Runs Test for Randomness
- Further Applications of the Runs Test
- Spearman's Rank Correlation
- Chapter 11 Bayesian Methods
- Subjective Probability
- Prior and Posterior Distributions
- Sampling From a Binomial Population
- Sampling From a Poisson Population
- Sampling From a Normal Population with Known Variance
- Improper Prior Distributions
- Conjugate Prior Distributions
- Bayesian Point Estimation
- Bayesian Interval Estimation
- Bayesian Hypothesis Tests
- Bayes Factors
- Bayesian Predictive Distributions
- Appendix A Mathematical Topics
- Special Sums
- Euler's Formulas
- The Gamma Function
- The Beta Function
- Special Integrals
- Appendix B Ordinates y of the Standard Normal Curve at z
- Appendix C Areas under the Standard Normal Curve from 0 to z
- Appendix D Percentile Values tp for Student's t Distribution with v Degrees of Freedom
- Appendix E Percentile Values ?2p for the Chi-Square Distribution with v Degrees of Freedom
- Appendix F 95th and 99th Percentile Values for the F Distribution with v1 v2, Degrees of Freedom
- Appendix G Values of e-?
- Appendix H Random Numbers
- Subject Index
- Index for Solved Problems
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