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CITATION

Schiller, John J.; Srinivasan, R. Alu; and Spiegel, Murray R. Schaum's Outline of Probability and Statistics, 3/E. McGraw-Hill, 2008.

Schaum's Outline of Probability and Statistics, 3/E

Authors: John J. Schiller, R. Alu Srinivasan and Murray R Spiegel

Published:  August 2008

eISBN: 9780071544269 0071544267 | ISBN: 9780071544252
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  • 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 t[sub(p)] for Student’s Distribution with ν Degrees of Freedom
  • Appendix E: Percentile Values χ[sup(2)][sub(p)] for the Chi-Square Distribution with ν Degrees of Freedom
  • Appendix F: 95th and 99th Percentile Values for the F Distribution with ν[sub(1)], ν[sub(2)] Degrees of Freedom
  • Appendix G: Values of e[sup(–&#955)]
  • Appendix H: Random Numbers
  • Subject Index
  • A
  • B
  • C
  • D
  • E
  • F
  • G
  • H
  • I
  • J
  • K
  • L
  • M
  • N
  • O
  • P
  • Q
  • R
  • S
  • T
  • U
  • V
  • W
  • Y
  • Z
  • Index for Solved Problems
  • B
  • C
  • D
  • E
  • F
  • G
  • H
  • I
  • J
  • K
  • L
  • M
  • N
  • O
  • P
  • Q
  • R
  • S
  • T
  • U
  • V
  • W