Probability and statistics

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Author Notes

John J. Schiller is an associate professor of mathematics at Temple University. He received his Ph.D. at the University of Pennsylvania.

R. Alu Srinivasan is a professor of mathematics at Temple University. He received his Ph.D. at Wayne State University and has published extensively in probability and statistics.

Murray R. Spiegel (deceased) received the M.S. degree in physics and the Ph.D. in mathematics from Cornell University. He had positions at Harvard University, Columbia University, Oak Ridge and Rensselaer Polytechnic Institute, and served as a mathematical consultant at several large companies. His last position was professor and chairman of Mathematics at the Rensselaer Polytechnic Institute, Hartford Graduate Center.

Part I Probability	p. 1
Chapter 1 Basic Probability	p. 3
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	p. 34
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	p. 75
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	p. 108
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	p. 151
Chapter 5 Sampling Theory	p. 153
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	p. 195
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	p. 213
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	p. 265
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	p. 314
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	p. 348
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	p. 372
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	p. 411
Special Sums
Euler's Formulas
The Gamma Function
The Beta Function
Special Integrals
Appendix B Ordinates y of the Standard Normal Curve at z	p. 413
Appendix C Areas under the Standard Normal Curve from 0 to z	p. 414
Appendix D Percentile Values t p for Student's t Distribution with v Degrees of Freedom	p. 415
Appendix E Percentile Values x p 2 for the Chi-Square Distribution with v Degrees of Freedom	p. 416
Appendix F 95th and 99th Percentile Values for the F Distribution with v 1 v 2 Degrees of Freedom	p. 417
Appendix G Values of e -¿	p. 419
Appendix H Random Numbers	p. 419
Subject Index	p. 420
Index for Solved Problems	p. 423

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