Schaum's Outline Of Theory and Problems of Probability and Statistics

Includes Index

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! --
Random Variables and Probability Distributions --
Random Variables --
Discrete Probability Distributions --
Distribution Functions for Random Variables --
Distribution Functions for Discete Random Variables --
Continuous Random Variables --
Graphical Intepretations --
Joint Distributions --
Independent Random Variables --
Change of Variables --
Probability Distributions of Functions of Random Variables --
Convolutions --
Conditional Distributions --
Applications to Geometric Probability --
Mathematical Expectation --
Definition of Mathematical Expectation --
Functions of Randem 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 --
Characteristics 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 --
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 Distribution --
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 --
Statistics --
Sampling Theory --
Population and Sample --
Statistical Interference --
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 --
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 --
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 --
Curve Fitting, Regression, and Correlation --
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 --
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 --
Nonparametric Tests --
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.

Helps to master probability and statistics. This guide includes chapters such as: Basic Probability; Random Variables and Probability Distributions; Mathematical Expectation; Special Probability