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Probability | |

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Basic Probability | |

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Random Experiments | |

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Sample Spaces | |

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Events | |

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The Concept of Probability | |

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The Axioms of Probability | |

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Some Important Theorems on Probability | |

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Assignment of Probabilities Conditional Probability | |

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Theorems on Conditional Probability | |

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Independent Events Bayes' Theorem or Rule | |

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Combinatorial Analysis | |

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Fundamental Principle of Counting Tree Diagrams | |

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Permutations | |

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Combinations-' Binomial Coefficients | |

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Stirling's Approximation to n! | |

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Random Variables and Probability Distributions | |

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Random Variables | |

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Discrete Probability Distributions | |

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Distribution Functions for Random Variables | |

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Distribution Functions for Discrete Random Variables | |

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Continuous Random Variables | |

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Graphical Interpretations | |

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Joint Distributions | |

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Independent Random Variables Change of Variables | |

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Probability Distributions of Functions of Random Variables | |

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Convolutions | |

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Conditional Distributions | |

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Applications to Geometric Probability | |

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Mathematical Expectation | |

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Definition of Mathematical Expectation | |

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Functions of Random Variables | |

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Some Theorems on Expectation | |

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The Variance and Standard Deviation | |

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Some Theorems on Variance | |

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Standardized Random Variables | |

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Moments | |

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Moment Generating Functions | |

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Some Theorems on Moment Generating Functions | |

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Characteristic Functions | |

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Variance for Joint Distributions. Covariance | |

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Correlation Coefficient | |

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Conditional Expectation, Variance, and Moments Chebyshev's Inequality | |

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Law of Large Numbers | |

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Other Measures of Central Tendency Percentiles | |

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Other Measures of Dispersion | |

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Skewness and Kurtosis | |

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Special Probability Distributions | |

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The Binomial Distribution | |

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Some Properties of the Binomial Distribution | |

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The Law of Large Numbers for Bernoulli Trials | |

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The Normal Distribution | |

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Some Properties of the Normal Distribution | |

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Relation Between Binomial and Normal Distributions | |

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The Poisson Distribution | |

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Some Properties of the Poisson Distribution | |

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Relation Between the Binomial and Poisson Distributions | |

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Relation Between the Poisson and Normal Distributions | |

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The Central Limit Theorem | |

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The Multinomial Distribution | |

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The Hypergeometric Distribution | |

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The Uniform Distribution | |

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The Cauchy Distribution | |

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The Gamma Distribution | |

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The Beta Distribution | |

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The Chi-Square Distribution | |

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Student's t Distribution | |

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The F Distribution | |

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Relationships Among Chi-Square, t, and F Distributions | |

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The Bivariate Normal Distribution Miscellaneous Distributions | |

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Statistics | |

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Sampling Theory | |

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Population and Sample. Statistical Inference | |

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Sampling With and Without Replacement Random Samples. Random Numbers | |

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Population Parameters | |

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Sample Statistics Sampling Distributions | |

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The Sample Mean | |

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Sampling Distribution of Means | |

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Sampling Distribution of Proportions | |

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Sampling Distribution of Differences and Sums | |

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The Sample Variance | |

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Sampling Distribution of Variances | |

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Case Where Population Variance Is Unknown | |

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Sampling Distribution of Ratios of Variances | |

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Other Statistics | |

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Frequency Distributions | |

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Relative Frequency Distributions | |

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Computation of Mean, Variance, and Moments for Grouped Data | |

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Estimation Theory | |

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Unbiased Estimates and Efficient Estimates | |

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Point Estimates and Interval Estimates. Reliability | |

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Confidence Interval Estimates of Population Parameters | |

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Confidence Intervals for Means | |

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Confidence Intervals for Proportions Confidence Intervals for Differences and Sums | |

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Confidence Intervals for the Variance of a Normal Distribution | |

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Confidence Intervals for Variance Ratios | |

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Maximum Likelihood Estimates | |

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Tests of Hypotheses and Significance | |

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Statistical Decisions | |

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Statistical Hypotheses. Null Hypotheses | |

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Tests of Hypotheses and Significance | |

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Type I and Type II Errors | |

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Level of Significance | |

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Tests Involving the Normal Distribution | |

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One-Tailed and Two-Tailed Tests | |

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P Value | |

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Special Tests of Significance for Large Samples | |

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Special Tests of Significance for Small Samples | |

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Relationship Between Estimation Theory and Hypothesis Testing | |

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Operating Characteristic Curves. Power of a Test Quality Control Charts | |

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Fitting Theoretical Distributions to Sample Frequency Distributions The Chi-Square Test for Goodness of Fit | |

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Contingency Tables | |

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Yates' Correction for Continuity | |

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Coefficient of Contingency | |

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Curve Fitting, Regression, and Correlation | |

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Curve Fitting | |

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Regression | |

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The Method of Least Squares | |

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The Least-Squares Line | |

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The Least-Squares Line in Terms of Sample Variances and Covariance | |

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The Least-Squares Parabola | |

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Multiple Regression | |

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Standard Error of Estimate | |

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The Linear Correlation Coefficient | |

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Generalized Correlation Coefficient | |

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Rank Correlation | |

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Probability Interpretation of Regression | |

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Probability Interpretation of Correlation | |

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Sampling Theory of Regression Sampling Theory of Correlation | |

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Correlation and Dependence | |

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Analysis of Variance | |

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The Purpose of Analysis of Variance | |

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One-Way Classification or One-Factor Experiments Total Variation. Variation Within Treatments. Variation Between Treatments Shortcut Methods for Obtaining Variations | |

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Linear Mathematical Model for Analysis of Variance | |

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Expected Values of the Variations | |

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Distributions of the Variations | |

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The F Test for the Null Hypothesis of Equal Means | |

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Analysis of Variance Tables Modifications for Unequal Numbers of Observations Two-Way Classification or Two-Factor Experiments | |

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Notation for Two-Factor Experiments | |

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Variations for Two-Factor Experiments | |

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Analysis of Variance for Two-Factor Experiments | |

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Two-Factor Experiments with Replication | |

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Experimental Design | |

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Nonparametric Tests | |

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Introduction | |

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The Sign Test | |

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The Mann-Whitney U Test | |

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The Kruskal-Wallis H Test | |

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The H Test Corrected for Ties | |

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The Runs Test for Randomness | |

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Further Applications of the Runs Test | |

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Spearman's Rank Correlation | |

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Bayesian Methods | |

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Subjective Probability | |

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Prior and Posterior Distributions | |

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Sampling From a Binomial Population | |

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Sampling From a Poisson Population | |

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Sampling From a Normal Population with Known Variance | |

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Improper Prior Distributions | |

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Conjugate Prior Distributions | |

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Bayesian Point Estimation | |

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Bayesian Interval Estimation | |

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Bayesian Hypothesis Tests | |

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Bayes Factors | |

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Bayesian Predictive Distributions | |

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Mathematical Topics | |

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Special Sums | |

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Euler's Formulas | |

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The Gamma Function | |

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The Beta Function | |

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Special Integrals | |

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Ordinates y of the Standard Normal Curve at z | |

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Areas under the Standard Normal Curve from 0 to z | |

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Percentile Values t<sub>p</sub> for Student's t Distribution with v Degrees of Freedom | |

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Percentile Values x<sub>p</sub></sup>2</sup> for the Chi-Square Distribution with v Degrees of Freedom | |

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95th and 99th Percentile Values for the F Distribution with v<sub>1</sub> v<sub>2</sub> Degrees of Freedom | |

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Values of e<sup>-ï¿½</sup> | |

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Random Numbers | |

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Subject Index | |

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Index for Solved Problems | |