MATHEMATICAL STATISTICS

I. Probability1. Sample Space2. Events3. Counting Sample Points4. Probability of an Event5. Additive Rules6. Conditional Probability, Independence, and the Product Rule7. Bayes Rule

II. Random Variables and Probability Distribution1. Concept of a Random Variable2. Discrete Probability Distributions3. Continuous Probability Distributions4. Joint Probability Distributions

III. Mathematical Expectation1. Mean of a Random Variable2. Variance and Covariance of Random Variables3. Means and Linear Combinations of Random Variables4. Chebyshevs Theorem

IV. Discrete Probability Distributions1. Binomial and Multinomial Distributions2. Hypergeometric Distribution3. Negative and Geometric Distributions4. Poisson Distribution and the Poisson Process

V. Continuous Probability Distributions1. Continuous Uniform Distribution2. Normal Distribution3. Areas Under the Normal Curve4. Applications of the Normal Distribution5. Gamma and Exponential Distributions6. Chi-Squared Distribution7. Beta-Distribution8. Lognormal Distribution

VI. Sampling Distributions and Data Distributions1. Random Sampling2. Sampling Distributions3. Sampling Distribution of Means and the Central Limit Theorem4. Sampling Distribution of S25. t-Distribution6. F-Distribution

VII. One- and Two-Sample Estimation Problems1. Introduction2. Statistical Inference3. Classical Methods of Estimation4. Single Sample: Estimating the Mean5. Standard Error of a Point Estimate6. Prediction Intervals7. Two Samples: Estimating the Difference between Two Means8. Paired Observations9. Single Sample: Estimating a Proportion10. Estimating the Difference between Two Proportions11. Single Sample: Estimating the Variance12. Two Samples: Estimating the Ratio of Two Variances

VIII. One- and Two-Sample Tests of Hypothesis1. Statistical Hypothesis: General Concepts2. Testing a Statistical Hypothesis3. The Use of P-Values4. Single Sample: Tests Concerning a Single Mean5. Two Samples: Tests on Two Means6. Choice of Sample Size for Testing Means7. One Sample: Test on a Single Proportion8. Two Samples: Tests on Two Proportions9. One- and Two-Sample Tests Concerning Variance10. Goodness-of-Fit Test

IX. Simple Linear Regression and Correlation1. Introduction to Linear Regression2. The Simple Linear Regression Model3. Least Squares and the Fitted Model4. Properties of the Least Squares Estimators5. Inference Concerning the Regression Coefficients6. Prediction7. Analysis-of-Variance Approach8. Tests of Linearity of Regression9. Correlation

X. Multiple Linear Regression1. Introduction2. Estimating the Coefficients3. Linear Regression Model Using Matrices4. Properties of the Least Squares Estimators5. Inferences in Multiple Linear Regression

XI. One-Factor Experiments: General1. Analysis-of-Variance Technique2. One-Way ANOVA: Completely Randomized Design3. Tests for the Equality of Several Variances4. Single-Degree-of-Freedom Comparisons5. Multiple Comparisons6. Comparing a Set of Treatments in Blocks7. Randomized Complete Block Designs

XII. Factorial Experiments (Two or More Factors)1. Introduction2. Interaction in the Two-Factor Experiment3. Two-Factor Analysis of Variance4. Three-Factor Experiments5. 2k Factorial Experiments

XIII. Nonparametric Statistics1. Nonparametric Tests2. Signed-Rank Test3. Wicoxon Rank-Sum Test4. Kruskal-Wallis Test5. Runs Test6. Rank Correlation Coefficient

Reference: Probability and Statistics for Engineers (9th Ed.) by Walpole, Myers, Myers, etc.