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Chapter 1: Special Continuous Random Variables

• 1.1. Normal (Gaussian) Distribution
• 1.2. Chi-square Distribution
• 1.3. T-student Distribution
• 1.4. Fisher Distribution
• 1.5. Continuous Uniform Distribution
• 1.6. Exponential Distribution
• 1.7. Gamma Distribution
• 1.8. Beta Distribution
• 1.9. Weibull Distribution
• 1.10. Cauchy Distribution
• 1.11. Laplace Distribution
• 1.12. Logistic Distribution

Chapter 2: Special Discrete Random Variables

• 2.1. Bernoulli Distribution
• 2.2. Binomial Distribution
• 2.3. Negative Binomial (Pascal) Distribution
• 2.4. Geometric Distribution
• 2.5. Poisson Distribution
• 2.6. Discrete Uniform Distribution
• 2.7. Hypergeometric Distribution

Chapter 3: Confidence Intervals

• 3.1. Confidence Interval for the Mean of a Normal Population
  • 3.1.1. Known Standard Deviation
  • 3.1.2. Unknown Standard Deviation
• 3.2. Confidence Interval for the Variance of a Normal Population
  • 3.2.1. Unknown Mean of the Population
  • 3.2.2. Known Mean of the Population
• 3.3. Confidence Interval for the Difference in Means of Two Normal Population
  • 3.3.1. Known Variances
  • 3.3.2. Unknown but Equal Variances
• 3.4. Confidence Interval for the Ratio of Variances of Two Normal Populations
• 3.5. Confidence Interval for the Mean of a Bernoulli Random Variable

Chapter 4: Parametric Hypothesis Testing

• 4.1. Introduction
• 4.2. Test Concerning the Mean of a Normal Population
  • 4.2.1. Known Standard Deviation
  • 4.2.2. Unknown Standard Deviation
• 4.3. Test Concerning the Equality of Means of Two Normal Populations
  • 4.3.1. Known Variances
  • 4.3.2. Unknown but Equal Variances
• 4.4. Paired t-test
• 4.5. Test Concerning the Variance of a Normal Population
• 4.6. Test Concerning the Equality of Variances of Two Normal Populations
• 4.7. Test Concerning P in Bernoulli Populations
• 4.8. Test Concerning the Equality of P in Two Bernoulli Populations

Chapter 5: Statistical Hypothesis Testing

• 5.1. Normality Tests
  • 5.1.1. Shapiro-Wilk Test
  • 5.1.2. D’Agostino’s Test
  • 5.1.3. Anderson-Darling Test
• 5.2. Correlation Tests
  • 5.2.1. Pearson’s Correlation Coefficient
  • 5.2.2. Spearman’s Rank Correlation
  • 5.2.3. Kendall’s Rank Correlation
  • 5.2.4. Chi-Squared Test
• 5.3. Stationary Tests
  • 5.3.1. Augmented Dickey-Fuller Unit Root Test
  • 5.3.2. Kwiatkowski-Phillips-Schmidt-Shin Test
• 5.4. Other Tests
  • 5.4.1. Mann-Whitney U-Test
  • 5.4.2. Wilcoxon Signed-Rank Test
  • 5.4.3. Kruskal-Wallis H Test
  • 5.4.4. Friedman Test

Chapter 6: Regression

• 6.1. Introduction
• 6.2. Least Squares Estimators of the Regression Parameters
• 6.3. Statistical Inferences about the Regression Parameters
  • 6.3.1. Inferences Concerning B
    • 6.3.1.1. Known Variance
    • 6.3.1.2. Unknown Variance
  • 6.3.2. Inferences Concerning A
    • 6.3.2.1. Unknown Variance
  • 6.3.3. T-tests for Regression Parameters with statsmodels
  • 6.3.4. F-statistic for Overall Significance in Regression
• 6.4. Confidence Intervals Concerning Regression Models
  • 6.4.1. Confidence Interval for B
    • 6.4.1.1. Known Variance
    • 6.4.1.2. Unknown Variance
  • 6.4.2. Confidence Interval for A
    • 6.4.2.1. Unknown Variance
  • 6.4.3. Confidence Interval for A+Bx
    • 6.4.3.1. Unknown Variance
  • 6.4.4. Prediction Interval of a Future Response
• 6.5. Residuals
  • 6.5.1. Regression Diagnostic
  • 6.5.2. Multicollinearity

Chapter 7: Analysis of Variance (ANOVA)

• 7.1. One-Way Analysis of Variance
  • 7.1.1. Equal Sample Sizes
  • 7.1.2. Unequal Sample Sizes
• 7.2. Two-Way Analysis of Variance