![[Probability and Statistical Inference (Hogg - 2020) - Cover.png]] ## 1 Probability - 1.1 [[Properties of Probability]] - 1.2 [[Methods of Enumeration]] - 1.3 [[Conditional Probability]] - 1.4 [[Independent Events]] - 1.5 [[Bayes' Theorem]] ## 2 Discrete Distributions - 2.1 [[Random Variable]]s of the Discrete Type - 2.2 [[Mathematical Expectation]] - 2.3 Special [[Mathematical Expectation]]s - 2.4 The [[Binomial Distribution]] - 2.5 The [[Hypergeometric Distribution]] - 2.6 The [[Negative Binomial Distribution]] - 2.7 The [[Poisson Distribution]] ## 3 Continuous Distributions - 3.1 [[Random Variable]]s of the Continuous Type - 3.2 The [[Exponential Distribution|Exponential]], [[Gamma Distribution|Gamma]], and [[Chi-Square Distribution]]s - 3.3 The [[Normal Distribution]] - 3.4 Additional Models ## 4 Bivariate Distributions - 4.1 [[Bivariate Distribution]]s of the Discrete Type - 4.2 The [[Correlation Coefficient]] - 4.3 [[Conditional Distribution]]s - 4.4 [[Bivariate Distribution]]s of the Continuous Type - 4.5 The [[Bivariate Normal Distribution]] ## 5 Distributions of Functions of Random Variables - 5.1 Functions of One [[Random Variable]] - 5.2 [[Transformation]]s of Two [[Random Variable]]s - 5.3 Several Independent [[Random Variable]]s - 5.4 The [[Moment-Generating Function]] Technique - 5.5 [[Random Variable|Random Functions]] Associated with [[Normal Distribution]]s - 5.6 The [[Central Limit Theorem]] - 5.7 Approximations for Discrete Distributions - 5.8 [[Chebyshev's Inequality]] and [[Convergence in Probability]] - 5.9 Limiting [[Moment-Generating Function]]s ## 6 Point Estimation - 6.1 [[Descriptive Statistics]] - 6.2 [[Exploratory Data Analysis]] - 6.3 [[Order Statistics]] - 6.4 [[Maximum Likelihood Estimation|Maximum Likelihood]] and [[Method of Moments]] Estimation - 6.5 A Simple [[Regression]] Problem - 6.6 [[Asymptotic Distribution]]s of [[Maximum Likelihood Estimator]]s - 6.7 [[Sufficient Statistics]] - 6.8 [[Bayesian Estimation]] ## 7 Interval Estimation - 7.1 [[Confidence Interval]]s for Means - 7.2 [[Confidence Interval]]s for the Difference of Two Means - 7.3 [[Confidence Interval]]s for Proportions - 7.4 [[Sample Size]] - 7.5 [[Distribution-Free]] [[Confidence Interval]]s for [[Percentile]]s - 7.6 More [[Regression]] - 7.7 [[Resampling Methods]] ## 8 Tests of Statistical Hypotheses - 8.1 Tests About One Mean - 8.2 Tests of the Equality of Two Means - 8.3 Tests for [[Variance]]s - 8.4 Tests About [[Proportion]]s - 8.5 Some [[Distribution-Free Test]]s - 8.6 [[Power of a Statistical Test]] - 8.7 [[Best Critical Region]]s - 8.8 [[Likelihood Ratio Test]]s ## 9 More Tests - 9.1 [[Chi-Square Goodness-of-Fit Test]]s - 9.2 [[Contingency Table]]s - 9.3 [[One-Factor Analysis of Variance]] - 9.4 [[Two-Way Analysis of Variance]] - 9.5 General [[Factorial Design|Factorial]] and [[2^k Factorial Design]]s - 9.6 Tests Concerning [[Regression]] and [[Correlation]] - 9.7 [[Statistical Quality Control]] ## Appendices - A References - B Tables - C Answers to Odd-Numbered Exercises - D Review of Selected Mathematical Techniques - D.1 [[Algebra of Sets]] - D.2 Mathematical Tools for the [[Hypergeometric Distribution]] - D.3 [[Limits]] - D.4 [[Infinite Series]] - D.5 [[Integration]] - D.6 [[Multivariate Calculus]]