Probability and Statistical Inference

Table of Contents

 

Chapter 1: Probability Basic Concepts

Properties of Probability

Methods of Enumeration

Conditional Probability

Independent Events

Bayes' Theorem

 

Chapter 2: Discrete Distributions Random Variables of the Discrete Type

Mathematical Expectation

Bernoulli Trials and the Binomial Distribution

The Moment-Generating Function

The Poisson Distribution

 

Chapter 3: Continuous Distributions Continuous-Type Data and EDA

Random Variables of the Continuous Type

The Uniform and Exponential Distributions

The Gamma and Chi-Square Distributions

Distributions of Functions of a Random Variable

Additional Models

 

Chapter 4: Multivariate Distributions Distributions of Two Random Variables

The Correlation Coefficient

Conditional Distributions

Transformations of Random Variables

Independent Random Variables

Distributions of Sums of Independent Random Variables

Chebyshev's Inequality and Convergence in Probability

 

Chapter 5: The Normal Distribution A Brief History of Probability

The Normal Distribution

Random Functions Associated with Normal Distributions

The Central Limit Theorem

Approximations for Discrete Distributions

The Bivariate Normal Distribution

Limiting Moment-Generating Functions

Importance of Understanding Variability

 

Chapter 6: Estimation Sample Characteristics

Point Estimation

Sufficient Statistics

Confidence Intervals for Means

Confidence Intervals for Difference of Two Means

Confidence Intervals for Variances

Confidence Intervals for Proportions

Sample Size

Order Statistics

Distribution-Free Confidence Intervals for Percentiles

A Simple Regression Problem

More Regression

Resampling Methods

Asymptotic Distributions of Maximum Likelihood Estimators

 

Chapter 7: Bayesian Methods Subjective Probability

Bayesian Estimation

More Bayesian Concepts

 

Chapter 8: Tests of Statistical Hypotheses Tests About Proportions

Tests About One Mean and One Variance

Tests of the Equality of Two Normal Distributions

The Wilcoxon Tests

Chi-Square Goodness of Fit Tests

Contingency Tables

One-Factor Analysis of Variance

Two-Factor Analysis of Variance

Tests Concerning Regression and Correlation

Kolmogorov-Smirnov Goodness of Fit Test

Run Test and Test for Randomness

 

Chapter 9: Theory of Statistical Inference Power of a Statistical Test

Best Critical Regions

Likelihood Ratio Tests

 

Chapter 10: Quality Improvement Through Statistical Methods

Time Sequences

Statistical Quality Control

General Factorial and 2 k Factorial Designs

More on Design of Experiments

Epilogue

A Review of Selected Mathematical Techniques

Algebra of Sets

Mathematical Tools for the Hypergeometric Distribution

Limits

Infinite Series

Integration

Multivariate Calculus